Construction of abstract state graphs with PVS

Graf, Susanne; Saïdi, Hassen

doi:10.1007/3-540-63166-6_10

Cited by 1,001 publications

(833 citation statements)

References 18 publications

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“…Several recent verification approaches [2,15], based on predicate abstraction [14], avoid imprecision (e.g., due to aliasing or infeasible paths) by iteratively refining the abstractions as necessary, but are fundamentally exponential algorithms. These techniques use symbolic and theorem-proving techniques (during verification) to identify a set P of "relevant" predicates, and then use the powerset lattice 2 P →{true,f alse} for abstraction, and then model check the resulting finite state system (and usually iterate with increasingly larger sets of predicates until a satisfactory result is obtained).…”

Section: Related Workmentioning

confidence: 99%

Typestate Verification: Abstraction Techniques and Complexity Results

Field¹,

Goyal²,

Ramalingam³

et al. 2003

Static Analysis

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Abstract. We consider the problem of typestate verification for shallow programs; i.e., programs where pointers from program variables to heap-allocated objects are allowed, but where heap-allocated objects may not themselves contain pointers. We prove a number of results relating the complexity of verification to the nature of the finite state machine used to specify the property. Some properties are shown to be intractable, but others which appear to be quite similar admit polynomial-time verification algorithms. While there has been much progress on many aspects of automated program verification, we are not aware of any previous work relating the difficulty of typestate verification to properties of the finite state automaton. Our results serve to provide insight into the inherent complexity of important classes of verification problems. In addition, the program abstractions used for the polynomial-time verification algorithms may be of independent interest.

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Section: Related Workmentioning

confidence: 99%

Typestate Verification: Abstraction Techniques and Complexity Results

Field¹,

Goyal²,

Ramalingam³

et al. 2003

Static Analysis

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“…Predicate abstraction [GS97] (an instance of the more general theory of abstract interpretation [CC77]) is a technique for constructing finite-state abstractions from large or infinite-state systems. The resulting finite-state abstraction can be analyzed efficiently using Boolean techniques.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, our experiments reveal that (i) for small cube sizes, the computation times are extremely small, and that (ii) computing the full G P (ϕ) in successive steps slightly increasing the cube size can be done almost as efficiently as computing it directly, if each step is done incrementally from the previous one. Although several approaches have been developed in recent years to compute coarser approximations [GS97,BMMR01,DD01], the process of refining the approximations is not incremental, and can sometimes be the main bottleneck in the verification [BCDR04].…”

Section: Introductionmentioning

confidence: 99%

SMT Techniques for Fast Predicate Abstraction

Lahiri

Nieuwenhuis

Oliveras

2006

Computer Aided Verification

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Abstract. Predicate abstraction is a technique for automatically extracting finite-state abstractions for systems with potentially infinite state space. The fundamental operation in predicate abstraction is to compute the best approximation of a Boolean formula ϕ over a set of predicates P . In this work, we demonstrate the use for this operation of a decision procedure based on the DPLL(T) framework for SAT Modulo Theories (SMT). The new algorithm is based on a careful generation of the set of all satisfying assignments over a set of predicates. It consistently outperforms previous methods by a factor of at least 20, on a diverse set of hardware and software verification benchmarks. We report detailed analysis of the results and the impact of a number of variations of the techniques. We also propose and evaluate a scheme for incremental refinement of approximations for predicate abstraction in the above framework.

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“…In Predicate Abstraction [GS97], predicates of the original program are represented with boolean variables in the abstract program. For a predicate p, we letp denote its corresponding boolean variable.…”

Section: Predicate Abstractionmentioning

confidence: 99%

“…This guarantees that if the transformed property holds on the abstract program, then the original property holds on the concrete program. Common examples of abstraction are those resulting from symmetry reduction [ES93,CFJ93], data independence [Wol86], and predicate abstraction [GS97].…”

Section: Introductionmentioning

confidence: 99%

Lifting Temporal Proofs through Abstractions

Namjoshi¹

2002

Lecture Notes in Computer Science

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Abstract. Model checking is often performed by checking a transformed property on a suitable finite-state abstraction of the source program. Examples include abstractions resulting from symmetry reduction, data independence, and predicate abstraction. The two programs are linked by a structural relationship, such as simulation or bisimulation, guaranteeing that if the transformed property holds on the abstract program, the property holds on the original program. Recently, several algorithms have been developed to automatically generate a deductive proof of correctness from a model checker. A natural question, therefore, is how to 'lift' a deductive proof that is generated for an abstract program back into the original program domain. In this paper, we show how this can be done for general temporal properties, relative to several types of abstraction relationships between the two programs. We develop simplifications of the lifting scheme for common types of abstractions, such as predicate abstraction. We also show how one may generate easily checkable lifted proofs, which find use in applications such as proof-carrying code, and in the use of model checkers as decision procedures in theorem proving.

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Construction of abstract state graphs with PVS

Cited by 1,001 publications

References 18 publications

Typestate Verification: Abstraction Techniques and Complexity Results

Typestate Verification: Abstraction Techniques and Complexity Results

SMT Techniques for Fast Predicate Abstraction

Lifting Temporal Proofs through Abstractions

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