Conference Paper

The Zonotope Abstract Domain Taylor1+.

DOI: 10.1007/978-3-642-02658-4_47 Conference: Computer Aided Verification, 21st International Conference, CAV 2009, Grenoble, France, June 26 - July 2, 2009. Proceedings
Source: DBLP

ABSTRACT Static analysis by abstract interpretation [1] aims at automatically inferring properties on the behaviour of programs. We
focus here on a specific kind of numerical invariants: the set of values taken by numerical variables, with a real numbers
semantics, at each control point of a program.

0 Followers
 · 
110 Views
  • Formal Methods in System Design 10/2013; 45(2):213-245. DOI:10.1007/s10703-013-0203-7 · 0.40 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This dissertation shows that satisfiability procedures are abstract interpreters. This insight provides a unified view of program analysis and satisfiability solving and enables technology transfer between the two fields. The framework underlying these developments provides systematic recipes that show how intuition from satisfiability solvers can be lifted to program analyzers, how approximation techniques from program analyzers can be integrated into satisfiability procedures and how program analyzers and satisfiability solvers can be combined. Based on this work, we have developed new tools for checking program correctness and for solving satisfiability of quantifier-free first-order formulas. These tools outperform existing approaches. We introduce abstract satisfaction, an algebraic framework for applying abstract interpretation to obtain sound, but potentially incomplete satisfiability procedures. The framework allows the operation of satisfiability procedures to be understood in terms of fixed point computations involving deduction and abduction transformers on lattices. It also enables satisfiability solving and program correctness to be viewed as the same algebraic problem. Using abstract satisfaction, we show that a number of satisfiability procedures can be understood as abstract interpreters, including Boolean constraint propagation, the dpll and cdcl algorithms, Stalmarck’s procedure, the dpll(t) framework and solvers based on congruence closure and the Bellman-Ford algorithm. Our work leads to a novel understanding of satisfiability architectures as refinement procedures for abstract analyses and allows us to relate these procedures to independent developments in program analysis. We use this perspective to develop Abstract Conflict-Driven Clause Learning (acdcl), a rigorous, lattice-based generalization of cdcl, the central algorithm of modern satisfiability research. The acdcl framework provides a solution to the open problem of lifting cdcl to new prob- lem domains and can be instantiated over many lattices that occur in practice. We provide soundness and completeness arguments for acdcl that apply to all such instantiations. We evaluate the effectiveness of acdcl by investigating two practical instantiations: fp-acdcl, a satisfiability procedure for the first-order theory of floating point arithmetic, and cdfpl, an interval-based program analyzer that uses cdcl-style learning to improve the precision of a program analysis. fp-acdcl is faster than competing approaches in 80% of our benchmarks and it is faster by more than an order of magnitude in 60% of the benchmarks. Out of 33 safe programs, cdfpl proves 16 more programs correct than a mature interval analysis tool and can conclusively determine the presence of errors in 24 unsafe benchmarks. Compared to bounded model checking, cdfpl is on average at least 260 times faster on our benchmark set.
    01/2013, Degree: DPhil, Supervisor: Daniel Kroening
  • [Show abstract] [Hide abstract]
    ABSTRACT: Being able to analyze programs function by function, or module by module is a key ingredient to scalable static analyses. The main difficulty for modular static analysis is to be able to do so while not losing too much precision. In this paper, we present a new summary-based approach that builds on previous work of the authors, a zonotopic functional abstraction, that is economical both in space and time complexity. This approach has been implemented, and experiments on numerical programs, reported here, show that this approach is very efficient, and that we still obtain precise analyses in realistic cases.
    Proceedings of the 19th international conference on Static Analysis; 09/2012

Full-text (2 Sources)

Download
62 Downloads
Available from
May 31, 2014