# SATbased verification: underlying methods - PowerPoint PPT Presentation

PPT – SATbased verification: underlying methods PowerPoint presentation | free to download - id: 10db47-YTA3N

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## SATbased verification: underlying methods

Description:

### Invent a lemma, L(s) that we believe to hold in the reachable states. Prove Q(s) = P(s) and L(s) ... relations between signals as lemmas. Reachability analysis ... – PowerPoint PPT presentation

Number of Views:34
Avg rating:3.0/5.0
Slides: 40
Provided by: provertec
Category:
Tags:
Transcript and Presenter's Notes

Title: SATbased verification: underlying methods

1
SAT-based verification underlying methods
• Mary Sheeran
• Chalmers University of Technology and
• Prover Technology AB

2
Synchronous Observer
ok
Program
Obs
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
I
9
(No Transcript)
10
(No Transcript)
11
Satisfying a formula
I(s0) and path(s0..si) and B(si)
12
I
B
13
• Finds a shortest countermodel
• Error trace for debugging

14
But when can we stop?
when
i
15
Not quite, but
when
i
loop-free
16
And symmetrically
when
loop-free
B
17
Algorithm 1
i 0
i
i
if not Sat
or
not Sat
B
then return True
then return error trace
if Sat
i i1
18
Tighten termination (Alg. 2)
i 0
i
i
if not Sat
or
not Sat
all (not I)
B
all (not B)
then return True
then return error trace
if Sat
i i1
19
Avoid iteration from zero (Alg. 3)
i some constant which can be greater than zero
i
not (all P)
then return error trace
if Sat
I
i1
i1
if not Sat
or not Sat
I
all (not I)
B
all (not B)
then return True
i i1
20
Base
I
21
Base
I
22
Step
23
Step
24
Base
B
25
Base
B
26
Step
27
Step
28
Complete method
i some constant which can be greater than zero
i
not (all P)
then return error trace
if Sat
I
i1
i1
if not Sat
or not Sat
I
all (not I)
B
all (not B)
then return True
i i1
29
Strengthen
i some constant which can be greater than zero
i
not (all P)
then return error trace
if Sat
I
i1
i1
if not Sat
or not Sat
I
all (not I)
B
all (not B)
then return True
i i1
30
Another way to strengthen
• Invent a lemma, L(s) that we believe to hold in
the reachable states
• Prove Q(s) P(s) and L(s)
• If both P and L hold in the reachable states,
this can reduce induction depth

31
Choosing lemmas?
• Domain knowledge
• Analysis of the program
• Strongest possibility is the characterization of
the reachable states
• Van Eijks method uses relations between signals
as lemmas

32
Reachability analysis
• Standard approach to safety property verification
using Binary Decision Diagrams (BDDs)
• Generate larger and larger subset of the
reachable states. Stop when no new states added
• Check whether intersects with bad states

33
Reachability analysis
• Standard algorithms can be adapted to use a
SAT-solver.
• Need to be able to deal with quantifiers in a way
that doesnt just blow up
• A fascinating research area!

34
References (bounded model checking)
• A. Biere, A. Cimatti, E.M. Clarke, M. Fujita and
Y. Zhu. Symbolic model checking using SAT
procedures instead of BDDs. In Proc. 36th Design
Automation Conference, 1999.
• P. Bjesse, T. Leonard and A. Mokkedem. Finding
bugs in an Alpha microprocessor using
satisfiability solvers. In Proc. 13th Int. Conf.
On Computer Aided Verification, 2001.

35
References (induction with SAT-solvers)
• M. Sheeran, S. Singh and G. Stålmarck. Checking
safety properties using induction and a
SAT-solver. In Proc. 3rd Int. Conf. On Formal
Methods in Computer Aided Design, LNCS, Springer
Verlag, 2000.
• P. Bjesse and K. Claessen. SAT-based verification
without state space traversal. In Proc. 3rd Int.
Conf. On Formal Methods in Computer Aided Design,
LNCS, Springer Verlag, 2000.

36
References (SAT-based reachability analysis)
• P. A. Abdulla, P. Bjesse and N. Een. Symbolic
reachability analysis based on SAT-solvers. In
Proc. TACAS00.
• P. F. Williams, A. Biere, E. M. Clarke and A.
Gupta. Combining decision diagrams and SAT
procedures for efficient symbolic model checking.
In CAV00.
• A. Gupta, Z. Yang and P. Ashar, SAT-based image
computation with application in reachability

37
SAT
38
BMC
IND
SAT
RA

ARITH
39
The future?
• Increasingly powerful proof engines
• Integration in system development tools
• Combining different engines or methods (for
example BDDs and SAT or interactive and
automatic methods)
• Use of formal methods in test pattern generation