From 38fc3f253c0713c4ab13fea83388ab89494719b4 Mon Sep 17 00:00:00 2001
From: Anna Shaleva <anna@nspcc.ru>
Date: Wed, 15 Feb 2023 20:18:12 +0300
Subject: [PATCH] models: add original dBFT 2.0 specifications

---
 .gitignore                                    |   3 +
 README.md                                     |   6 +-
 formal-models/.github/dbft.png                | Bin 0 -> 94064 bytes
 formal-models/README.md                       | 141 ++++++
 formal-models/dbft/dbft.tla                   | 379 ++++++++++++++
 formal-models/dbft/dbft___AllGoodModel.launch |  42 ++
 formal-models/dbftMultipool/dbftMultipool.tla | 466 ++++++++++++++++++
 .../dbftMultipool___AllGoodModel.launch       |  44 ++
 8 files changed, 1080 insertions(+), 1 deletion(-)
 create mode 100644 formal-models/.github/dbft.png
 create mode 100644 formal-models/README.md
 create mode 100644 formal-models/dbft/dbft.tla
 create mode 100644 formal-models/dbft/dbft___AllGoodModel.launch
 create mode 100644 formal-models/dbftMultipool/dbftMultipool.tla
 create mode 100644 formal-models/dbftMultipool/dbftMultipool___AllGoodModel.launch

diff --git a/.gitignore b/.gitignore
index 61ead866..2247a5f8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,4 @@
 /vendor
+
+# TLC Model Checker files
+formal-models/*/*.toolbox/
diff --git a/README.md b/README.md
index 902ae367..cf4411a5 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,8 @@
 [![Report](https://goreportcard.com/badge/github.com/nspcc-dev/dbft)](https://goreportcard.com/report/github.com/nspcc-dev/dbft)
 
 # DBFT
-This repo contains Go implementation of the dBFT 2.0 consensus algorithm.
+This repo contains Go implementation of the dBFT 2.0 consensus algorithm and its models
+written in [TLA⁺](https://lamport.azurewebsites.net/tla/tla.html) language.
 
 ## Design and structure
 1. All control flow is done in main package. Most of the code which communicates with external
@@ -23,6 +24,9 @@ own payloads in order to sign and verify messages.
 5. `timer` contains default time provider. It should make it easier to write tests
 concerning dBFT's time depending behaviour.
 6. `simulation` contains an example of dBFT's usage with 6-node consensus. 
+7. `formal-models` contains the set of dBFT's models written in [TLA⁺](https://lamport.azurewebsites.net/tla/tla.html)
+   language and instructions on how to run and check them. Please, refer to the [README](./formal-models/README.md)
+   for more details.
 
 ## Usage
 A client of the library must implement its own event loop.
diff --git a/formal-models/.github/dbft.png b/formal-models/.github/dbft.png
new file mode 100644
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diff --git a/formal-models/README.md b/formal-models/README.md
new file mode 100644
index 00000000..9c700e0d
--- /dev/null
+++ b/formal-models/README.md
@@ -0,0 +1,141 @@
+## dBFT formal models
+
+This section contains a set of dBFT's formal specifications written in
+[TLA⁺](https://lamport.azurewebsites.net/tla/tla.html) language. The models
+describe the core algorithm logic represented in a high-level way and can be used
+to illustrate some basic dBFT concepts and to validate the algorithm in terms of
+liveness and fairness. It should be noted that presented models do not precisely
+follow the dBFT implementation presented in the repository and may omit some
+implementation details in favor of the specification simplicity and the
+fundamental philosophy of the TLA⁺. However, the presented models directly
+reflect some liveness problems dBFT 2.0 has; the models can and are aimed to be
+used for the dBFT 2.0 liveness evaluation and further algorithm improvements.
+
+Any contributions, questions and discussions on the presented models are highly
+appreciated.
+
+## Models
+
+### Basic dBFT 2.0 model
+
+This specification is a basis that was taken for the further algorithm
+investigation. We recommend to begin acquaintance with the dBFT models from this
+one.
+ 
+The specification describes the process of a single block acceptance: the set of
+resource managers `RM` (which is effectively a set of consensus nodes)
+communicating via the shared consensus message pool `msgs` and taking the
+decision in a few consensus rounds (views). Each consensus node has its own state
+at each step of the behaviour. Consensus node may send a consensus message by
+adding it to the `msgs` pool. To perform the transition between states the
+consensus node must send a consensus message or there must be a particular set of
+consensus messages in the shared message pool required for a particular
+transition.
+
+Here's the scheme of transitions between consensus node states:
+
+![Basic dBFT model transitions scheme](./.github/dbft.png)
+
+The specification also describes two kinds of malicious nodes behaviour that can
+be combined, i.e. enabled or disabled independently for each particular node:
+
+1. "Dead" nodes. "Dead" node is completely excluded from the consensus process
+   and not able to send the consensus messages and to perform state transitions.
+   The node may become "dead" at any step in the middle of the consensus process.
+   Once the node becomes "dead" there's no way for it to rejoin the consensus
+   process.
+2. "Faulty" nodes. "Faulty" node is allowed to send consensus messages of *any*
+   type at *any* step and to change its view without regarding the dBFT view
+   changing rules. The node may become "faulty" at any step in the middle of the
+   consensus process. Once the node becomes "faulty" there's no way for it to
+   become "good" again.
+
+The specification contains several invariants and liveness properties that must
+be checked by the TLC Model Checker. These formulas mostly describe two basic
+concepts that dBFT algorithm expected to guarantee:
+
+1. No fork must happen. There must be no situation such that two different
+   blocks are accepted at two different consensus rounds (views).
+2. The block must always be accepted. There must be no situation such that nodes
+   are stuck in the middle of consensus process and can't take any further steps.
+
+The specification is written and working under several assumptions:
+
+1. All consensus messages are valid. In real life it is guaranteed by verifiable
+   message signatures. In case if malicious or corrupted message is received it
+   won't be handled by the node.
+2. The exact timeouts (e.g. t/o on waiting a particular consensus message, etc.)
+   are not included into the model. However, the model covers timeouts in
+   general, i.e. the timeout is just the possibility to perform a particular
+   state transition.
+3. All consensus messages must eventually be delivered to all nodes, but the
+   exact order of delivering isn't guaranteed.
+4. The maximum number of consensus rounds (views) is restricted. This constraint
+   was introduced to reduce the number of possible model states to be checked.
+   The threshold may be specified via model configuration, and it is highly
+   recommended to keep this setting less or equal to the number of consensus
+   nodes.
+
+Here you can find the specification file and the TLC Model Checker launch
+configuration:
+
+* [TLA⁺ specification](./dbft/dbft.tla)
+* [TLC Model Checker configuration](./dbft/dbft___AllGoodModel.launch)
+
+### Extended dBFT 2.0 model
+
+This is an experimental dBFT 2.0 specification that extends the
+[basic model](#basic-dbft-20-model) in the following way: besides the shared pool
+of consensus messages `msgs` each consensus node has its own local pool of
+received and handled messages. Decisions on transmission between the node states
+are taken by the node based on the state of the local message pool. This approach
+allows to create more accurate low-leveled model which is extremely close to the
+dBFT implementation presented in this repository. At the same time such approach
+*significantly* increases the number of considered model states which leads to
+abnormally long TLC Model Checker runs. Thus, we do not recommend to use this
+model in development and place it here as an example of alternative (and more
+detailed) dBFT specification. These two models are expected to be equivalent in
+terms of the liveness locks that can be discovered by both of them, and, speaking
+the TLA⁺ language, the Extended dBFT specification implements the
+[basic one](#basic-dbft-20-model) (which can be proven and written in TLA⁺, but
+stays out of the task scope).
+
+Except for this remark and a couple of minor differences all the
+[basic model](#basic-dbft-20-model) description, constraints and assumptions are
+valid for the Extended specification as far. Thus, we highly recommend to
+consider the [basic model](#basic-dbft-20-model) before going to the Extended
+one.
+ 
+Here you can find the specification file and the TLC Model Checker launch
+configuration:
+
+* [TLA⁺ specification](./dbftMultipool/dbftMultipool.tla)
+* [TLC Model Checker configuration](./dbftMultipool/dbftMultipool___AllGoodModel.launch)
+
+## How to run/check the TLA⁺ specification
+
+### Prerequirements
+
+1. Download and install the TLA⁺ Toolbox following the
+   [official guide](http://lamport.azurewebsites.net/tla/toolbox.html).
+2. Read the brief introduction to the TLA⁺ language and TLC Model Checker at the
+   [official site](http://lamport.azurewebsites.net/tla/high-level-view.html).
+3. Download and take a look at the
+   [TLA⁺ cheat sheet](https://lamport.azurewebsites.net/tla/summary-standalone.pdf).
+4. For a proficient learning watch the
+   [TLA⁺ Video Course](https://lamport.azurewebsites.net/video/videos.html) and
+   read the [Specifying Systems book](http://lamport.azurewebsites.net/tla/book.html?back-link=tools.html#documentation).
+
+### Running the TLC model checker
+
+1. Clone the [repository](https://github.com/nspcc-dev/dbft.git).
+2. Open the TLA⁺ Toolbox, open new specification and provide path to the desired
+   `*.tla` file that contains the specification description.
+3. Create the model named `AllGoodModel` in the TLA⁺ Toolbox.
+4. Copy the corresponding `*___AllGoodModel.launch` file to the `*.toolbox`
+   folder.
+5. Open the `Model Overview` window in the TLA⁺ Toolbox  and check that behaviour
+   specification, declared constants, invariants and properties of the model are
+   filled in with some values.
+6. Press `Run TLC on the model` bottom to start the model checking process and
+   explore the progress in the `Model Checkng Results` window.
\ No newline at end of file
diff --git a/formal-models/dbft/dbft.tla b/formal-models/dbft/dbft.tla
new file mode 100644
index 00000000..e291ebcf
--- /dev/null
+++ b/formal-models/dbft/dbft.tla
@@ -0,0 +1,379 @@
+-------------------------------- MODULE dbft --------------------------------
+
+EXTENDS
+  Integers,
+  FiniteSets
+
+CONSTANTS
+  \* RM is the set of consensus node indexes starting from 0.
+  \* Example: {0, 1, 2, 3}
+  RM,
+
+  \* RMFault is a set of consensus node indexes that are allowed to become
+  \* FAULT in the middle of every considered behavior and to send any
+  \* consensus message afterwards. RMFault must be a subset of RM. An empty
+  \* set means that all nodes are good in every possible behaviour.
+  \* Examples: {0}
+  \*           {1, 3}
+  \*           {}
+  RMFault,
+
+  \* RMDead is a set of consensus node indexes that are allowed to die in the
+  \* middle of every behaviour and do not send any message afterwards. RMDead
+  \* must be a subset of RM. An empty set means that all nodes are alive and
+  \* responding in in every possible behaviour. RMDead may intersect the
+  \* RMFault set which means that node which is in both RMDead and RMFault
+  \* may become FAULT and send any message starting from some step of the
+  \* particular behaviour and may also die in the same behaviour which will
+  \* prevent it from sending any message.
+  \* Examples: {0}
+  \*           {3, 2}
+  \*           {}
+  RMDead,
+
+  \* MaxView is the maximum allowed view to be considered (starting from 0,
+  \* including the MaxView itself). This constraint was introduced to reduce
+  \* the number of possible model states to be checked. It is recommended to
+  \* keep this setting not too high (< N is highly recommended).
+  \* Example: 2
+  MaxView
+
+VARIABLES
+  \* rmState is a set of consensus node states. It is represented by the
+  \* mapping (function) with domain RM and range RMStates. I.e. rmState[r] is
+  \* the state of the r-th consensus node at the current step.
+  rmState,
+
+ \* msgs is the shared pool of messages sent to the network by consensus nodes.
+ \* It is represented by a subset of Messages set.
+  msgs
+
+\* vars is a tuple of all variables used in the specification. It is needed to
+\* simplify fairness conditions definition.
+vars == <<rmState, msgs>>
+
+\* N is the number of validators.
+N == Cardinality(RM)
+
+\* F is the number of validators that are allowed to be malicious.
+F == (N - 1) \div 3
+
+\* M is the number of validators that must function correctly.
+M == N - F
+
+\* These assumptions are checked by the TLC model checker once at the start of
+\* the model checking process. All the input data (declared constants) specified
+\* in the "Model Overview" section must satisfy these constraints.
+ASSUME
+  /\ RM \subseteq Nat
+  /\ N >= 4
+  /\ 0 \in RM
+  /\ RMFault \subseteq RM
+  /\ RMDead \subseteq RM
+  /\ Cardinality(RMFault) <= F
+  /\ Cardinality(RMDead) <= F
+  /\ Cardinality(RMFault \cup RMDead) <= F
+  /\ MaxView \in Nat
+  /\ MaxView <= 2
+
+\* RMStates is a set of records where each record holds the node state and
+\* the node current view.
+RMStates == [
+              type: {"initialized", "prepareSent", "commitSent", "cv", "blockAccepted", "bad", "dead"},
+              view : Nat
+            ]
+
+\* Messages is a set of records where each record holds the message type,
+\* the message sender and sender's view by the moment when message was sent.
+Messages == [type : {"PrepareRequest", "PrepareResponse", "Commit", "ChangeView"}, rm : RM, view : Nat]
+
+\* -------------- Useful operators --------------
+
+\* IsPrimary is an operator defining whether provided node r is primary
+\* for the current round from the r's point of view. It is a mapping
+\* from RM to the set of {TRUE, FALSE}.
+IsPrimary(r) == rmState[r].view % N = r
+
+\* GetPrimary is an operator defining mapping from round index to the RM that
+\* is primary in this round.
+GetPrimary(view) == CHOOSE r \in RM : view % N = r
+
+\* GetNewView returns new view number based on the previous node view value.
+\* Current specifications only allows to increment view.
+GetNewView(oldView) == oldView + 1
+
+\* CountCommitted returns the number of nodes that have sent the Commit message
+\* in the current round (as the node r sees it).
+CountCommitted(r) == Cardinality({rm \in RM : Cardinality({msg \in msgs : msg.rm = rm /\ msg.type = "Commit" /\ msg.view = rmState[r].view}) /= 0})
+
+\* MoreThanFNodesCommitted returns whether more than F nodes have been committed
+\* in the current round (as the node r sees it).
+MoreThanFNodesCommitted(r) == CountCommitted(r) > F
+
+\* PrepareRequestSentOrReceived denotes whether there's a PrepareRequest
+\* message received from the current round's speaker (as the node r sees it).
+PrepareRequestSentOrReceived(r) == [type |-> "PrepareRequest", rm |-> GetPrimary(rmState[r].view), view |-> rmState[r].view] \in msgs
+
+\* -------------- Safety temporal formula --------------
+
+\* Init is the initial predicate initializing values at the start of every
+\* behaviour.
+Init ==
+  /\ rmState = [r \in RM |-> [type |-> "initialized", view |-> 0]]
+  /\ msgs = {}
+
+\* RMSendPrepareRequest describes the primary node r broadcasting PrepareRequest.
+RMSendPrepareRequest(r) ==
+  /\ rmState[r].type = "initialized"
+  /\ IsPrimary(r)
+  /\ rmState' = [rmState EXCEPT ![r].type = "prepareSent"]
+  /\ msgs' = msgs \cup {[type |-> "PrepareRequest", rm |-> r, view |-> rmState[r].view]}
+  /\ UNCHANGED <<>>
+
+\* RMSendPrepareResponse describes non-primary node r receiving PrepareRequest from
+\* the primary node of the current round (view) and broadcasting PrepareResponse.
+\* This step assumes that PrepareRequest always contains valid transactions and
+\* signatures.
+RMSendPrepareResponse(r) ==
+  /\ \/ rmState[r].type = "initialized"
+     \* We do allow the transition from the "cv" state to the "prepareSent" or "commitSent" stage
+     \* as it is done in the code-level dBFT implementation by checking the NotAcceptingPayloadsDueToViewChanging
+     \* condition (see
+     \* https://github.com/nspcc-dev/dbft/blob/31c1bbdc74f2faa32ec9025062e3a4e2ccfd4214/dbft.go#L419
+     \* and
+     \* https://github.com/neo-project/neo-modules/blob/d00d90b9c27b3d0c3c57e9ca1f560a09975df241/src/DBFTPlugin/Consensus/ConsensusService.OnMessage.cs#L79).
+     \* However, we can't easily count the number of "lost" nodes in this specification to match precisely
+     \* the implementation. Moreover, we don't need it to be counted as the RMSendPrepareResponse enabling
+     \* condition specifies only the thing that may happen given some particular set of enabling conditions.
+     \* Thus, we've extended the NotAcceptingPayloadsDueToViewChanging condition to consider only MoreThanFNodesCommitted.
+     \* It should be noted that the logic of MoreThanFNodesCommittedOrLost can't be reliable in detecting lost nodes
+     \* (even with neo-project/neo#2057), because real nodes can go down at any time.
+     \/ /\ rmState[r].type = "cv"
+        /\ MoreThanFNodesCommitted(r)
+  /\ \neg IsPrimary(r)
+  /\ PrepareRequestSentOrReceived(r)
+  /\ rmState' = [rmState EXCEPT ![r].type = "prepareSent"]
+  /\ msgs' = msgs \cup {[type |-> "PrepareResponse", rm |-> r, view |-> rmState[r].view]}
+  /\ UNCHANGED <<>>
+
+\* RMSendCommit describes node r sending Commit if there's enough PrepareResponse
+\* messages.
+RMSendCommit(r) ==
+  /\ \/ rmState[r].type = "prepareSent"
+     \* We do allow the transition from the "cv" state to the "prepareSent" or "commitSent" stage,
+     \* see the related comment inside the RMSendPrepareResponse definition.
+     \/ /\ rmState[r].type = "cv"
+        /\ MoreThanFNodesCommitted(r)
+  /\ Cardinality({
+                   msg \in msgs : /\ (msg.type = "PrepareResponse" \/ msg.type = "PrepareRequest")
+                                  /\ msg.view = rmState[r].view
+                 }) >= M
+  /\ PrepareRequestSentOrReceived(r)
+  /\ rmState' = [rmState EXCEPT ![r].type = "commitSent"]
+  /\ msgs' = msgs \cup {[type |-> "Commit", rm |-> r, view |-> rmState[r].view]}
+  /\ UNCHANGED <<>>
+
+\* RMAcceptBlock describes node r collecting enough Commit messages and accepting
+\* the block.
+RMAcceptBlock(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ PrepareRequestSentOrReceived(r)
+  /\ Cardinality({msg \in msgs : msg.type = "Commit" /\ msg.view = rmState[r].view}) >= M
+  /\ rmState' = [rmState EXCEPT ![r].type = "blockAccepted"]
+  /\ UNCHANGED <<msgs>>
+
+\* RMSendChangeView describes node r sending ChangeView message on timeout.
+RMSendChangeView(r) ==
+  /\ \/ rmState[r].type = "initialized"
+     \/ rmState[r].type = "prepareSent"
+  /\ LET cv == [type |-> "ChangeView", rm |-> r, view |-> rmState[r].view]
+     IN /\ cv \notin msgs
+        /\ rmState' = [rmState EXCEPT ![r].type = "cv"]
+        /\ msgs' = msgs \cup {[type |-> "ChangeView", rm |-> r, view |-> rmState[r].view]}
+
+\* RMReceiveChangeView describes node r receiving enough ChangeView messages for
+\* view changing.
+RMReceiveChangeView(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ rmState[r].type /= "blockAccepted"
+  /\ rmState[r].type /= "commitSent"
+  /\ Cardinality({
+                  rm \in RM : Cardinality({
+                                            msg \in msgs : /\ msg.type = "ChangeView"
+                                                           /\ msg.rm = rm
+                                                           /\ GetNewView(msg.view) >= GetNewView(rmState[r].view)
+                                         }) /= 0
+                 }) >= M
+  /\ rmState' = [rmState EXCEPT ![r].type = "initialized", ![r].view = GetNewView(rmState[r].view)]
+  /\ UNCHANGED <<msgs>>
+
+\* RMBeBad describes the faulty node r that will send any kind of consensus message starting
+\* from the step it's gone wild. This step is enabled only when RMFault is non-empty set.
+RMBeBad(r) ==
+  /\ r \in RMFault
+  /\ Cardinality({rm \in RM : rmState[rm].type = "bad"}) < F
+  /\ rmState' = [rmState EXCEPT ![r].type = "bad"]
+  /\ UNCHANGED <<msgs>>
+
+\* RMFaultySendCV describes sending CV message by the faulty node r.
+RMFaultySendCV(r) ==
+  /\ rmState[r].type = "bad"
+  /\ LET cv == [type |-> "ChangeView", rm |-> r, view |-> rmState[r].view]
+     IN /\ cv \notin msgs
+        /\ msgs' = msgs \cup {cv}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultyDoCV describes view changing by the faulty node r.
+RMFaultyDoCV(r) ==
+  /\ rmState[r].type = "bad"
+  /\ rmState' = [rmState EXCEPT ![r].view = GetNewView(rmState[r].view)]
+  /\ UNCHANGED <<msgs>>
+
+\* RMFaultySendPReq describes sending PrepareRequest message by the primary faulty node r.
+RMFaultySendPReq(r) ==
+  /\ rmState[r].type = "bad"
+  /\ IsPrimary(r)
+  /\ LET pReq == [type |-> "PrepareRequest", rm |-> r, view |-> rmState[r].view]
+     IN /\ pReq \notin msgs
+        /\ msgs' = msgs \cup {pReq}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultySendPResp describes sending PrepareResponse message by the non-primary faulty node r.
+RMFaultySendPResp(r) ==
+  /\ rmState[r].type = "bad"
+  /\ \neg IsPrimary(r)
+  /\ LET pResp == [type |-> "PrepareResponse", rm |-> r, view |-> rmState[r].view]
+     IN /\ pResp \notin msgs
+        /\ msgs' = msgs \cup {pResp}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultySendCommit describes sending Commit message by the faulty node r.
+RMFaultySendCommit(r) ==
+  /\ rmState[r].type = "bad"
+  /\ LET commit == [type |-> "Commit", rm |-> r, view |-> rmState[r].view]
+     IN /\ commit \notin msgs
+        /\ msgs' = msgs \cup {commit}
+        /\ UNCHANGED <<rmState>>
+
+\* RMDie describes node r that was removed from the network at the particular step
+\* of the behaviour. After this node r can't change its state and accept/send messages.
+RMDie(r) ==
+  /\ r \in RMDead
+  /\ Cardinality({rm \in RM : rmState[rm].type = "dead"}) < F
+  /\ rmState' = [rmState EXCEPT ![r].type = "dead"]
+  /\ UNCHANGED <<msgs>>
+
+\* Terminating is an action that allows infinite stuttering to prevent deadlock on
+\* behaviour termination. We consider termination to be valid if at least M nodes
+\* has the block being accepted.
+Terminating ==
+  /\ Cardinality({rm \in RM : rmState[rm].type = "blockAccepted"}) >= M
+  /\ UNCHANGED <<msgs, rmState>>
+
+\* Next is the next-state action describing the transition from the current state
+\* to the next state of the behaviour.
+Next ==
+  \/ Terminating
+  \/ \E r \in RM:
+       RMSendPrepareRequest(r) \/ RMSendPrepareResponse(r) \/ RMSendCommit(r)
+         \/ RMAcceptBlock(r) \/ RMSendChangeView(r) \/ RMReceiveChangeView(r)
+         \/ RMDie(r) \/ RMBeBad(r)
+         \/ RMFaultySendCV(r) \/ RMFaultyDoCV(r) \/ RMFaultySendCommit(r) \/ RMFaultySendPReq(r) \/ RMFaultySendPResp(r)
+
+\* Safety is a temporal formula that describes the whole set of allowed
+\* behaviours. It specifies only what the system MAY do (i.e. the set of
+\* possible allowed behaviours for the system). It asserts only what may
+\* happen; any behaviour that violates it does so at some point and
+\* nothing past that point makes difference.
+\*
+\* E.g. this safety formula (applied standalone) allows the behaviour to end
+\* with an infinite set of stuttering steps (those steps that DO NOT change
+\* neither msgs nor rmState) and never reach the state where at least one
+\* node is committed or accepted the block.
+\*
+\* To forbid such behaviours we must specify what the system MUST
+\* do. It will be specified below with the help of fairness conditions in
+\* the Fairness formula.
+Safety == Init /\ [][Next]_vars
+
+\* -------------- Fairness temporal formula --------------
+
+\* Fairness is a temporal assumptions under which the model is working.
+\* Usually it specifies different kind of assumptions for each/some
+\* subactions of the Next's state action, but the only think that bothers
+\* us is preventing infinite stuttering at those steps where some of Next's
+\* subactions are enabled. Thus, the only thing that we require from the
+\* system is to keep take the steps until it's impossible to take them.
+\* That's exactly how the weak fairness condition works: if some action
+\* remains continuously enabled, it must eventually happen.
+Fairness == WF_vars(Next)
+
+\* -------------- Specification --------------
+
+\* The complete specification of the protocol written as a temporal formula.
+Spec == Safety /\ Fairness
+
+\* -------------- Liveness temporal formula --------------
+
+\* For every possible behaviour it's true that eventually (i.e. at least once
+\* through the behaviour) block will be accepted. It is something that dBFT
+\* must guarantee (an in practice this condition is violated).
+TerminationRequirement == <>(Cardinality({r \in RM : rmState[r].type = "blockAccepted"}) >= M)
+
+\* A liveness temporal formula asserts only what must happen (i.e. specifies
+\* what the system MUST do). Any behaviour can NOT violate it at ANY point;
+\* there's always the rest of the behaviour that can always make the liveness
+\* formula true; if there's no such behaviour than the liveness formula is
+\* violated. The liveness formula is supposed to be checked as a property
+\* by the TLC model checker.
+Liveness == TerminationRequirement
+
+\* -------------- ModelConstraints --------------
+
+\* MaxViewConstraint is a state predicate restricting the number of possible
+\* behaviour states. It is needed to reduce model checking time and prevent
+\* the model graph size explosion. This formulae must be specified at the
+\* "State constraint" section of the "Additional Spec Options" section inside
+\* the model overview.
+MaxViewConstraint == /\ \A r \in RM : rmState[r].view <= MaxView
+                     /\ \A msg \in msgs : msg.view <= MaxView
+
+\* -------------- Invariants of the specification --------------
+
+\* Model invariant is a state predicate (statement) that must be true for
+\* every step of every reachable behaviour. Model invariant is supposed to
+\* be checked as an Invariant by the TLC Model Checker.
+
+\* TypeOK is a type-correctness invariant. It states that all elements of
+\* specification variables must have the proper type throughout the behaviour.
+TypeOK ==
+  /\ rmState \in [RM -> RMStates]
+  /\ msgs \subseteq Messages
+
+\* InvTwoBlocksAccepted states that there can't be two different blocks accepted in
+\* the two different views, i.e. dBFT must not allow forks.
+InvTwoBlocksAccepted == \A r1 \in RM:
+                  \A r2 \in RM \ {r1}:
+                  \/ rmState[r1].type /= "blockAccepted"
+                  \/ rmState[r2].type /= "blockAccepted"
+                  \/ rmState[r1].view = rmState[r2].view
+
+\* InvFaultNodesCount states that there can be F faulty or dead nodes at max.
+InvFaultNodesCount == Cardinality({
+                                    r \in RM : rmState[r].type = "bad" \/ rmState[r].type = "dead"
+                                 }) <= F
+
+\* This theorem asserts the truth of the temporal formula whose meaning is that
+\* the state predicates TypeOK, InvTwoBlocksAccepted and InvFaultNodesCount are
+\* the invariants of the specification Spec. This theorem is not supposed to be
+\* checked by the TLC model checker, it's here for the reader's understanding of
+\* the purpose of TypeOK, InvTwoBlocksAccepted and InvFaultNodesCount.
+THEOREM Spec => [](TypeOK /\ InvTwoBlocksAccepted /\ InvFaultNodesCount)
+
+=============================================================================
+\* Modification History
+\* Last modified Fri Feb 17 15:47:41 MSK 2023 by anna
+\* Last modified Sat Jan 21 01:26:16 MSK 2023 by rik
+\* Created Thu Dec 15 16:06:17 MSK 2022 by anna
diff --git a/formal-models/dbft/dbft___AllGoodModel.launch b/formal-models/dbft/dbft___AllGoodModel.launch
new file mode 100644
index 00000000..eb14599a
--- /dev/null
+++ b/formal-models/dbft/dbft___AllGoodModel.launch
@@ -0,0 +1,42 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<launchConfiguration type="org.lamport.tla.toolbox.tool.tlc.modelCheck">
+    <stringAttribute key="configurationName" value="AllGoodModel"/>
+    <intAttribute key="distributedFPSetCount" value="0"/>
+    <stringAttribute key="distributedNetworkInterface" value="172.200.0.254"/>
+    <intAttribute key="distributedNodesCount" value="1"/>
+    <stringAttribute key="distributedTLC" value="off"/>
+    <intAttribute key="fpIndex" value="47"/>
+    <intAttribute key="maxHeapSize" value="50"/>
+    <stringAttribute key="modelBehaviorInit" value=""/>
+    <stringAttribute key="modelBehaviorNext" value=""/>
+    <stringAttribute key="modelBehaviorSpec" value="Spec"/>
+    <intAttribute key="modelBehaviorSpecType" value="1"/>
+    <stringAttribute key="modelBehaviorVars" value="msgs, rmState"/>
+    <stringAttribute key="modelComments" value=""/>
+    <booleanAttribute key="modelCorrectnessCheckDeadlock" value="true"/>
+    <listAttribute key="modelCorrectnessInvariants">
+        <listEntry value="1TypeOK"/>
+        <listEntry value="1InvTwoBlocksAccepted"/>
+        <listEntry value="1InvFaultNodesCount"/>
+    </listAttribute>
+    <listAttribute key="modelCorrectnessProperties">
+        <listEntry value="1Liveness"/>
+    </listAttribute>
+    <intAttribute key="modelEditorOpenTabs" value="10"/>
+    <stringAttribute key="modelParameterActionConstraint" value=""/>
+    <listAttribute key="modelParameterConstants">
+        <listEntry value="RMFault;;{};0;0"/>
+        <listEntry value="MaxView;;2;0;0"/>
+        <listEntry value="RMDead;;{};0;0"/>
+        <listEntry value="RM;;{0, 1, 2, 3};0;0"/>
+    </listAttribute>
+    <stringAttribute key="modelParameterContraint" value="MaxViewConstraint"/>
+    <listAttribute key="modelParameterDefinitions"/>
+    <stringAttribute key="modelParameterModelValues" value="{}"/>
+    <stringAttribute key="modelParameterNewDefinitions" value=""/>
+    <intAttribute key="modelVersion" value="20191005"/>
+    <intAttribute key="numberOfWorkers" value="8"/>
+    <stringAttribute key="result.mail.address" value=""/>
+    <stringAttribute key="specName" value="dbft"/>
+    <stringAttribute key="tlcResourcesProfile" value="local custom"/>
+</launchConfiguration>
diff --git a/formal-models/dbftMultipool/dbftMultipool.tla b/formal-models/dbftMultipool/dbftMultipool.tla
new file mode 100644
index 00000000..3eb395ec
--- /dev/null
+++ b/formal-models/dbftMultipool/dbftMultipool.tla
@@ -0,0 +1,466 @@
+---------------------------- MODULE dbftMultipool ----------------------------
+
+EXTENDS
+  Integers,
+  FiniteSets
+
+CONSTANTS
+  \* RM is the set of consensus node indexes starting from 0.
+  \* Example: {0, 1, 2, 3}
+  RM,
+
+  \* RMFault is a set of consensus node indexes that are allowed to become
+  \* FAULT in the middle of every considered behavior and to send any
+  \* consensus message afterwards. RMFault must be a subset of RM. An empty
+  \* set means that all nodes are good in every possible behaviour.
+  \* Examples: {0}
+  \*           {1, 3}
+  \*           {}
+  RMFault,
+
+  \* RMDead is a set of consensus node indexes that are allowed to die in the
+  \* middle of every behaviour and do not send any message afterwards. RMDead
+  \* must be a subset of RM. An empty set means that all nodes are alive and
+  \* responding in in every possible behaviour. RMDead may intersect the
+  \* RMFault set which means that node which is in both RMDead and RMFault
+  \* may become FAULT and send any message starting from some step of the
+  \* particular behaviour and may also die in the same behaviour which will
+  \* prevent it from sending any message.
+  \* Examples: {0}
+  \*           {3, 2}
+  \*           {}
+  RMDead,
+
+  \* MaxView is the maximum allowed view to be considered (starting from 0,
+  \* including the MaxView itself). This constraint was introduced to reduce
+  \* the number of possible model states to be checked. It is recommended to
+  \* keep this setting not too high (< N is highly recommended).
+  \* Example: 2
+  MaxView,
+
+  \* MaxUndeliveredMessages is the maximum number of messages in the common
+  \* messages pool (msgs) that were not received and handled by all consensus
+  \* nodes. It must not be too small (>= 3) in order to allow model taking
+  \* at least any steps. At the same time it must not be too high (<= 6 is
+  \* recommended) in order to avoid states graph size explosion.
+  MaxUndeliveredMessages
+
+VARIABLES
+  \* rmState is a set of consensus node states. It is represented by the
+  \* mapping (function) with domain RM and range RMStates. I.e. rmState[r] is
+  \* the state of the r-th consensus node at the current step.
+  rmState,
+
+ \* msgs is the shared pool of messages sent to the network by consensus nodes.
+ \* It is represented by a subset of Messages set.
+  msgs
+
+\* vars is a tuple of all variables used in the specification. It is needed to
+\* simplify fairness conditions definition.
+vars == <<rmState, msgs>>
+
+\* N is the number of validators.
+N == Cardinality(RM)
+
+\* F is the number of validators that are allowed to be malicious.
+F == (N - 1) \div 3
+
+\* M is the number of validators that must function correctly.
+M == N - F
+
+\* These assumptions are checked by the TLC model checker once at the start of
+\* the model checking process. All the input data (declared constants) specified
+\* in the "Model Overview" section must satisfy these constraints.
+ASSUME
+  /\ RM \subseteq Nat
+  /\ N >= 4
+  /\ 0 \in RM
+  /\ RMFault \subseteq RM
+  /\ RMDead \subseteq RM
+  /\ Cardinality(RMFault) <= F
+  /\ Cardinality(RMDead) <= F
+  /\ Cardinality(RMFault \cup RMDead) <= F
+  /\ MaxView \in Nat
+  /\ MaxView <= 2
+  /\ MaxUndeliveredMessages \in Nat
+  /\ MaxUndeliveredMessages >= 3 \* First value when block can be accepted in some behaviours.
+
+\* Messages is a set of records where each record holds the message type,
+\* the message sender and sender's view by the moment when message was sent.
+Messages == [type : {"PrepareRequest", "PrepareResponse", "Commit", "ChangeView"}, rm : RM, view : Nat]
+
+\* RMStates is a set of records where each record holds the node state, the node current view
+\* and the pool of messages the nde has been sent or received and handled.
+RMStates == [
+              type: {"initialized", "prepareSent", "commitSent", "blockAccepted", "bad", "dead"},
+              view : Nat,
+              pool : SUBSET Messages
+            ]
+
+\* -------------- Useful operators --------------
+
+\* IsPrimary is an operator defining whether provided node r is primary
+\* for the current round from the r's point of view. It is a mapping
+\* from RM to the set of {TRUE, FALSE}.
+IsPrimary(r) == rmState[r].view % N = r
+
+\* GetPrimary is an operator defining mapping from round index to the RM that
+\* is primary in this round.
+GetPrimary(view) == CHOOSE r \in RM : view % N = r
+
+\* GetNewView returns new view number based on the previous node view value.
+\* Current specifications only allows to increment view.
+GetNewView(oldView) == oldView + 1
+
+\* IsViewChanging denotes whether node r have sent ChangeView message for the
+\* current (or later) round.
+IsViewChanging(r) == Cardinality({msg \in rmState[r].pool : msg.type = "ChangeView" /\ msg.view >= rmState[r].view /\ msg.rm = r}) /= 0
+
+\* CountCommitted returns the number of nodes that have sent the Commit message
+\* in the current round (as the node r sees it).
+CountCommitted(r) == Cardinality({rm \in RM : Cardinality({msg \in rmState[r].pool : msg.rm = rm /\ msg.type = "Commit"}) /= 0})
+
+\* CountFailed returns the number of nodes that haven't sent any message since
+\* the last round (as the node r sees it from the point of its pool).
+CountFailed(r) == Cardinality({rm \in RM : Cardinality({msg \in rmState[r].pool : msg.rm = rm /\ msg.view >= rmState[r].view}) = 0 })
+
+\* MoreThanFNodesCommittedOrLost denotes whether more than F nodes committed or
+\* failed to communicate in the current round.
+MoreThanFNodesCommittedOrLost(r) == CountCommitted(r) + CountFailed(r) > F
+
+\* NotAcceptingPayloadsDueToViewChanging returns whether the node doesn't accept
+\* payloads in the current step.
+NotAcceptingPayloadsDueToViewChanging(r) ==
+  /\ IsViewChanging(r)
+  /\ \neg MoreThanFNodesCommittedOrLost(r)
+
+\* PrepareRequestSentOrReceived denotes whether there's a PrepareRequest
+\* message received from the current round's speaker (as the node r sees it).
+PrepareRequestSentOrReceived(r) == [type |-> "PrepareRequest", rm |-> GetPrimary(rmState[r].view), view |-> rmState[r].view] \in rmState[r].pool
+
+\* CommitSent returns whether the node has its commit sent for the current block.
+CommitSent(r) == Cardinality({msg \in rmState[r].pool : msg.rm = r /\ msg.type = "Commit"}) > 0
+
+\* -------------- Safety temporal formula --------------
+
+\* Init is the initial predicate initializing values at the start of every
+\* behaviour.
+Init ==
+  /\ rmState = [r \in RM |-> [type |-> "initialized", view |-> 1, pool |-> {}]]
+  /\ msgs = {}
+
+\* RMSendPrepareRequest describes the primary node r broadcasting PrepareRequest.
+RMSendPrepareRequest(r) ==
+  /\ rmState[r].type = "initialized"
+  /\ IsPrimary(r)
+  /\ LET pReq == [type |-> "PrepareRequest", rm |-> r, view |-> rmState[r].view]
+         commit == [type |-> "Commit", rm |-> r, view |-> rmState[r].view]
+     IN /\ pReq \notin msgs
+        /\ IF Cardinality({m \in rmState[r].pool : m.type = "PrepareResponse" /\ m.view = rmState[r].view}) < M - 1 \* -1 is for the current PrepareRequest.
+           THEN /\ rmState' = [rmState EXCEPT ![r].type = "prepareSent", ![r].pool = rmState[r].pool \cup {pReq}]
+                /\ msgs' = msgs \cup {pReq}
+           ELSE /\ msgs' = msgs \cup {pReq, commit}
+                /\ IF Cardinality({m \in rmState[r].pool : m.type = "Commit" /\ m.view = rmState[r].view}) < M-1 \* -1 is for the current Commit
+                   THEN rmState' = [rmState EXCEPT ![r].type = "commitSent", ![r].pool = rmState[r].pool \cup {pReq, commit}]
+                   ELSE rmState' = [rmState EXCEPT ![r].type = "blockAccepted", ![r].pool = rmState[r].pool \cup {pReq, commit}]
+        /\ UNCHANGED <<>>
+
+\* RMSendChangeView describes node r sending ChangeView message on timeout.
+RMSendChangeView(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ rmState[r].type /= "blockAccepted"
+  /\ \/ (IsPrimary(r) /\ PrepareRequestSentOrReceived(r))
+     \/ (\neg IsPrimary(r) /\ \neg CommitSent(r))
+  /\ LET msg == [type |-> "ChangeView", rm |-> r, view |-> rmState[r].view]
+     IN /\ msg \notin msgs
+        /\ msgs' = msgs \cup {msg}
+        /\ IF Cardinality({m \in rmState[r].pool : m.type = "ChangeView" /\ GetNewView(m.view) >= GetNewView(msg.view)}) >= M-1 \* -1 is for the currently sent CV
+           THEN rmState' = [rmState EXCEPT ![r].type = "initialized", ![r].view = GetNewView(msg.view), ![r].pool = rmState[r].pool \cup {msg}]
+           ELSE rmState' = [rmState EXCEPT ![r].pool = rmState[r].pool \cup {msg}]
+
+\* OnTimeout describes two actions the node can take on timeout for waiting any event.
+OnTimeout(r) ==
+  \/ RMSendPrepareRequest(r)
+  \/ RMSendChangeView(r)
+
+\* RMOnPrepareRequest describes non-primary node r receiving PrepareRequest from the
+\* primary node of the current round (view) and broadcasts PrepareResponse.
+\* This step assumes that PrepareRequest always contains valid transactions and
+\* signatures.
+RMOnPrepareRequest(r) ==
+  /\ rmState[r].type = "initialized"
+  /\ \E msg \in msgs \ rmState[r].pool:
+        /\ msg.rm /= r
+        /\ msg.type = "PrepareRequest"
+        /\ msg.view = rmState[r].view
+        /\ \neg IsPrimary(r)
+        /\ \neg NotAcceptingPayloadsDueToViewChanging(r) \* dbft.go -L296, in C# node, but not in ours
+        /\ LET pResp == [type |-> "PrepareResponse", rm |-> r, view |-> rmState[r].view]
+               commit == [type |-> "Commit", rm |-> r, view |-> rmState[r].view]
+           IN IF Cardinality({m \in rmState[r].pool : m.type = "PrepareResponse" /\ m.view = rmState[r].view}) < M - 1 - 1 \* -1 is for reveived PrepareRequest; -1 is for current PrepareResponse
+              THEN /\ rmState' = [rmState EXCEPT ![r].type = "prepareSent", ![r].pool = rmState[r].pool \cup {msg, pResp}]
+                   /\ msgs' = msgs \cup {pResp}
+              ELSE /\ msgs' = msgs \cup {msg, pResp, commit}
+                   /\ IF Cardinality({m \in rmState[r].pool : m.type = "Commit" /\ m.view = rmState[r].view}) < M-1 \* -1 is for the current Commit
+                      THEN rmState' = [rmState EXCEPT ![r].type = "commitSent", ![r].pool = rmState[r].pool \cup {msg, pResp, commit}]
+                      ELSE rmState' = [rmState EXCEPT ![r].type = "blockAccepted", ![r].pool = rmState[r].pool \cup {msg, pResp, commit}]
+        /\ UNCHANGED <<>>
+
+\* RMOnPrepareResponse describes node r accepting PrepareResponse message and handling it.
+\* If there's enough PrepareResponses collected it will send the Commit; in case if there's
+\* enough Commits it will accept the block.
+RMOnPrepareResponse(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ rmState[r].type /= "blockAccepted"
+  /\ \E msg \in msgs \ rmState[r].pool:
+        /\ msg.rm /= r
+        /\ msg.type = "PrepareResponse"
+        /\ msg.view = rmState[r].view
+        /\ \neg NotAcceptingPayloadsDueToViewChanging(r)
+        /\ IF \/ Cardinality({m \in rmState[r].pool : (m.type = "PrepareRequest" \/ m.type = "PrepareResponse") /\ m.view = rmState[r].view}) < M - 1 \* -1 is for the currently received PrepareResponse.
+              \/ CommitSent(r)
+              \/ \neg PrepareRequestSentOrReceived(r)
+           THEN /\ rmState' = [rmState EXCEPT ![r].pool = rmState[r].pool \cup {msg}]
+                /\ UNCHANGED <<msgs>>
+           ELSE LET commit == [type |-> "Commit", rm |-> r, view |-> rmState[r].view]
+                IN /\ msgs' = msgs \cup {msg, commit}
+                   /\ IF Cardinality({m \in rmState[r].pool : m.type = "Commit" /\ m.view = rmState[r].view}) < M-1 \* -1 is for the current Commit
+                      THEN rmState' = [rmState EXCEPT ![r].type = "commitSent", ![r].pool = rmState[r].pool \cup {msg, commit}]
+                      ELSE rmState' = [rmState EXCEPT ![r].type = "blockAccepted", ![r].pool = rmState[r].pool \cup {msg, commit}]
+
+\* RMOnCommit describes node r accepting Commit message and (in case if there's enough Commits)
+\* accepting the block.
+RMOnCommit(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ rmState[r].type /= "blockAccepted"
+  /\ \E msg \in msgs \ rmState[r].pool:
+        /\ msg.rm /= r
+        /\ msg.type = "Commit"
+        /\ msg.view = rmState[r].view
+        /\ IF Cardinality({m \in rmState[r].pool : m.type = "Commit" /\ m.view = rmState[r].view}) < M-1 \* -1 is for the currently accepting commit
+           THEN rmState' = [rmState EXCEPT ![r].pool = rmState[r].pool \cup {msg}]
+           ELSE rmState' = [rmState EXCEPT ![r].type = "blockAccepted", ![r].pool = rmState[r].pool \cup {msg}]
+        /\ UNCHANGED <<msgs>>
+
+\* RMOnChangeView describes node r receiving ChangeView message and (in case if enough ChangeViews
+\* is collected) changing its view.
+RMOnChangeView(r) ==
+  /\ rmState[r].type /= "bad"
+  /\ rmState[r].type /= "dead"
+  /\ rmState[r].type /= "blockAccepted"
+  /\ \E msg \in msgs \ rmState[r].pool:
+        /\ msg.rm /= r
+        /\ msg.type = "ChangeView"
+        /\ msg.view = rmState[r].view
+        /\ \neg CommitSent(r)
+        /\ Cardinality({m \in rmState[r].pool : m.type = "ChangeView" /\ m.rm = msg.rm /\ m.view > msg.view}) = 0
+        /\ IF Cardinality({m \in rmState[r].pool : m.type = "ChangeView" /\ GetNewView(m.view) >= GetNewView(msg.view)}) < M-1 \* -1 is for the currently accepting CV
+           THEN rmState' = [rmState EXCEPT ![r].pool = rmState[r].pool \cup {msg}]
+           ELSE rmState' = [rmState EXCEPT ![r].type = "initialized", ![r].view = GetNewView(msg.view), ![r].pool = rmState[r].pool \cup {msg}]
+        /\ UNCHANGED <<msgs>>
+
+\* RMBeBad describes the faulty node r that will send any kind of consensus message starting
+\* from the step it's gone wild. This step is enabled only when RMFault is non-empty set.
+RMBeBad(r) ==
+  /\ r \in RMFault
+  /\ Cardinality({rm \in RM : rmState[rm].type = "bad"}) < F
+  /\ rmState' = [rmState EXCEPT ![r].type = "bad"]
+  /\ UNCHANGED <<msgs>>
+
+\* RMFaultySendCV describes sending CV message by the faulty node r.
+RMFaultySendCV(r) ==
+  /\ rmState[r].type = "bad"
+  /\ LET cv == [type |-> "ChangeView", rm |-> r, view |-> rmState[r].view]
+     IN /\ cv \notin msgs
+        /\ msgs' = msgs \cup {cv}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultyDoCV describes view changing by the faulty node r.
+RMFaultyDoCV(r) ==
+  /\ rmState[r].type = "bad"
+  /\ rmState' = [rmState EXCEPT ![r].view = GetNewView(rmState[r].view)]
+  /\ UNCHANGED <<msgs>>
+
+\* RMFaultySendPReq describes sending PrepareRequest message by the primary faulty node r.
+RMFaultySendPReq(r) ==
+  /\ rmState[r].type = "bad"
+  /\ IsPrimary(r)
+  /\ LET pReq == [type |-> "PrepareRequest", rm |-> r, view |-> rmState[r].view]
+     IN /\ pReq \notin msgs
+        /\ msgs' = msgs \cup {pReq}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultySendPResp describes sending PrepareResponse message by the non-primary faulty node r.
+RMFaultySendPResp(r) ==
+  /\ rmState[r].type = "bad"
+  /\ \neg IsPrimary(r)
+  /\ LET pResp == [type |-> "PrepareResponse", rm |-> r, view |-> rmState[r].view]
+     IN /\ pResp \notin msgs
+        /\ msgs' = msgs \cup {pResp}
+        /\ UNCHANGED <<rmState>>
+
+\* RMFaultySendCommit describes sending Commit message by the faulty node r.
+RMFaultySendCommit(r) ==
+  /\ rmState[r].type = "bad"
+  /\ LET commit == [type |-> "Commit", rm |-> r, view |-> rmState[r].view]
+     IN /\ commit \notin msgs
+        /\ msgs' = msgs \cup {commit}
+        /\ UNCHANGED <<rmState>>
+
+\* RMDie describes node r that was removed from the network at the particular step
+\* of the behaviour. After this node r can't change its state and accept/send messages.
+RMDie(r) ==
+  /\ r \in RMDead
+  /\ Cardinality({rm \in RM : rmState[rm].type = "dead"}) < F
+  /\ rmState' = [rmState EXCEPT ![r].type = "dead"]
+  /\ UNCHANGED <<msgs>>
+
+\* Terminating is an action that allows infinite stuttering to prevent deadlock on
+\* behaviour termination. We consider termination to be valid if at least M nodes
+\* has the block being accepted.
+Terminating ==
+  /\ Cardinality({rm \in RM : rmState[rm].type = "blockAccepted"}) >=1
+  /\ UNCHANGED <<msgs, rmState>>
+
+\* Next is the next-state action describing the transition from the current state
+\* to the next state of the behaviour.
+Next ==
+  \/ Terminating
+  \/ \E r \in RM :
+       \/ OnTimeout(r)
+       \/ RMOnPrepareRequest(r) \/ RMOnPrepareResponse(r) \/ RMOnCommit(r) \/ RMOnChangeView(r)
+       \/ RMDie(r) \/ RMBeBad(r)
+       \/ RMFaultySendCV(r) \/ RMFaultyDoCV(r) \/ RMFaultySendCommit(r) \/ RMFaultySendPReq(r) \/ RMFaultySendPResp(r)
+
+\* Safety is a temporal formula that describes the whole set of allowed
+\* behaviours. It specifies only what the system MAY do (i.e. the set of
+\* possible allowed behaviours for the system). It asserts only what may
+\* happen; any behaviour that violates it does so at some point and
+\* nothing past that point makes difference.
+\*
+\* E.g. this safety formula (applied standalone) allows the behaviour to end
+\* with an infinite set of stuttering steps (those steps that DO NOT change
+\* neither msgs nor rmState) and never reach the state where at least one
+\* node is committed or accepted the block.
+\*
+\* To forbid such behaviours we must specify what the system MUST
+\* do. It will be specified below with the help of fairness conditions in
+\* the Fairness formula.
+Safety == Init /\ [][Next]_vars
+
+\* -------------- Fairness temporal formula --------------
+
+\* Fairness is a temporal assumptions under which the model is working.
+\* Usually it specifies different kind of assumptions for each/some
+\* subactions of the Next's state action, but the only think that bothers
+\* us is preventing infinite stuttering at those steps where some of Next's
+\* subactions are enabled. Thus, the only thing that we require from the
+\* system is to keep take the steps until it's impossible to take them.
+\* That's exactly how the weak fairness condition works: if some action
+\* remains continuously enabled, it must eventually happen.
+Fairness == WF_vars(Next)
+
+\* -------------- Specification --------------
+
+\* The complete specification of the protocol written as a temporal formula.
+Spec == Safety /\ Fairness
+
+\* -------------- Liveness temporal formula --------------
+
+\* For every possible behaviour it's true that there's at least one PrepareRequest
+\* message from the speaker, there's at lest one PrepareResponse message and at
+\* least one Commit message.
+PrepareRequestSentRequirement == <>(\E msg \in msgs : msg.type = "PrepareRequest")
+PrepareResponseSentRequirement == <>(\E msg \in msgs : msg.type = "PrepareResponse")
+CommitSentRequirement == <>(\E msg \in msgs : msg.type = "Commit")
+
+\* For every possible behaviour it's true that eventually (i.e. at least once
+\* through the behaviour) block will be accepted. It is something that dBFT
+\* must guarantee (an in practice this condition is violated).
+TerminationRequirement == <>(Cardinality({r \in RM : rmState[r].type = "blockAccepted"}) >= M)
+
+\* A liveness temporal formula asserts only what must happen (i.e. specifies
+\* what the system MUST do). Any behaviour can NOT violate it at ANY point;
+\* there's always the rest of the behaviour that can always make the liveness
+\* formula true; if there's no such behaviour than the liveness formula is
+\* violated. The liveness formula is supposed to be checked as a property
+\* by the TLC model checker.
+Liveness == /\ PrepareRequestSentRequirement
+            /\ PrepareResponseSentRequirement
+            /\ CommitSentRequirement
+            /\ TerminationRequirement
+
+\* -------------- Model constraints --------------
+
+\* Model constraints are a set of state predicates restricting the number of possible
+\* behaviour states. It is needed to reduce model checking time and prevent
+\* the model graph size explosion. These formulaes must be specified at the
+\* "State constraint" section of the "Additional Spec Options" section inside
+\* the model overview.
+
+\* MaxViewConstraint is a state predicate restricting the maximum view of messages
+\* and consensus nodes state.
+MaxViewConstraint == /\ \A r \in RM : rmState[r].view <= MaxView
+                     /\ \A msg \in msgs : msg.view <= MaxView
+
+\* MaxUndeliveredMessageConstraint is a state predicate restricting the maximum
+\* number of messages undelivered to any of the consensus nodes.
+MaxUndeliveredMessageConstraint == Cardinality({msg \in msgs : \E rm \in RM : msg \notin rmState[rm].pool}) <= MaxUndeliveredMessages
+
+\* ModelConstraint is overall model constraint rule.
+ModelConstraint == MaxViewConstraint /\ MaxUndeliveredMessageConstraint
+
+\* -------------- Invariants of the specification --------------
+
+\* Model invariant is a state predicate (statement) that must be true for
+\* every step of every reachable behaviour. Model invariant is supposed to
+\* be checked as an Invariant by the TLC Model Checker.
+
+\* TypeOK is a type-correctness invariant. It states that all elements of
+\* specification variables must have the proper type throughout the behaviour.
+TypeOK ==
+  /\ rmState \in [RM -> RMStates]
+  /\ msgs \subseteq Messages
+
+\* InvTwoBlocksAccepted states that there can't be two different blocks accepted in
+\* the two different views, i.e. dBFT must not allow forks.
+InvTwoBlocksAccepted == \A r1 \in RM:
+                  \A r2 \in RM \ {r1}:
+                  \/ rmState[r1].type /= "blockAccepted"
+                  \/ rmState[r2].type /= "blockAccepted"
+                  \/ rmState[r1].view = rmState[r2].view
+
+\* InvDeadlock is a deadlock invariant, it states that the following situation expected
+\* never to happen: one node is committed in a single view, two others are committed in
+\* a larger view, and the last one has its view changing.
+InvDeadlock == \A r1 \in RM :
+               \A r2 \in RM \ {r1} :
+               \A r3 \in RM \ {r1, r2} :
+               \A r4 \in RM \ {r1, r2, r3} :
+               \/ rmState[r1].type /= "commitSent"
+               \/ rmState[r2].type /= "commitSent"
+               \/ rmState[r3].type /= "commitSent"
+               \/ \neg IsViewChanging(r4)
+               \/ rmState[r1].view >= rmState[r2].view
+               \/ rmState[r2].view /= rmState[r3].view
+               \/ rmState[r3].view /= rmState[r4].view
+
+\* InvFaultNodesCount states that there can be F faulty or dead nodes at max.
+InvFaultNodesCount == Cardinality({
+                                    r \in RM : rmState[r].type = "bad" \/ rmState[r].type = "dead"
+                                 }) <= F
+
+\* This theorem asserts the truth of the temporal formula whose meaning is that
+\* the state predicates TypeOK, InvTwoBlocksAccepted, InvDeadlock and InvFaultNodesCount are
+\* the invariants of the specification Spec. This theorem is not supposed to be
+\* checked by the TLC model checker, it's here for the reader's understanding of
+\* the purpose of TypeOK, InvTwoBlocksAccepted, InvDeadlock and InvFaultNodesCount.
+THEOREM Spec => [](TypeOK /\ InvTwoBlocksAccepted /\ InvDeadlock /\ InvFaultNodesCount)
+
+=============================================================================
+\* Modification History
+\* Last modified Fri Feb 17 15:51:19 MSK 2023 by anna
+\* Created Tue Jan 10 12:28:45 MSK 2023 by anna
diff --git a/formal-models/dbftMultipool/dbftMultipool___AllGoodModel.launch b/formal-models/dbftMultipool/dbftMultipool___AllGoodModel.launch
new file mode 100644
index 00000000..e522df66
--- /dev/null
+++ b/formal-models/dbftMultipool/dbftMultipool___AllGoodModel.launch
@@ -0,0 +1,44 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<launchConfiguration type="org.lamport.tla.toolbox.tool.tlc.modelCheck">
+    <stringAttribute key="configurationName" value="AllGoodModel"/>
+    <intAttribute key="distributedFPSetCount" value="0"/>
+    <stringAttribute key="distributedNetworkInterface" value="172.200.0.254"/>
+    <intAttribute key="distributedNodesCount" value="1"/>
+    <stringAttribute key="distributedTLC" value="off"/>
+    <intAttribute key="fpIndex" value="70"/>
+    <intAttribute key="maxHeapSize" value="50"/>
+    <stringAttribute key="modelBehaviorInit" value=""/>
+    <stringAttribute key="modelBehaviorNext" value=""/>
+    <stringAttribute key="modelBehaviorSpec" value="Spec"/>
+    <intAttribute key="modelBehaviorSpecType" value="1"/>
+    <stringAttribute key="modelBehaviorVars" value="msgs, rmState"/>
+    <stringAttribute key="modelComments" value=""/>
+    <booleanAttribute key="modelCorrectnessCheckDeadlock" value="true"/>
+    <listAttribute key="modelCorrectnessInvariants">
+        <listEntry value="1TypeOK"/>
+        <listEntry value="1InvTwoBlocksAccepted"/>
+        <listEntry value="1InvDeadlock"/>
+        <listEntry value="1InvFaultNodesCount"/>
+    </listAttribute>
+    <listAttribute key="modelCorrectnessProperties">
+        <listEntry value="1Liveness"/>
+    </listAttribute>
+    <intAttribute key="modelEditorOpenTabs" value="10"/>
+    <stringAttribute key="modelParameterActionConstraint" value=""/>
+    <listAttribute key="modelParameterConstants">
+        <listEntry value="RMFault;;{};0;0"/>
+        <listEntry value="MaxView;;2;0;0"/>
+        <listEntry value="RMDead;;{};0;0"/>
+        <listEntry value="RM;;{0, 1, 2, 3};0;0"/>
+        <listEntry value="MaxUndeliveredMessages;;6;0;0"/>
+    </listAttribute>
+    <stringAttribute key="modelParameterContraint" value="ModelConstraint"/>
+    <listAttribute key="modelParameterDefinitions"/>
+    <stringAttribute key="modelParameterModelValues" value="{}"/>
+    <stringAttribute key="modelParameterNewDefinitions" value=""/>
+    <intAttribute key="modelVersion" value="20191005"/>
+    <intAttribute key="numberOfWorkers" value="8"/>
+    <stringAttribute key="result.mail.address" value=""/>
+    <stringAttribute key="specName" value="dbftMultipool"/>
+    <stringAttribute key="tlcResourcesProfile" value="local custom"/>
+</launchConfiguration>