can we efficiently verify concurrent programs under relaxed memory models in maude?

Can we efficiently verify concurrent programs under relaxed memory

models in Maude?

Yehia Abd Arrahman, Marina Andric,Alessandro Beggiato, and Alberto Lluch Lafuente

WRLA 2014, 5-6 April 2014, Grenoble

I would say yes.

Worth investigating

Can we efficiently verify concurrent programsunder relaxed memory models in Maude?

SOMEMOTIVATIONS

x := 1;if y == 0 then u := 1else skip

y := 1;if x == 0 then v := 1else skip

A SIMPLE PROGRAM

u v=== 0 0 0 11 01 1

What are the possible outcomes for u and v?

x := 1;if y == 0 then u := 1else skip

y := 1;if x == 0 then v := 1else skip

A SIMPLE PROGRAM

u v=== 0 0 0 11 01 1 ✓

???

✓✓

What are the possible outcomes for u and v?

✓

MORE ANNOYANCES...

x := 1

Maude> search P =>* Q ....States: 10!?

x := 2P =

while true do x := 0

Maude> search P =>* Q .Zzz...

P =

MORE ANNOYANCES...

THE FREE LUNCH IS OVER

Herb Sutter. “The free lunch is over”, Dr. Dobb's Journal, 30(3), March 2005 and C/C++ Users Journal, 23(2), February 2005.

“Software and the concurrency revolution” ACM Queue:Tomorrow’s Computing Today, 3(7):54–62, Sept. 2005.

<

“some optimizations are actually far more than optimizations, in that they can change the meaning of programs and cause visible effects that can break reasonable programmer expectations.

CPU designers are generally sane and well-adjusted folks but they are under so much pressure that they'll risk changing the meaning of your program, and possibly break it, in order to make it run faster. “

Dekker Peterson Lamport Szymanski0

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1000Sequentially ConsistentRelaxed (incorrect)Relaxed (corrected)

STATE SPACE SIZE: SC vs RMM

Dekker Peterson Lamport Szymanski

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No reductionSome approximationSome other approximationPartial-Order-ReductionSome combination

REDUCTIONS (verification)


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450 Breadth-First SearchBest-First with some heuristicBest-First with some other heuristicBest-First with yet another heuristic

REDUCTIONS (bug-finding)

RELAXEDMEMORY MODELS

SEQUENTIAL CONSISTENCY“A multiprocessor system is sequentially consistent if the result of any execution is the same as if the operations of all the processors were executed in some sequential order, and the operations of each individual processor appear in this sequence in the order specified by its program.”

- Leslie Lamport, "How to Make a Multiprocessor Computer That Correctly Executes Multiprocess Programs", IEEE Trans. Comput, 1979

Program order: among operations from individual processorsAtomicity: memory operations must execute atomically with respect to each other

RELAXING CONSISTENCY

Relaxing program order: Write-to-Read Write-to-Write Read-to-Read Read-to-Write

Relaxing atomicity: Read own write early Read others’ write early

HIERARCHY OF RELAXATIONSSC

TSO IBM-370

PC

RCscPowerPC

WO Alpha

RCPcRMO

PSO

Write-to-Read

Write-to-Write

Read-to-ReadRead-to-Write

source: http://wiki.expertiza.ncsu.edu/index.php/CSC/ECE_506_Spring_2013/10c_ks

http://wiki.expertiza.ncsu.edu/index.php/CSC/ECE_506_Spring_2013/10c_ks

TOTAL STORE ORDERING (TSO)

Relaxations: Write-to-Read Read own write early

Why? Mitigate write latency Some programs may still be “correct”

(e.g. sequentially consistent)

TSO “AXIOMATICALLY”TSO-executions are sequences of reads and writes

r(x,u) < r(y,v) < w(z,w) < ...

r(x,u) < r(y,v) < w(z,w) < ...

such thatr r < r' [r-r preserved]r r < w' [r-w preserved]w w < w' [w-w preserved]

w-r allowed

r(x,u) < r(y,v) < w(z,w) < ...

such thatr r < r' [r-r preserved]r r < w' [r-w preserved]w w < w' [w-w preserved]

and r(x,u) are such that

(1) v if s(x,v) is the max wrt. < among all s(x,v) s.t.s(x,v) < r(x,u) ors(x,v) <p r(x,u)

(2) x0 (initial value for x) if there is no s(x,v) above.

(read own's write early)

w-r allowed

TSO “OPERATIONALLY”

SHARED MEMORY

THREAD THREAD

TSO “OPERATIONALLY”

SHARED MEMORY

THREAD THREAD

WRITE BUFFER WRITE BUFFER

Formalization of memory models Axiomatic [Adve, Alglage, Sewel, Owens, Higham,...] Operational [Boudol, Petri, Atig, Bouajjani, Burckhardt,...] Adequacy, generality, etc.

Correctness criteria Sequential consistency, linearizability, serializability,

quiescent/eventual consistency... [Herlihy, Shavit, Shapiro,...] “Fundamental property” (data-race free programs are

sequential consistent) [Saraswat et al.]

Portability of programs Check whether P/SC ≈ P/RMM Otherwise repair P e.g. inserting fences [Wolper, Bouajjani...]

SOME KEY ISSUES

Verification approaches Directly use SC verification tools

e.g. for programs that are linearizable even under RMMs [Burckhardt, Cohen, Owens]

Program Transformation and then SC toolse.g. [Alglave, Bouajjani]

Ad-hoc verification under RMMs.e.g. Some... (see later)

Some tools CBMC [Alglave et al] CheckFence [Burckhardt et al] DFENCE [Lui et al]

SOME KEY ISSUES

THIS TALK'sPERSPECTIVE

OUR SPIRIT HERE

Language designers prototyping new RMM-aware languages with Maude (the natural framework!).

Interested in “search” for P/RMM (for checking properties, for fence insertions, etc.).

Willing to make search efficient but not willing to modify the Maude engine.

A SIMPLEMULTI-THREADEDLANGUAGE

A SIMPLE LANGUAGE

CONFIGURATIONS

MEMORIES AND VIEWSMemory updates

Local to Global

In the following abbreviates

SEMANTICS: thread interleaving

sorry...

SEMANTICS: skip

SEMANTICS: assignments

SEMANTICS: fences

SEMANTICS: sequential composition

SEMANTICS: branches

SEMANTICS: loops

SEMANTICS: wait

SEMANTICS: buffer commits

MORE ANNOYANCES...

x := 1

Maude> search P =>* Q ....States: 10!?

x := 2P =

x|->0===============

||---------------x:=1; || x:=2;

x|->0===============x|->1 || --------------- skip || x:=2;

x|->0=============== || x|->2

--------------- x:=1 || skip

x|->0===============x|->1 || x|->2---------------skip || skip

x|->1===============

||--------------- skip || x:=2;

x|->2===============

||---------------x:=1 || skip

x|->1=============== || x|->2

---------------skip || skip

x|->1===============

||---------------skip || skip

x|->2===============x|->1 || ---------------skip || skip

x:=1;

x:=1;

x:=1;

x:=2;

x:=2;

x:=2;

commit commit

commit commit

commitcommit

x|->2===============

||---------------skip || skip

state

Shared memory

Thread buffer

Thread program

x|->0===============

||---------------x:=1; || x:=2;

x|->0===============x|->1 || --------------- skip || x:=2;

x|->0=============== || x|->2

--------------- x:=1 || skip

x|->0===============x|->1 || x|->2---------------skip || skip

x|->1===============

||--------------- skip || x:=2;

x|->2===============

||---------------x:=1 || skip

x|->1=============== || x|->2

---------------skip || skip

x|->1===============

||---------------skip || skip

x|->2===============x|->1 || ---------------skip || skip

x:=1;

x:=1;

x:=1;

x:=2;

x:=2;

x:=2;

commit commit

commit commit

commitcommit

x|->2===============

||---------------skip || skip

state

Shared memory

Thread buffer

Thread program

Usual state space with SC


Maude> search P =>* Q .Zzz...

P =

MORE ANNOYANCES...

x|->0====================--------------------while(true) do x:=0

x|->0====================--------------------x:=0;while(true) do x:=0

while(true)

x:=0;

x|->0====================

x|->0--------------------while(true) do x:=0

x|->0====================

x|->0--------------------x:=0;while(true) do x:=0

while(true)

x|->0====================

x|->0x|->0

--------------------while(true) do x:=0

while(true)

x:=0;

commit

commit

commit

...

SOME REDUCTIONTECHNIQUES

Partial Order Reduction Techniques Partial Orders [Alglave et al. @ CAV 2013] Persistent Sets [Linden&Wolper @ TACAS 2013] Ample sets (via SPIN) [Jonson @ CAN2009]

Approximation/abstraction techniques Predicate abstraction [Dan et al. @ SAS 2013] Bounded context-switches [Abdulla et al. @ TACAS 2012] Single-buffer semantics [Atig et al. @ CAV 2011] Buffers-as-sets abstraction [Kuperstein et al. @ PLDI 2011] Bounded buffers [Kuperstein et al. @ FMCAD 2011]

Other SAT/BMC [Burckhardt et al @ CAV 6/7/8, Gopalakrishnan et al. @ CAV 04] Buffer automata [Linden&Wolper @ SPIN2010, TACAS 2013] Monitors [Burnim et al. @ TACAS 2011, Burckhardt&Musuvathi @ CAV 2008]

TEN+ YEARS OF RESEARCH

Equational abstractions? [Meseguer&Palomino&Martí-Oliet @ TCS 2008]

Partial-order reduction? [Farzan&Meseguer @ TERMGRAPH 2006]

Search strategies? [Martí-Oliet&Meseguer&Verdejo @ WRLA 2004]

SOME SIMPLEAPPROXIMATIONS FOR TSO

Disclaimer: proof-of-concepts, for the “good” ones see the above cited papers.

ONE OF OUR ANOYANCES


Maude> search P =>* Q .Zzz..

BUFFERS AS SETS OF UPDATES

Abstract buffers as sets of updates: Make ACI1 (i.e. buffer becomes sets of updates); Make commit non-deterministic (usual+no effect); Make evaluation of expressions non-deterministic.

You get an over-approximation: Finite state space; Preservation of reachability properties. (Possibly) some “spurious” behaviours;


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MORE STATES

BUFFERS AS ORDERED MAPS

Approximation that Guarantees finite state space; Introduces some executions; Preserves some reachability properties???

(under investigation)

“SPURIOUS” EXECUTIONS

x:=1;y:=1;x:=2

wait x=0 & y=1

x|->0 , y |->0 ===============

|| ---------------

x:=1; || wait(...)y:=1; || x:=2 ||

x|->0 , y |->0 ===============

x|->1 || ---------------

y:=1; || wait(...)x:=2; ||

x|->0 , y |->0 ===============

x|->1 || y|->1 || ---------------

x:=2; || wait(...)

x|->0 , y |->0 ===============

x|->1 || y|->1 || x|->2 || ---------------

skip || wait(...)

x|->1 , y |->0 =============== || ---------------

y:=1; || wait(...)x:=2; ||

x|->1 , y |->0 ===============

y|->1 || ---------------

x:=2; || wait(...)

x|->1 , y |->0 =============== y|->1 || x|->2 || ---------------

skip || wait(...)

x|->1 , y |->1 ===============

|| ---------------

x:=2; || wait(...)

x|->1 , y |->1 =============== x|->2 || ---------------

skip || wait(...)

x|->2 , y |->1 =============== || ---------------

skip || wait(...)

commit

commitcommit

commit

commit

commit

x|->0 , y |->0 ===============

y|->1 || x|->2 || ---------------

skip || wait(...)

wait!

ONE “SPURIOUS” EXECUTION

x|->0 , y |->1 ===============

y|->1 || ---------------

skip || wait(...)

commit


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REDUCTIONS

FORCE-FLUSH APPROXIMATION

Under-approximation that Does not guarantee finite state space ; Some behaviours may be lost; Does not introduce spurious behaviours.

(up to some equivalence: stuttering and depending on the state observations).

M===============x|->u || ... || x|->v || ---------------

S || T

M ◦ x|->u===============

... || x|->v || ---------------

S || T

NO “SPURIOUS” EXECUTION

M===============x|->u || ... || ||

--------------- x:=v; S || T

M ◦ x|->u===============

... || ||

--------------- x:=v; S || T

commit

x:=v x:=v

(up to some equivalence: stuttering and depending on the state observations).


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REDUCTIONS

PARTIAL-ORDERREDUCTIONFOR RMMs

AMPLE SETS

Main idea Explore only a subset ample(s) of the succesors of s... ...such that ample(s):

C0: ample(s) empty only if s is a deadlock;C1: ample(s) contains invisible actions;C2: no transition that is dependent on a transition in

ample(s) occurs in the original system without atransition in ample(s) occurring first;

C3: no action outside ample(s) is delayed forever. You will get a stutter equivalent transition system.

SIMPLE POR FOR TSOSimple heuristic: assignments

x := u

are independent of actions of other threads since their effect is local (on the buffer).

They are also invisible unless one wants to observe buffers or programs.


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No reductionPartial-Order Reduction

REDUCTIONS (verification)

SEARCH STRATEGIESFOR RMMs

DIRECTED MODEL CHECKINGMain idea Replace the exploration algorithm (NDFS/BFS)

by a “guided” algorithm (A*, Best-First, etc.) Domain/property-based “heuristic” functions

to rank states or executions

“Heuristics for model checking Java” [Groce&Visser] Promote interleavings (we think “sequentially”) Promote code coverageDone for JPF, SPIN, etc.

x|->0 , y|->0===============

||---------------x:=1; || y:=1;y==0? || x==0?

x|->0 , y|->0===============x->1 ||

--------------- y==0? || y:=1;

|| x==0?

x|->0 , y|->0=============== || y->1

--------------- x:=1 || x==0? y==0? ||

x|->0 , y|->0===============x->1 || y->1

---------------y==0? || x==0?

x|->1 , y|->0===============

||---------------

y==0? || y:=1; || x==0?

x|->0 , y|->1===============

||--------------- X:=1 || x==0?

y==0? ||

x:=1;

x:=1;

y:=1;

y:=1;flush flush

... ...x|->0 , y|->0===============x->1 || y->1

--------------- cs || x==0?

x|->0 , y|->0===============x->1 || y->1

---------------y==0? || cs

x|->0 , y|->0===============

||---------------x:=1; || y:=1;y==0? || x==0?

x|->0 , y|->0===============x->1 ||

--------------- y==0? || y:=1;

|| x==0?

x|->0 , y|->0=============== || y->1

--------------- x:=1 || x==0? y==0? ||

x|->0 , y|->0===============x->1 || y->1

---------------y==0? || x==0?

x|->1 , y|->0===============

||---------------

y==0? || y:=1; || x==0?

x|->0 , y|->1===============

||--------------- X:=1 || x==0?

y==0? ||

x:=1;

x:=1;

y:=1;

y:=1;flush flush

0

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... ...x|->0 , y|->0===============x->1 || y->1

--------------- cs || x==0?

x|->0 , y|->0===============x->1 || y->1

---------------y==0? || cs

2 2

Count number ofnon-empty buffers


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REDUCTIONS (bug-finding)

CONCLUDINGREMARKS

I would say yes.

Worth investigating

Can we efficiently verify concurrent programsunder relaxed memory models in Maude?

Beyond TSO: PSO, RMO, etc.1

2

FUTURE WORK?

Other languages/primitives: see e.g. KernelC/x86-TSO in K [Serbanuta]

3 Proof techniques (with Maude)

TAHNSK!

REFERENCES

[Linden&Wolper @ TACAS 2013]Alexander Linden, Pierre Wolper: A Verification-Based Approach to Memory Fence Insertion in PSO Memory Systems. TACAS 2013: 339-353

[Dan&MMeshman&Vechev&Yahav @ SAS 2013]Andrei Marian Dan, Yuri Meshman, Martin T. Vechev, Eran Yahav: Predicate Abstraction for Relaxed Memory Models. SAS 2013: 84-104

[Alglave et al. @ CAV 2013]Jade Alglave, Daniel Kroening, Michael Tautschnig: Partial Orders for Efficient Bounded Model Checking of Concurrent Software. CAV 2013: 141-157

[Abdulla&Atig&Chen&Leonardsson&Rezine @ TACAS 2012]Abdulla, P.A., Atig, M.F., Chen, Y.-F., Leonardsson, C., Rezine, A.: Counter- Example Guided Fence Insertion under TSO. In: TACAS 2012. LNCS, vol. 7214 (2012)

[Atig&Bouajjani&Parlato @ CAV 2011]Atig, M.F., Bouajjani, A., Parlato, G.: Getting Rid of Store-Buffers in TSO Analysis. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806 (2011)

[Kuperstein&Vechev&Yahav @ PLDI 2011]Kuperstein, M., Vechev, M., Yahav, E.: Partial-coherence abstractions for relaxed memory models. In: PLDI 2011 (2011)

REFERENCES (1)

[Burnim&Sen&Stergiou @ TACAS 2011]Jacob Burnim, Koushik Sen, Christos Stergiou: Sound and Complete Monitoring of Sequential Consistency for Relaxed Memory Models. TACAS 2011: 11-25

[Burnim&Sen& C. Stergiou @ TACAS 2011]J. Burnim, K. Sen, and C. Stergiou. Sound and complete monitoring of sequential consistency in relaxed memory models. In TACAS, 2011.

[Kuperstein&Vechev&Yahav @ FMCAD 2011]M. Kuperstein, M. Vechev, and E. Yahav. Automatic inference of memory fences. In FMCAD, 2011.

[Linedn&Wolper @ SPIN 2010] A. Linden and P. Wolper. An automata-based symbolic approach for verifying programs on relaxed memory models. In SPIN, 2010.

[Jonson @ CAN2009]Jonsson, B.: State-space exploration for concurrent algorithms under weak memory orderings: (preliminary version). SIGARCH Comput. Archit. News 36, 65–71 (2009)

[Burckhardt&Musuvathi @ CAV 2008]Burckhardt,S.,Musuvathi,M.: Effective Program Verification for Relaxed Memory Models. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 107–120. Springer, Heidelberg (2008)

REFERENCES (2)

[Burckhardt&Alur&Martin @ CAV 2007]Burckhardt, S., Alur, R., Martin, M.M.K.: Checkfence: checking consistency of concurrent data types on relaxed memory models. In: ACM SIGPLAN 2007 Conference on Programming Lan- guage Design and Implementation (2007)

[Burckhardt&Alur&Martin @ CAV 2006]Burckhardt,S.,Alur,R.,Martin,M.M.K.: Bounded Model Checking of Concurrent Data Types on Relaxed Memory Models: A Case Study. In: CAV 2006. LNCS 4144. (2006)

[Gopalakrishnan&Yang&Sivaraj @ CAV 2004]Gopalakrishnan, G., Yang, Y., Sivaraj, H.: QB or not QB: An efficient execution verification tool for memory orderings. In: CAV 2004. LNCS, vol. 3114 (2004)

[Park&Dill @ PAA 1995]Park, S., Dill, D.L.: An executable specification, analyzer and verifier for rmo (relaxed memory order). In: SPAA 1995: Proceedings of the Seventh Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 34–41. ACM, New York (1995)

REFERENCES (3)

[Meseguer&Palomino&Martí-Oliet @ TCS 2008]José Meseguer, Miguel Palomino, Narciso Martí-Oliet: Equational abstractions. Theor. Comput. Sci. 403(2-3): 239-264 (2008)

[Farzan&Meseguer @ TERMGRAPH 2006]Azadeh Farzan, José Meseguer: Partial Order Reduction for Rewriting Semantics of Programming Languages. Electr. Notes Theor. Comput. Sci. 176(4): 61-78 (2007)

[Rodríguez 2009 @ WRLA 2009]Rodríguez, D.E.: Combining techniques to reduce state space and prove strongproperties. In: WRLA. Volume 238(3) of ENTCS. (2009) 267 – 280

[Lluch&Meseguer&Vandin @ ICFEM 2012]Alberto Lluch-Lafuente, José Meseguer, Andrea Vandin: State Space c-Reductions of Concurrent Systems in Rewriting Logic. ICFEM 2012: 430-446

[Martí-Oliet&Meseguer&Verdejo @ WRLA 2004]Narciso Martí-Oliet, José Meseguer, Alberto Verdejo: Towards a Strategy Language for Maude. Electr. Notes Theor. Comput. Sci. 117: 417-441 (2005)

[Groce&Visser @ STTT 2004]Alex Groce, Willem Visser: Heuristics for model checking Java programs. STTT 6(4): 260-276 (2004)

REFERENCES (4)

can we efficiently verify concurrent programs under relaxed memory models in maude?

Science

skip x

whiletrue x

commitcommit x

simple program u v

maude search p

memory operations

relaxed memory models

sequential order