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317
Abstract interpretation frameworks
- Journal of Logic and Computation
, 1992
"... We introduce abstract interpretation frameworks which are variations on the archetypal framework using Galois connections between concrete and abstract semantics, widenings and narrowings and are obtained by relaxation of the original hypotheses. We consider various ways of establishing the correctn ..."
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Cited by 290 (25 self)
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We introduce abstract interpretation frameworks which are variations on the archetypal framework using Galois connections between concrete and abstract semantics, widenings and narrowings and are obtained by relaxation of the original hypotheses. We consider various ways of establishing the correctness of an abstract interpretation depending on how the relation between the concrete and abstract semantics is defined. We insist upon those correspondences allowing for the inducing of the approximate abstract semantics from the concrete one. Furthermore we study various notions interpretation.
A Static Analyzer for Large Safety-Critical Software
, 2003
"... We show that abstract interpretation-based static program analysis can be made e#cient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to p ..."
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Cited by 271 (54 self)
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We show that abstract interpretation-based static program analysis can be made e#cient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing).
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
, 1992
"... The use of infinite abstract domains with widening and narrowing for accelerating the convergence of abstract interpretations is shown to be more powerful than the Galois connection approach restricted to finite lattices (or lattices satisfying the chain condition). ..."
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Cited by 196 (27 self)
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The use of infinite abstract domains with widening and narrowing for accelerating the convergence of abstract interpretations is shown to be more powerful than the Galois connection approach restricted to finite lattices (or lattices satisfying the chain condition).
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 140 (31 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previously-used methods. The d=dt system can, so far, treat non-trivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems. 1 Introduction The problem of calculating reachable states for continuous and hybrid systems has emerged as one of the major problems in hybrid systems research [G96,GM98,DM98,KV97,V98,GM99,CK99,PSK99,HHMW99]. It constitutes a prerequisite for exporting algorithmic verification methodology outside discrete systems or hybrid systems with piecewise-trivial dynamics. For computer scientists it poses new challenges in treating continuous functions and their approximations and in applying computational geometry...
Verification of Real-Time Systems using Linear Relation Analysis
- FORMAL METHODS IN SYSTEM DESIGN
, 1997
"... Linear Relation Analysis [CH78] is an abstract interpretation devoted to the automatic discovery of invariant linear inequalities among numerical variables of a program. In this paper, we apply such an analysis to the verification of quantitative time properties of two kinds of systems: synchronous ..."
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Cited by 134 (7 self)
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Linear Relation Analysis [CH78] is an abstract interpretation devoted to the automatic discovery of invariant linear inequalities among numerical variables of a program. In this paper, we apply such an analysis to the verification of quantitative time properties of two kinds of systems: synchronous programs and linear hybrid systems.
Synchronous Observers and the Verification of Reactive Systems
- Third Int. Conf. on Algebraic Methodology and Software Technology, AMAST'93, Twente
, 1993
"... This paper is a survey of our specification and verification techniques, in a very general, language independent, framework. Section 1 introduces a simple model of synchronous input/output machines, which will be used throughout the paper. In section 2, we show how such a machine can be designed to ..."
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Cited by 127 (12 self)
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This paper is a survey of our specification and verification techniques, in a very general, language independent, framework. Section 1 introduces a simple model of synchronous input/output machines, which will be used throughout the paper. In section 2, we show how such a machine can be designed to check the satisfaction of a safety property, and we discuss the use of such an observer in program verification. In section 3, we use an observer to restrict the behavior of a machine. This is the basic way for representing assumptions about the environment. Applications to modular and inductive verification are considered. In modular verification, one has to find, by intuition, a property of a subprogram that is strong enough to allow the verification of the whole program without fully considering the subprogram. In section 4, we consider the automatic synthesis of such a property, and in section 5, we investigate the possibility of deducing the subprogram from such a synthesized specification.
Making Abstract Interpretations Complete
, 1997
"... Completeness in abstract interpretation is an ideal situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. Thus, complete abstract interpretations can be rightfully considered as optimal. In this article, we develop a g ..."
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Cited by 106 (36 self)
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Completeness in abstract interpretation is an ideal situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. Thus, complete abstract interpretations can be rightfully considered as optimal. In this article, we develop a general theory of completeness in abstract interpretation, also dealing with the most frequent case of least fixpoint semantics. We show that both completeness and least fixpoint completeness are properties that only depend on the underlying abstract domain. In this context, we demonstrate that there always exist both the greatest complete and least fixpoint complete restrictions of any abstract d...
Proving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming
- IN VMCAI’2005: VERIFICATION, MODEL CHECKING, AND ABSTRACT INTERPRETATION, VOLUME 3385 OF LNCS
, 2005
"... In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametr ..."
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Cited by 90 (1 self)
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In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstraction into numerical constraints by Lagrangian relaxation. The remaining universal quantification is handled by semidefinite programming relaxation. Finally the parameters are computed using semidefinite programming solvers. This new approach exploits the recent progress in the numerical resolution of linear or bilinear matrix inequalities by semidefinite programming using efficient polynomial primal/dual interior point methods generalizing those well-known in linear programming to convex optimization. The framework is applied to invariance and termination proof of sequential, nondeterministic, concurrent, and fair parallel imperative polynomial programs and can easily be extended to other safety and liveness properties.