sequentializationtargetedto boundedmodel-checkerssequentialization • alters the original program...
TRANSCRIPT
Sequentialization targeted to
Bounded Model-Checkers
Salvatore La Torre
Dipartimento di Informatica Università degli Studi di Salerno
• Code-to-code translation from a multithreaded program to an “equivalent” sequential one
Conc.program
Sequentialization
T1 T2 Tm
shared vars
…loc loc loc
• Re-use of existing tools (delegate the analysis to the backend tool)
• Fast prototyping (designers can concentrate only concurrency features)
• Can work with different backends
Seq.Verifier
Seq. progam
Sequentialization
• alters the original program structure by injecting control code
(which is an overhead for the backend)
• requires careful attention to the details of the translation for well-performing tools
• replaces concurrency with nondeterminism
Backend: Bounded Model Checkers
• Reduce program verification to SAT/SMT solvers
• Very effective technique to discover bugs in seq. programs
• Performance relies on the performance of underlyingsolvers
• Impressive improvement of
SAT solvers in last years
1
10
100
1000
10000
100000
1960 1970 1980 1990 2000 2010
Year
Var
s
Implementations with BMC backend
• LR seq. [Lal-Reps, CAV’08]: eager, bounded round-robin
• LMP seq. [La Torre-Madhusudan-Parlato]: lazy, any scheduling
• With BMC, LR works better than LMP[Ghafari-Hu-Rakamaric, SPIN’10]
• Implementations of LR:– CSeq: Pthreads C programs [Fischer-Inverso-Parlato, ASE’13]
– STORM: also dynamic memory allocation[Lahiri-Qadeer-Rakamaric, CAV’09]
– Corral [Lal-Qadeer-Lahiri, CAV’12]
– Delay bounded-scheduling [Emmi-Qadeer-Rakamaric, POPL’11]– Real-time systems [Chaki, Gurfinkel, Strichman – FMCAD’11]
Lal/Reps Sequentialization
• considers only round-robin scheduleswith k rounds
– thread → function, run to completion
• global memory copy for each round
– scalar → array
• context switch → round counter++
• first thread starts with
nondeterministic memory contents
– other threads continue with content left by predecessor
T0 T1
S2,1
S0,1
S1,1
Sk,1
Tn
...
......
...
...
...
S2,0
S0,0
S1,0
Sk,0
S2,n
S0,n
S1,n
Sk,n
Lal/Reps Sequentialization
• considers only round-robin scheduleswith k rounds
– thread → function, run to completion
• global memory copy for each round
– scalar → array
• context switch → round counter++
• first thread starts with
nondeterministic memory contents
– other threads continue with content left by predecessor
• checker prunes away inconsistent simulations
– assume(Si+1,0 == S i,n);
– requires second set of memory copies
– errors can only be checked at end of simulation
• requires explicit error checks
T0 T1
S2,1
S0,1
S1,1
Sk,1
Tn
...
......
...
...
...
S2,0
S0,0
S1,0
Sk,0
S2,n
S0,n
S1,n
Sk,n
CSeq Tool Architecture [Fischer-Inverso-Parlato, ASE’13]
• pycparser, AST traversal with unparsing– insert new type declarations, modify memory accesses
– insert context switch simulation code at each sequence point
– insert explicit error checks
– insert checker and code for pthread functions
sequential
non-deterministic
C program
P'
concurrent
C program
P
SAFE
UNSAFE
CSeq
sequential tool
k, N
Can we improve this?
• Eager sequentializations
– cannot rely on error checks built into the backend
– also requires specific techniques to handle programs with heap-allocated memory
• LR (but also LMP) uses additional copies of shared variables
– BMC will make more copies with loop/recursion unwinding
– can seriously affect the formula size
Two new sequentializations[Inverso-Tomasco-Fischer-LaTorre-Parlato]
• Lazy-CSeq [CAV’14-TACAS/SVCOMP’14]– lazy
– light-weight: few additional variables and code
• MU-CSeq [TACAS/SVCOMP’14]– Bound on memory unwindings
– Extension message-passing programs
Outline
• Bounded Model-checking for programs
• Lazy sequentialization: Lazy-CSeq
• Memory unwindings: MU-CSeq
• Experiments
• Conclusions
How does it work
Transform a programs into a set of equations
• Simplify control flow
• Unwind all of the loops
• Convert into Static Single Assignment (SSA)
• Convert into equations
• Bit-blast
• Solve with a SAT Solver
• Convert SAT assignment into a counterexample
Control Flow Simplifications
• All side effect are removed
– e.g., j=i++ becomes j=i; i=i+1
• Control Flow is made explicit
– continue, break replaced by goto
• All loops are simplified into one form
– for, do, while replaced by while
Loop Unwinding
while() loops are unwound iteratively
Break / continue replaced by goto
void f(...) {void f(...) {...
while(cond) {Body;
}
Remainder;}
Loop Unwinding
while() loops are unwound iteratively
Break / continue replaced by goto
void f(...) {void f(...) {...
if(cond) {Body;
while(cond) {Body;
}}
Remainder;}
Loop Unwinding
while() loops are unwound iteratively
Break / continue replaced by goto
void f(...) {void f(...) {...
if(cond) {Body;
if(cond) {Body;
while(cond) {Body;
}}
}
Remainder;}
Unwinding assertion
while() loops are unwound iteratively
Break / continue replaced by goto
Assume statements inserted after last iteration: block execution if program runs longer than bound permits
void f(...) {void f(...) {...
if(cond) {Body;
if(cond) {Body;
if(cond) {Body;
while(cond) {Body;
}}
}}
Remainder;}
Unwinding assertion
while() loops are unwound iteratively
Break / continue replaced by goto
Assume statements inserted after last iteration: block execution if program runs longer than bound permits
void f(...) {void f(...) {...
if(cond) {Body;
if(cond) {Body;
if(cond) {Body;
assume(!cond);
}}
}}
Remainder;} Unwinding
assume
Transforming Loop-Free Programs Into
Equations (1)
• Easy to transform when every variable is only assigned once!
x = a;y = x + 1;z = y – 1;
Program Constraints
x = a &&y = x + 1 &&z = y – 1 &&
Transforming Loop-Free Programs Into
Equations (2)
• When a variable is assigned multiple times,
• use a new variable for the RHS of each assignment
Program SSA Program
What about conditionals?
Program SSA Program
if (v)x = y;
elsex = z;
w = x;
if (v 0)x0 = y 0;
elsex1 = z 0;
w1 = x?? ; What should ‘x’ be?
What about conditionals?
For each join point, add new variables with selectors
Program SSA Program
if (v)x = y;
elsex = z;
w = x;
if (v 0)x0 = y 0;
elsex1 = z 0;
x2 = v 0 ? x 0 : x 1;w1 = x 2
Example
CBMC: Bounded Model Checker for CA tool by D. Kroening/Oxford and Ed Clarke/CMU
Parser Static Analysis
CNF-genSAT solver
CEX-gen CBMC
C Program
SAFE
UNSAFE + CEX
SAT
UNSAT CNF
goto-program
equations
BMC: from sequential to concurrent
• BMC for sequential programs has been used to discover subtle errors in applications
• robust BMC tools exist for C programs (e.g. CBMC, LLBMC, ESBMC)
• attempts to apply BMC to multi-threaded programs face problems
�number of interleavings grows exponentially with #threads and #statements
Recent solutions for multi-threaded programs
• partial orders
• sequentializations
Outline
�Bounded Model-checking for programs
• Lazy sequentialization: Lazy-CSeq
• Memory unwindings: MU-CSeq
• Experiments
• Conclusions
Lazy-CSeq schema
• P' simulates all computations (up to K rounds) of P
• lazy: avoid exploring unfeasible runs
T₁ ∥ T₂ ∥ … ∥ Tn ↝ (T'1 ; T'2 ; … ; T'n)K
Lazy-CSeq Sequentialization
Translation P ↝ P':– unwinding, inlining (bounded program)
– thread T ↝ function T'– main driver:
For each round in [1..K]
for each thread in [1..N]
T' thread ();
Main driver
K: roundsct: thread count
active[j]: true iff thread j is active
cs: guessed context-switch position for coming simulation
pc[j]: position when context-switched out of thread j
size[j]: last position for context-switches
void main(void) {
for(r=1; r<=K; r++) {
ct=1; // thread 1
if(active[ct]) { //only active theads
cs=pc[ct]+nondet uint(); // guess cs
assume(cs<=size[ct]); // legal?
fseq_1(arg[ct]); // simulate thread
pc[ct]=cs; // store cs
}
: : : : : : : : :
ct=n; // thread n
if(active[ct]) {
: : : : : : : : : }
}}
Thread T ↝ function T'
Translation P ↝ P':– unwinding, inlining– thread T ↝ function T'– main driver:
• for round in [1..K]
• for thread in [1..N]• T' thread ();
Thread T ↝ function T'• var x; ↝ static var x;
• stmt; ↝ guard; stmt;
T'
guard; stmt;
...
Thread T ↝ function T'
T'
Thread simulation: round 1• guess context-switch point cs1 (in main)
• execute stmts before cs1
• jump in multiple hops to the end
and return
Thread T ↝ function T'• var x; ↝ static var x;
• stmt; ↝ guard; stmt; context-switch cs1
...
simulation round 1exec
skip
...
Thread T ↝ function T'
Thread simulation: round i• guess context-switch point csi (in main)
• jump in multiple hops to pci-1
• execute stmts from pci-1 to csi
• jump in multiple hops to the end
and return
Thread T ↝ function T'• var x; ↝ static var x;
• stmt; ↝ guard; stmt;
simulation round i >1
T'
context-switch csi
...
exec
skip
skip
resume from pci-1
Instrumenting jumping
in and out of
thread executions(stmt; ↝ guard; stmt;)
Multiple hops:
#define J(A,B) if ( pc[ct] > A || A >= cs )
goto B;
• Ex. At position 5,
J(5,6) jumps to 6 (next position)
when not in [ pc[ct], cs [
Branching stmts
Use macro:
#define G(L) assume(cs >= L);
• Rules out spurious thread executionswhen context-switch position isinside the not picked branch
Thread T ↝ function T'• var x; ↝ static var x;
• stmt; ↝ guard; stmt;
if cond
{
body1 ↝}else{
body2
}
if cond
{
body1
}else{ G(A)
body2
} G(B)
Example
2:J(2,3) if(c>0)
3:J(3,4) c++;
else {
4:J(4,5) c=0;
if(!(tmp>0)) goto l1;
5:J(5,6) c++; tmp--;
if(!(tmp>0)) goto l1;
6:J(6,7) c++; tmp--;
assume(!(tmp>0));
l1: G(7);
} G(7)
7:J(7,8) pthread mutex unlock(&m);
Assume pc=2 and cs=3(only 2: must be executed)
Additionally suppose c<=0 holds
Execution jumps to the else stmt and exits
In main pc is then set to 3 (cs)
When resumed, the tread will start from 3:
executing c++!!!!!
Adding guard G(4) right after the else stmt rules out this unfeasible computation
G(4)
Note this is not ruling outany good exectutions
The sketched one is captured by guessing cs=4 instead of cs=3
Outline
�Bounded Model-checking for programs
�Lazy sequentialization: Lazy-CSeq
• Memory unwindings: MU-CSeq
• Experiments
• Conclusions
Main idea
• Guess a memory unwinding of the shared memory
– sequence of writes into the shared memory of an execution
• Execute each thread s.t. its local computation isconsistent with the memory unwinding
– any scheduling that fits it is considered
• Crucial notion: all the shared memory operationsare done through a memory object
Memory object
• Stores a sequence of writes
– Each write is a triple (thread, variable, value)
• Is used through an interface
• Several implementations are possible
Memory object interface
int mem_init(uint V, uint W, uint T);
• instantiate a memory object
• V = number of variables
• W = number of writes
• T = max number of threads
Memory object interface
int read(uint th_id, uint var);
void write(uint th_id, uint var, int value);
int mem_thread_create(uint parent_id);
• returns id for created thread
void terminate(uint th_id);
• checks that all writes of th_id have beenexecuted
……………
MU-Cseq sequentialization
– A funciton for each thread
thread T ↝ function T'
– main driver:
void proc main(void)
call memory_init(V, W, T); // instantiate memory
ct := mem_thread_create(0); // register main thread
call mainW;T(x1,..., xk);
call terminate(ct); // all writes are executed
assert(_error != 1) // error check
Basic Idea:
• uses auxiliary variables– pos (current index into memory object)– ct (id of currently simulated thread)
• every thread is translated into a function– simulation starts from main thread
• each thread creation interrupts simulation of current thread– new thread is called with current value of pos
• terminated threads must have completed their memory writes– terminate(ct) must hold
• old thread resumed with old memory position (in the activation record)
Simulation
simulate all executions compatible with guessed memory unwinding
Basic Idea:
• every read / write is translated into a function– simulates valid access into unwound memory
(similarly for pthread functions)
Simulation
simulate all executions compatible with guessed memory unwinding
Implementation I: Explicit Read
x y ... z“memory”
Guess and store sequence of individual write operations:
• add N copies of shared variables (“memory”)_memory[i,j] is value of j-th variable after i-th write
• add array to record writes (“writes”)i-th write is by _thr[i], which has written to _var[i]
• add array to record validity of writes (“barrier”)next write (after i) by thread t is at _next[i,t]
4 0 04 2 04 3 04 3 42... ... ... ...
0 3 42
1234...
W
pos
...
...
...
...
...0 0 0
1 x1 y2 y1 z... ...
2 x
varthr“writes”
0 00 ...
...
next[1]
“barrier”
N+1244
...
1
...
3
next[T]
N+1N+1N+1N+1
N+1
N+1
N+1 N+1
N
33N
...
...
...
...
...
...
N+1
...
Simulating reads and writes
4 0 04 2 04 3 04 3 42... ... ... ...
0 3 42
x y ... z
1 x1 y2 y1 z... ...
2 x
var
1234...
W
thr
int read(uint th, uint var) {
uint th_pos;
if is_terminated(th) then return;
th_pos = Jump(th_id);
return (mem[th_pos][var]);
}
“memory” “writes”pos
...
...
...
...
...0 0 0 0 00 ...
...
next[1]
“barrier”
N+1244
...
1
...
3
next[T]...
N+1N+1N+1N+1
N+1
N+1
N+1 N+1
N
33N
...
...
...
...
...
...
N+1
Simulating reads and writes
int write(uint th, uint var, int val) {
uint jump;
if is_terminated(th) then return;
jump=next[pos][th_id];
assume ( (jump<=last_write_pos)
&& (var[jump]==var)
&& (value[jump]==val) );
pos=jump;
}
Other implementations
• Implementation II: (Implicit Read)
– mem WxV-array is replaced with W-array
var_next_write[ i ] is smallest j>i s.t. var[ i ]=var[ j ]
– saves memory but causes more complexRead implementation (larger formula)
• Implementation III:– mixed I and II
Outline
�Bounded Model-checking for programs
�Lazy sequentialization: Lazy-CSeq
�Memory unwindings: MU-CSeq
• Experiments
• Conclusions
Lazy-CSeq won the Gold Medal and MU-CSeq I won the Silver Medal in the Concurrency category
– 76 concurrent C programs• UNSAFE instances: 20 programs containing a bug
• SAFE instances: all the others
– 4,500 l.o.c.
1) CSeq-Lazy: 1,000s, 136pts
2) CSeq-MU I: 1,200s, 136pts
3) CBMC: 29,000s, 128pts
Results:– small verification times
– small memory footprint
– no missed bugs!
Evaluation: SV-COMP2014
Lazy-Cseq vs Native Concurrency Handling (UNSAFE instances)
_1: timeout (750s) _2: internal error _3: manual translation not done
_4: test case rejected _5: unknown failure
Evaluation: bug-hunting
Evaluation: state space coverageLazy-CSeq + CBMC vs CBMC (SAFE instances)
How far is it possible to push the unwind bound with
the two different methods and still finish the analysis within
the given time and space requirements (10GB, 750s)?
• bounding the rounds
allows deeper
exploration of loops
• alternative coverage
of the state space
Evaluation: formula size
Lazy-CSeq + CBMC vs CBMC (v4.7)
(on SV-COMP14 SAFE instances)
MU-CSeq
Outline
�Bounded Model-checking for programs
�Lazy sequentialization: Lazy-CSeq
�Memory unwindings: MU-CSeq
�Experiments
• Conclusions
Conclusions• LR and LMP sequentializations
– complete analysis of concurrent programs up to a given number of context-switches (context-bounded analysis [Qadeer-Rehof, CAV’05]
– unbounded analysis within each context
• Lazy-CSeq and MU-CSeq use additional boundingcriteria– backend tool will bound the computations anyway– this can be exploited to induce simplifications of
the generated formula
• Effective for bug-hunting– many concurrency errors show up within few
context-switches
Lazy-CSeq
• Lightweight sequentialization
– designed to take advantage of modern sequ. BMC tools
– small BMC formulae for small number of rounds
– reduced memory footprint and verification times
• Laziness:
– avoid handling spurious errors typical of eager exploration
– inherit from the backend tool all checks for sequential C:
�array-bounds-check, division-by-zero, pointer- checks, overflow-checks, reachability of error labels and assertion failures, etc.
– no need to handle dynamic memory allocation
MU-CSeq
• Ongoing research
• Preliminary experiments show it is competitive with state-of-the-art model-checkers
• II improves on I on some benchmarks
• III – performs better than both I and II in general and – when it is outperfomed it stays close to the best of
the two
• NEXT: memory unwinding can be used to sequentializemessage-passing programs
– send/receive instead of read/write
Ermenegildo TomascoOmar Inverso Gennaro Parlato
UK
Lazy-CSeq and MU-CSeq joint work with
Bernd Fischer
South Africa