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Going with the Flow Parameterized Verification using Message FlowsPowerPoint Presentation

Going with the Flow Parameterized Verification using Message Flows

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### Going with the FlowParameterized Verification using Message Flows

Murali Talupur & Mark Tuttle

SCL, Intel Corporation

Protocol Verification

- Distributed protocols are crucial components of modern computer systems
- Cache coherence protocols for example

- Designed parametrically
- Full validation requires parametric reasoning

- Protocol verification involves two main issues
- Tightly coded
- So standard predicate abstraction and COI reduction will not work

- Unbounded or high degree of parallelism

- Tightly coded

Our Approach

Consists of two key elements

- CMP Method:
- A general framework for reasoning about systems with
- replication
- We simplified and generalized the method

- Flow based Invariants:
- A new method for discovering invariants of concurrent
- systems
- Implicit partial orders on system events yield valuable
- invariants

Existing Methods

Regular Model Checking

Aggregated Trans

Counter Abstraction

Theorem Proving

Invisible Invariants

CMP

Increasing Manual Effort

WS1S

Index predicates

Automatic methods don’t scale

Manual methods require human guidance but scale

CMP method

- Compositional reasoning based method
- Proposed by McMillan, elaborated by Chou et al [CTC] and further formalized by Krstic

- CMP: Pros and Cons
- Scales to large protocols
- This was one of the first techniques to handle Flash protocol
- Within Intel handled a cache protocol several orders of magnitude bigger than even Flash

- User has to supply “lemmas”/invariants
- Supplying lemmas is easier than supplying full blown inductive invariants
- Easier than pure theorem proving

- Supplying lemmas is easier than supplying full blown inductive invariants

- Scales to large protocols

Data Type Reduction

- Reduces unbounded range [1..N] to [1,2, o]
- Throws away the state spaces of [3..N]
- Any condition involving them is conservatively over-approximated

1

2

PA

Other

1

2

3

N-1

N

P(N)

rule “Local_Get"

UniMsg[src].Cmd = Get &

!Dir.Pending

==>

begin

Dir.Dirty := false;

UniMsg[src].Cmd := Put;

endrule;

endruleset;

ruleset src : [1,2] do

rule “Local_Get"

UniMsg[src].Cmd = Get &

!Dir.Pending

==>

begin

Dir.Dirty := false;

UniMsg[src].Cmd := Put;

endrule;

endruleset;

rule "ABSLocal_Get"

true & !Dir.Pending

==>

begin

Dir.Dirty := false;

NOP

endrule;

Rules are in

guarded command

form:

r: ! a

Data Type Reduction

- Data type reduction is syntactic
- Very fast
- Abstract model has small state space

- Behavior of “Other” is not constrained at all
- Need to refine “Other”

Refinement

User provides relevant lemmas

Proceeds in two steps:

- Strengthening of P(N) with the lemmas
- Abstracting the strengthened system

rule “Local_Get"

UniMsg[src].Cmd = Get &

!Dir.Pending

==>

begin

Dir.Dirty := false;

UniMsg[src].Cmd := Put;

endrule;

endruleset;

ruleset src : NODE do

rule "Local_Get"

UniMsg[src].Cmd = Get &

!Dir.Pending & forall dst: NODE do src != dst

-> !(Proc[dst].State = Excl) end

==>

begin

Dir.Dirty := false;

UniMsg[src].Cmd := Put;

endrule;

endruleset;

Strengtheninginvariant "Lemma"

forall src : NODE do forall dst : NODE do

dst != src -> (UniMsg[src].Cmd = Get -> !(Proc[dst].State = Excl))

rule "Local_Get"

UniMsg[src].Cmd = Get &

!Dir.Pending & forall dst: [1..N] do src != dst

-> !(Proc[dst].State = Excl) end

==>

begin

Dir.Dirty := false;

UniMsg[src].Cmd := Put;

endrule;

endruleset;

rule "ABSLocal_Get"

true & !Dir.Pending & forall dst: [1,2].

-> !(Proc[dst].State = Excl) end

==>

begin

Dir.Dirty := false;

NOP

endrule;

RefinementAbstracting strengthened system leads to a refined abstract model

CMP Method

Conjunction of property to be proved and lemmas

8 i,j. (i,j)

P(N) ²

P(N)

² (1,2)

Strengthen with

8 i,j. (i,j)

Apparent

Circular Reasoning

Paper has the proof details!

Ps(N)

² (1,2)

Abstraction

DTR is conservative

PA

² (1,2)

Flow based Invariants

- Rich partial orders on system events are implicit in the concurrent protocols
- We call these Message Flows or simply Flows

- And these can yield powerful invariants

Dir

i

j

Dir

i

j

SendReqS

SendReqS

RecvReqS

RecvReqS

SendInv

SendGntS

SendInvAck

RecvGntS

RecvInvAck

SendGntS

RecvGntS

Process i intiates a Request Shared transaction: Case 1

Process i intiates a Request Shared transaction: Case 2

Constraints from Flows

Dir

i

j

SendReqS

ReqShare(i)

SendReqS(i),RecvReqS(i),SendGntS(i),RecvGntS(i)

RecvReqS

Precedence between rules:

For instance, for process i, action RecvReqS(i)

must happen before SendGntS(i)

SendGntS

RecvGntS

Tracking Flows

A set Aux(i) of auxiliary variables to track

1) all the flows that a process i is involved in

2) for each such flow the last rule that was fired

Each aux 2 Aux(i) is initially ( no_flow, no_rule )

If process i fires rules rn in a flow

f: r1,….rn-1, rn,…..rm

update aux = (f,rn-1) to (f,rn)

If rn is the last rule reset the aux variable

Constraints from Flows

Dir

i

j

SendReqS

Precondition for process i firing rn in flow f:

C(rn,f): 9 aux 2 Aux(i). aux = (f, rn-1 )

RecvReqS

SendGntS

RecvGntS

Lemmas from Flows

Let r: ! a appear in flows f1,..,fn

Find precedence constraints

C1(r,f1), ..,Cn(r,fn)

Let pre(r) = C1(r,f1) Ç ..Ç Cn(r,fn)

Lemma: ) pre(r)

forall i : NODE do

Chan3[i].Cmd = InvAck & CurCmd != Empty & ExGntd = true ->

Chan3[i].Data = AuxData &

forall j : NODE do

j != i -> Cache[j].State != E & Chan2[j].Cmd != GntE & Chan3[j].Cmd != InvAck

Deriving Lemmas from Flows- We can easily convert message flows into invariants
- Our experiments indicate the resulting invariants are very powerful

- Advantages:
- Message flows are readily available in design documents
- Easy to understand
- Flows are local and linear
- No low level details of the protocol

- Valuable validation collateral

A German Flow

ReqShare: SendReqS,RecvReqS,SendInval,SendGntS,RecvGntS

Doc

Modified CMP FlowFlows

Done or Real Cex

Pa(N)

Add aux and

Flow lemmas

PA

Abstract

Model Check

P(N)

spurious cex

P#(N)

Strengthen

Invent

Lemma

Experimental Results

- We applied our method to two standard examples
- German and Flash
- Verified both control and data property
- Compared against CTC

- German
- 3 flows and 2 lemmas added manually
- Lemmas slightly simpler than ones in CTC

- Flash
- 6 flows and 2 lemmas in contrast to > 5 lemmas in CTC
- one trivial and one from CTC paper

- Lemma complexity reduced by 75%
- One auxiliary variable in contrast to 4 in CTC paper
- Different from flow auxiliary variables
- This helps our running times as well: couple of minutes compared to couple of hours in the CTC work

- 6 flows and 2 lemmas in contrast to > 5 lemmas in CTC

Conclusion/ Future Work

- A powerful new method for parameterized verification based on
- the CMP method and
- invariants from Flows

- CMP Method:
- (i) We have simplified and generalized the CMP method
- (ii) Allows more abstractions than simple data type reduction
- Thus, more widely applicable

- (ii) Allows more abstractions than simple data type reduction

- Flows:
- A new way to derive invariants for concurrent systems
- Look for implicit partial orders on system events!

Conclusion/Future Work

More can be done with flows:

Online monitoring to see all traces conform to flows

Extend flows to other distributed systems

Flows for shared memory systems using other types of system events…

Learn flows automatically…

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