Context-bounded model checking of concurrent software Shaz Qadeer Microsoft Research Joint work...

Context-bounded model checking of concurrent

softwareShaz Qadeer

Microsoft Research

Joint work with:•Jakob Rehof, Microsoft Research•Dinghao Wu, Princeton University

Concurrent software

•Operating systems, device drivers•Databases, web servers, browsers, GUIs, ...•Modern languages: C#, Java

Processor 1

Processor 2

Thread 1

Thread 2

Thread 3

Thread 4

Concurrency is increasingly important

• New classes of concurrent software– Web services– Workflows

• Single-chip multiprocessors are an architectural inflexion point– Software running on these chips will be

even more concurrent

Reliable concurrent software?

•Correctness Problem– does program behaves correctly for all

inputs and all interleavings?

•Bugs due to concurrency are insidious – non-deterministic, timing dependent– difficult to detect, reproduce, eliminate– coverage from testing very poor

Analysis of concurrent programs is difficult (1)

•Finite-data single-procedure program– n lines– m states for global data variables

•1 thread– n * m states

•K threads– (n)

K * m states

Analysis of concurrent programs is difficult (2)

• Finite-data program with procedures– n lines– m states for global data variables

• 1 thread– Infinite number of states– Can still decide assertions in O(n * m3)– SLAM, ESP, BLAST implement this algorithm

• K 2 threads– Undecidable! (Ramalingam 00)

Context-bounded verification of concurrent software

Context Context Context

Context switch Context switch

Analyze all executions with small number of context switches !

• Many subtle concurrency errors are manifested in executions with a small number of contexts

• Context-bounded analysis can be performed efficiently

Why context-bounded analysis?

KISS: A static checker for concurrent software

• An implementation of context-bounded analysis– Technique to use any sequential checker

to perform context-bounded concurrency analysis

• Has found a number of concurrency errors in NT device drivers

Sequentialprogram QKISS

Sequential Checker

Concurrentprogram P

No error found

Error in Q indicateserror in P



Concurrentprogram P


No error found


SDV


Concurrentprogram P


No error found


PREfix


Concurrentprogram P


No error found


ESP

Inside a static checker for sequential programs

int x, y, z;

void foo ( ) { if (x > y) { y = x; } if (y > z) { z = y; }

assert (x ≤ z);}

• Symbolically analyze all paths

• Check the assertion for each path

• Interprocedural analysis – e.g., PREfix, ESP, SLAM,

BLAST

KISS strategy

• Q encodes executions of P with small number of context switches– instrumentation introduces lots of extra

paths to mimic context switches

• Leverage all-path analysis of sequential checkers


Concurrentprogram P

SDV

KISS features• KISS trades off soundness for scalability • Cost of analyzing a concurrent program P

= cost of analyzing a sequential program Q– Size of Q asymptotically same as size of P

• Unsoundness is precisely quantifiable– for 2-thread program, explores all executions

with up to two context switches – for n-thread program, explores up to 2n-2

context switches

• Allows any sequential checker to analyze concurrency

Experimental Evaluation of KISS

Driver Stopping Error in Bluetooth Driver (1 KLOC)

DispatchRoutine() { int t; if (! de->stopping) { AtomicIncr(& de->count); assert ! driverStopped; // do useful work // … t = AtomicDecr(& de->count); if (t == 0) SetEvent(& de->stopEvent); }}

PnpStop() { int t; de->stopping = T; t = AtomicDecr(& de->count); if (t == 0) SetEvent(& de->stopEvent); WaitEvent(& de->stopEvent); driverStopped = T;}

int t;if (! de->stopping) {

int t;de->stopping = T;t = AtomicDecr(& de->count);if (t == 0) SetEvent(& de->stopEvent);WaitEvent(& de->stopEvent);driverStopped = T;

AtomicIncr(& de->count); assert ! driverStopped; // do useful work // … t = AtomicDecr(& de->count); if (t == 0) SetEvent(& de->stopEvent);}

Assertion fails!

DispatchRoutine(IRP *irp) { … irp->CancelRoutine = PacketCancelRoutine; Enqueue(irp); IoMarkIrpPending(irp); …}

IoCancelIrp(IRP *irp) { IoAcquireCancelSpinLock(); if (irp->CancelRoutine) { (irp->CancelRoutine)(irp); } …}

PacketCancelRoutine(IRP *irp) { … Dequeue(irp); IoCompleteRequest(irp); IoReleaseCancelSpinLock(); …}

IRP Cancellation Error in Packet Driver (2.5 KLOC)

…irp->CancelRoutine = PacketCancelRoutine;Enqueue(irp);

IoAcquireCancelSpinLock();if (irp->CancelRoutine) { // inline PacketCancelRoutine(irp) … Dequeue(irp); IoCompleteRequest(irp); IoReleaseCancelSpinLock();

IoMarkIrpPending(irp);

Error: An irp should not be marked pending after it has been completed !

Data-race Conditions in DDK Sample Drivers

• Device extension shared among threads• Data-races on device extension fields• 18 sample DDK drivers

– Range 0.5-9.2 KLOC– Total 70 KLOC

• Each field checked separately with resource limit of 20 minutes and 800MB

• Two threads: each calls nondeterministically chosen dispatch routine

9929.2Fdc

1347.6Mouser

1367.4Kbdclass

1 347.0Mouclass

5246.6Toaster/func

2415.9Serenum

0305.0Toaster/bus

6392.9Fakemodem

1182.81394vdev

0182.71394diag

0162.4Diskperf

181.4Toaster/toastmon

091.1Startio

151.1Imca

0151.1Kbfiltr

0141.0Moufiltr

030.5Tracedrv

# Races# FieldsKLOCDriver

Total:30 races

Keep It Simple and Sequential

• Context-bounded analysis by leveraging existing sequential checkers

• Validates the hypothesis that many concurrency errors require few context switches to show up

However…

• Hard limit on number of explored contexts– e.g., two context switches for concurrent

program with two threads

• Case study: Concurrent transaction management code written in C# (Naik-Rehof 04)– Analyzed by the Zing model checker after

automatically translating to the Zing input language

– Found three bugs each requiring between three and four context switches

Is a tuning knob possible?

Given a concurrent boolean program P and a positive integer c, does P go wrong by failing an assertion via anexecution with at most c contexts?

Given a concurrent boolean program P, does P go wrong by failing an assertion? Undecidable

Decidable

Given a concurrent boolean program P with unbounded fork-join parallelism and a positive integer c, does P go wrong by failing an assertion via an execution with at most c contexts? Decidable

Context Context Context

Context switch Context switch

Problem:• Unbounded computation possible within each context!• Unbounded execution depth and reachable state space• Different from bounded-depth model checking

Global store g, valuation to global variablesLocal store l, valuation to local variables Stack s, sequence of local storesState (g, s)

Sequential pushdown system

Transition relation:

(g, s) (g’, s’)

Reachability problem for sequential pushdown

systemGiven (g, s), is there s’ such that (g, s) * (error,s’)?

Aggregate state

Set of stacks ssAggregate state (g, ss) = { (g,s) | s ss }

Reach(g, ss, g’) = {s’ | (g’, s’) Reach(g, ss)}

Reach(g, ss) = { (g’, s’) | exists s ss such that (g, s) * (g’, s’) }

Theorem (Buchi, Schwoon00)

• If ss is regular, then Reach(g, ss, g’) is regular.

• If ss is given as a finite automaton A, then a finite automaton A’ for Reach(g, ss, g’) can be constructed from A in polynomial time.

Algorithm

Solution:Compute automaton for Reach(g, {s}, error) and report error if it is nonempty.

Problem:Given (g, s), is there s’ such that (g, s) * (error,s’)?

Global store g, valuation to global variablesLocal store l, valuation to local variables Stack s, sequence of local storesState (g, s1, s2)

Concurrent pushdown system

Transition relation:

(g, s1) (g’, s’1) in thread 1

(g, s1, s2) 1 (g, s’1, s2)

(g, s2) (g’, s’2) in thread 2

(g, s1, s2) 2 (g, s1, s’2)

Reachability problem for concurrent pushdown

system

Given (g, s1, s2), are there s’1 and s’2 such that (g, s1, s2) reaches (error, s’1, s’2) via an execution with at most c contexts?

Aggregate transition relation

ss’1 = Reach1(g, ss1, g’)

(g, ss1, ss2) 1 (g’, ss’1, ss2)

(g, ss1, ss2) 2 (g’, ss1, ss’2)

ss’2 = Reach2(g, ss2, g’)

Algorithm: 2 threads, c contexts

1 2

1 2

1 2Depth c

(g, {s1}, {s2})

Compute the set of reachable aggregate states.Report an error if (g, ss1, ss2) is reachable andg = error, ss1 is nonempty, and ss2 is nonempty.

Complexity: 2 threads, c contexts

1 2

1 2

1 2

Depth of tree = context bound cBranching factor bounded by G 2 (G = # of global stores)Number of edges bounded by (G 2) (c+1)

Each edge computable in polynomial time

Depth c

(g, {s1}, {s2})

Unbounded fork-join parallelism

• Fork operation: x = fork• Join operation: join(x)• Copy thread identifier from one

variable to another

Algorithm: unbounded fork-join parallelism, c contexts

• At most c threads may perform a transition

• Reduce to previously solved problem with c threads and c contexts– Nondeterministically pick c forked

threads for execution

Context-bounded analysis of concurrent software

• Many subtle concurrency errors are manifested in executions with few context switches – Experience with KISS on Windows drivers– Experience with Zing on transaction manager

• Algorithms for context-bounded analysis are more efficient than those for unbounded analysis– Reducibility to sequential checking with KISS– Decidability of assertion checking for

concurrent boolean programs

Context-bounded model checking of concurrent software Shaz Qadeer Microsoft Research Joint work...

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