349 research outputs found
Spatial Interpolants
We propose Splinter, a new technique for proving properties of
heap-manipulating programs that marries (1) a new separation logic-based
analysis for heap reasoning with (2) an interpolation-based technique for
refining heap-shape invariants with data invariants. Splinter is property
directed, precise, and produces counterexample traces when a property does not
hold. Using the novel notion of spatial interpolants modulo theories, Splinter
can infer complex invariants over general recursive predicates, e.g., of the
form all elements in a linked list are even or a binary tree is sorted.
Furthermore, we treat interpolation as a black box, which gives us the freedom
to encode data manipulation in any suitable theory for a given program (e.g.,
bit vectors, arrays, or linear arithmetic), so that our technique immediately
benefits from any future advances in SMT solving and interpolation.Comment: Short version published in ESOP 201
Automated incremental software verification
Software continuously evolves to meet rapidly changing human needs. Each evolved transformation of a program is expected to preserve important correctness and security properties. Aiming to assure program correctness after a change, formal verification techniques, such as Software Model Checking, have recently benefited from fully automated solutions based on symbolic reasoning and abstraction. However, the majority of the state-of-the-art model checkers are designed that each new software version has to be verified from scratch. In this dissertation, we investigate the new Formal Incremental Verification (FIV) techniques that aim at making software analysis more efficient by reusing invested efforts between verification runs. In order to show that FIV can be built on the top of different verification techniques, we focus on three complementary approaches to automated formal verification. First, we contribute the FIV technique for SAT-based Bounded Model Checking developed to verify programs with (possibly recursive) functions with respect to the set of pre-defined assertions. We present the function-summarization framework based on Craig interpolation that allows extracting and reusing over- approximations of the function behaviors. We introduce the algorithm to revalidate the summaries of one program locally in order to prevent re-verification of another program from scratch. Second, we contribute the technique for simulation relation synthesis for loop-free programs that do not necessarily contain assertions. We introduce an SMT-based abstraction- refinement algorithm that proceeds by guessing a relation and checking whether it is a simulation relation. We present a novel algorithm for discovering simulations symbolically, by means of solving ∀∃-formulas and extracting witnessing Skolem relations. Third, we contribute the FIV technique for SMT-based Unbounded Model Checking developed to verify programs with (possibly nested) loops. We present an algorithm that automatically derives simulations between programs with different loop structures. The automatically synthesized simulation relation is then used to migrate the safe inductive invariants across the evolution boundaries. Finally, we contribute the implementation and evaluation of all our algorithmic contributions, and confirm that the state-of-the-art model checking tools can successfully be extended by the FIV capabilities
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
- …