346 research outputs found
Interpolation Properties and SAT-based Model Checking
Craig interpolation is a widespread method in verification, with important
applications such as Predicate Abstraction, CounterExample Guided Abstraction
Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model
checking techniques based on interpolation require collections of interpolants
to satisfy particular properties, to which we refer as "collectives"; they do
not hold in general for all interpolation systems and have to be established
for each particular system and verification environment. Nevertheless, no
systematic approach exists that correlates the individual interpolation systems
and compares the necessary collectives. This paper proposes a uniform
framework, which encompasses (and generalizes) the most common collectives
exploited in verification. We use it for a systematic study of the collectives
and of the constraints they pose on propositional interpolation systems used in
SAT-based model checking
Reduction of Interpolants for Logic Synthesis
Abstract—Craig Interpolation is a state-of-the-art technique for logic synthesis and verification, based on Boolean Satisfiability (SAT). Leveraging the efficacy of SAT algorithms, Craig Interpolation produces solutions quickly to challenging problems such as synthesizing functional dependencies and performing bounded model-checking. Unfortunately, the quality of the solutions is often poor. When interpolants are used to synthesize functional dependencies, the resulting structure of the functions may be unnecessarily complex. In most applications to date, interpolants have been generated directly from the proofs of unsatisfiability that are provided by SAT solvers. In this work, we propose efficient methods based on incremental SAT solving for modifying resolution proofs in order to obtain more compact interpolants. This, in turn, reduces the cost of the logic that is generated for functional dependencies. I
Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability
The stochastic Boolean satisfiability (SSAT) problem has been introduced by
Papadimitriou in 1985 when adding a probabilistic model of uncertainty to
propositional satisfiability through randomized quantification. SSAT has many
applications, among them probabilistic bounded model checking (PBMC) of
symbolically represented Markov decision processes. This article identifies a
notion of Craig interpolant for the SSAT framework and develops an algorithm
for computing such interpolants based on a resolution calculus for SSAT. As a
potential application area of this novel concept of Craig interpolation, we
address the symbolic analysis of probabilistic systems. We first investigate
the use of interpolation in probabilistic state reachability analysis, turning
the falsification procedure employing PBMC into a verification technique for
probabilistic safety properties. We furthermore propose an interpolation-based
approach to probabilistic region stability, being able to verify that the
probability of stabilizing within some region is sufficiently large
Generating Non-Linear Interpolants by Semidefinite Programming
Interpolation-based techniques have been widely and successfully applied in
the verification of hardware and software, e.g., in bounded-model check- ing,
CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various
work for discovering interpolants for propositional logic, quantifier-free
fragments of first-order theories and their combinations have been proposed.
However, little work focuses on discovering polynomial interpolants in the
literature. In this paper, we provide an approach for constructing non-linear
interpolants based on semidefinite programming, and show how to apply such
results to the verification of programs by examples.Comment: 22 pages, 4 figure
Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories
The problem of computing Craig Interpolants has recently received a lot of
interest. In this paper, we address the problem of efficient generation of
interpolants for some important fragments of first order logic, which are
amenable for effective decision procedures, called Satisfiability Modulo Theory
solvers.
We make the following contributions.
First, we provide interpolation procedures for several basic theories of
interest: the theories of linear arithmetic over the rationals, difference
logic over rationals and integers, and UTVPI over rationals and integers.
Second, we define a novel approach to interpolate combinations of theories,
that applies to the Delayed Theory Combination approach.
Efficiency is ensured by the fact that the proposed interpolation algorithms
extend state of the art algorithms for Satisfiability Modulo Theories. Our
experimental evaluation shows that the MathSAT SMT solver can produce
interpolants with minor overhead in search, and much more efficiently than
other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
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