Synchronizability for Verification of Asynchronously Communicating Systems

Samik BasuIowa State University

Tevfik BultanUniversity of California at Santa Barbara

Meriem OuederniUniversity of Malaga

Asynchronously Communicating Systems

• Message-based asynchronous communication has been adopted in many domains:– Web service composition

• Interacting component services• Java API for XML Messaging (JAXM)

– Distributed programming• Interacting distributed programs• Erlang

– System programming• Interacting processes• Singularity OS, Go programming language

Asynchronous Messaging

• Sender does not have to wait for the receiver– Message is inserted to a message queue– Messaging platform guarantees the delivery of the message

• Why support asynchronous messaging?– Otherwise the sender has to block and wait for the receiver – Sender may not need any data to be returned– If the sender needs some data to be returned, it should only wait

when it needs to use that data– Asynchronous messaging can alleviate the latency of message

transmission– Asynchronous messaging can prevent sender from blocking if the

receiver service is temporarily unavailable• Rather then creating a thread to handle the send, use

asynchronous messaging

Objective & Challenge

• Automatic verification of desired properties of asynchronous systems

• Asynchronous communication is hard to analyze– Systems can have infinite-state spaces due to message queues– Asynchronously communicating finite state machines can simulate

Turing Machines– In general, automated verification of asynchronously

communicating finite state machines is undecidable

Motivation: Singularity OS

• Experimental OS developed by Microsoft Research to explore new ideas for operating system design

• Key design principles: – Dependability– Security

• Key architectural decision:– Implement a sealed process system

• Software Isolated Processes (SIPs)– Closed code space (no dynamic code loading or code generation)– Closed object space (no shared memory)

• Inter-process communication occurs via asynchronous message passing over channels

Singularity Channels

• Channels allow 2-Party asynchronous communication via FIFO message queues– Sends are non blocking– Receives block until a message is at the head of a receive queue

• Each channel has exactly two endpoints– Type exposed for each endpoint (Exp and Imp)– Each endpoint owned by at most one process at any time

• Owner of Exp referred to as Server• Owner of Imp referred to as Client

Channel Contracts

• Written in Sing #• Contracts specify two things:

1. The messages that may be sent over a channel• out message are sent from the

Server endpoint to the Client endpoint (SC)

• in messages are sent from the Client endpoint to the Server endpoint (CS)

– The set of allowed message sequences• out message marked with !• in messages marked with ?

public contract KeyboardDeviceContract { out message AckKey( uint key ); out message NakKey(); out message Success();

in message GetKey(); in message PollKey();

state Start { Success! -> Ready; }

state Ready { GetKey? -> Waiting; PollKey? -> (AckKey! or NakKey!) -> Ready; }

state Waiting { AckKey! -> Ready; NakKey! -> Ready; }}

public contract KeyboardDeviceContract { out message AckKey( uint key ); out message NakKey(); out message Success();

in message GetKey(); in message PollKey();

state Start { Success! -> Ready; }

state Ready { GetKey? -> Waiting; PollKey? -> (AckKey! or NakKey!) -> Ready; }

state Waiting { AckKey! -> Ready; NakKey! -> Ready; }}

• A contract specifies a finite state machine• Each message causes a transition from one state to another state

KeyboardDeviceContract

Channel Contracts

Start

Ready$0ReadyWaiting

SC:Success

SC:AckKey

SC:AckKey

CS:GetKey

CS:PollKey

SC:NakKey

SC:AckKey

Implicit State

Singularity Channel Contract Verification

• Singularity compiler automatically checks compliance of client and server processes to the specified contract

• Claim from Singularity documentation:– "clients and servers that have been verified separately against the

same contract C are guaranteed not to deadlock when allowed to communicate according to C.“

• This claim is wrong!

Bad Things Can Happen: The TpmContract

IO_RUNNING$0

IO_RUNNINGReadyState

ReadyState$1

ReadyState$0

Send?

IO_RUNNING$0

IO_RUNNINGReadyState

ReadyState$1

ReadyState$0

Server

Send!

AckStartSend!

AckStartSend?

SendComplete!

GetTpmStatus!

GetTpmStatus?TpmStatus!

GetTpmStatus!TpmStatus? TpmStatus?

SendComplete?

TpmStatus!GetTpmStatus?

ServerReceive Queue

ClientReceive Queue

Send

AckStartSendSendComplete

GetTpmStatus

TpmStatus

Send SequenceCS: SendSC: AckStartSendSC: SendCompleteCS: GetTpmStatusSC: TpmStatus

Client

Stuck!

Properties we may want to verify

• It would be nice if we can verify properties about channel contracts such as:

– After each SendComplete message is sent, eventually a Send or GetTpmStatus message is sent

– The processes can reach the ReadyState with empty message queues after the SendComplete and GetTpmStatus messages are sent

Our Approach

• We know that verifying properties of asynchronously communicating systems is difficult due to message queues– Model checking such systems is undecidable even for finite state

process models if the message queues are unbounded

• We ask the following question:– Can we identify asynchronously communicating systems where

asynchronous communication does not create new behaviors?• We call such systems synchronizable

Verification via Synchronizability

• If a system is synchronizable, then– behaviors of the system remain the same if we replace

asynchronous communication with synchronous communication

Synchronizable asynchronous behaviors = synchronous behaviors

• If a system is synchronizable, then– we can verify the synchronous version of the system

finite state processes + synchronous communication = finite state system

Synchronizableverification resultsfor asynchronoussystem

verification resultsfor synchronoussystem

=

Equivalence of what type of behaviors?

Synchronizability in terms of

– Sequences of send actions• Receive actions are considered local to the processes and their

ordering is not taken into account

– Reachability of states with no pending receives (we call such states synchronized states)

• States with pending receives imply some process has not yet reacted to messages sent to it, so the reachability of states where the messages queues are not empty are not taken into account

Three Examples, Example 1

server

• Sequences of send actions are identical for both asynchronous and Sequences of send actions are identical for both asynchronous and synchronous versions: (synchronous versions: (rr11aa11 | | rr22aa22)* )* ee

• During all executions the message queues use a fixed amount of space

?r2

!a1 !a2

?e

?r1

requester

!r2

?a1 ?a2

!e

!r1

Example 2

• Sequences of send actions for the asynchronous version is not a regular set and is not same as the synchronous version

• Queues can grow arbitrarily large

requester

!r2

?a1 ?a2

!e

!r1

server

?r2

!a1 !a2

?e

?r1

Example 3

• Sequences of send actions are identical for synchronous and Sequences of send actions are identical for synchronous and asynchronous versions: (asynchronous versions: (rr11 | | rr22 | | rara)* )* ee

• Queues can grow arbitrarily large

requester server

!r2

?a !r

!e!r1 ?r2

!a ?r

?e?r1

State Spaces of the Three Examples

queue length

# o

f st

ates

in

th

ou

san

ds

• Verification of Examples 2 and 3 are difficult even if we bound the queue length

• Example 1 is synchronizable• Example 2 is not synchronizable • Example 3 is synchronizable, so it can be verified efficiently!

Contributions of this paper

Synchronizability definition in terms of – Sequences of send actions – Reachability of states with no pending receives, i.e., synchronized

states

• Necessary and sufficient condition for this definition of synchronizability

• Implementation and experiments on the Singularity channel contracts

Main Result

I0 : Synchronous System (0 size message queue)

Ik: Bounded Asynchronous System (k size message queue)

I : Asynchronous System (unbounded queue)

I0 equivalent to I1 iff Ik equivalent to I

Equivalence is defined as:

Identical set of send sequences and identical reachability of synchronized states

Earlier Result

I0 equivalent to I1 iff Ik equivalent to I

When equivalence is defined as: Identical set of send sequences

Above condition was proved in an earlier paper:

“Choreography Conformance via Synchronizability”

[Basu and Bultan WWW’11]

In this paper we extend this earlier result by also considering reachability of synchronized states

Proof Summary

• Assume I0 and I1 are equivalent

• Assume for some k: Ik has some synchronized trace absent in I1 or I0

• Show contradiction

Proof Summary

• Assume I0 and I1 are equivalent

• Assume for some k: Ik has some synchronized trace absent in I1 or I0

• Case 1: There exists a new reachable synchronized state that differs from a prior one in exactly one local state

– Proof by contradiction leveraging the fact that I0 and I1 are equivalent

Proof Summary

• Assume I0 and I1 are equivalent

• Assume for some k: Ik has some synchronized trace absent in I1 or I0

• Case 1: There exists a new reachable synchronized state that differs from a prior one in exactly one local state

– Proof by contradiction leveraging the fact that I0 and I1 are equivalent

• Case 2: There exists a new reachable synchronized state that differs from a prior one in more that one local state– Proof by contradiction leveraging Case 1

Implementation

• Implemented using CADP toolbox for checking synchronizability of Singularity Channel Contracts

• We used the front end of an earlier tool called Tune for analyzing Singularity channel contracts [Stengel, Bultan ISSTA 2009]

• We generate Lotos specifications for synchronized (I0) and 1-bounded-asynchronous (I0) versions of the system

• Then we use the equivalence checking algorithms implemented in CADP toolbox to check their equivalence

• Using Tune, we can also generate Promela specifications for synchronized (I0) version which can then be used for model checking behaviors of synchronizable channel contracts

Experimental Results

• Checked synchronizability of 86 Singularity Channel Contracts– Synchronous Systems:

2 to 23 states; 1 to 60 transitions– Asynchronous System with buffer size 1:

3 to 99 states; 2 to 136 transitions

• We first construct and reduce the synchronous and 1-bounded asynchronous systems (takes about 10 secs on average) and then do the equivalence checking (takes about 3 secs on average)

• 84 Contracts are synchronizable

• 2 contracts that are not synchronizable cause deadlocks!– i.e., they are buggy!

Related Work

Synchronizability defined only in terms of equivalence of send action sequences:

• [Fu et al. TSE’05]: Sufficient conditions for synchronizability to verify asynchronously communicating Web services– Similar sufficient conditions in [Honda et al. POPL’08] for session

types

• [Basu and Bultan WWW’11]: Necessary and sufficient condition for synchronizability

Related Work

Restricted Asynchronous Communication:

• [Cece, Finkel Info. & Comp’05]: Reachability properties for half-duplex systems– At most one participating process has pending messages to be

consumed

• [Torre et al. TACAS’08]: Verification of asynchronous systems with restricted communication topologies (e.g., tree)

Related Work

Slack elasticity [Manohar, Martin MPC 98]

• Presents conditions under which changing the size of communication queues does not effect the behavior of the system

• Behavior definition also takes the decision points into account in addition to message sequences– does not consider the synchronized states

• It gives sufficient conditions for slack elasticity and discusses how to construct systems to ensure slack elasticity

Related Work

• Singularity:– [Hunt, Larus SIGOPS ‘07] Singularity: rethinking the software stack– [Fähndrich, Aiken, Hawblitzel, et. al SIGOPS/Eurosys ‘07]

Language support for fast and reliable message-based communication in singularity os.

– Influenced by work on Session Types• [Honda, Vasconcelos, Kubo ESOP ’98] Language primitives

and type discipline for structured communication-based programming

– Source code and RDK: http://codeplex.com/singularity

Related Work

• Synchronizability is also related to choreography realizability problem:– [Fu, Bultan, Su TCS’04]– [Kazhamiakin, Pistore FORTE’06]– [Lohmann, Wolf ICSOC’11]– [Basu, Bultan, Ouderni POPL’12]

Future Directions

• Beyond FIFO communication – out-of-order consumption of messages– unreliable messaging

• Beyond FSM for behavioral modeling– Synchronizability of programs modeld as push-down systems

• Apply to different languages

THE END