Abstraction Refinement for Emptiness Checking of Alternating Data Automata

Iosif, Radu; Xu, Xiao

doi:10.1007/978-3-319-89963-3_6

Cited by 10 publications

(7 citation statements)

References 26 publications

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“…We check emptiness of first order alternating automata using a version of the IM-PACT lazy annotation semi-algorithm [18]. An analogous procedure is given in [11], for a simpler model of alternating automata, that uses only predicates or arity zero (booleans) and no transition quantifiers. For simplicity, we do not present the details of this algorithm and shall content ourselves of several high-level definitions.…”

Section: The Emptiness Problemmentioning

confidence: 99%

“…The semi-algorithm stops when (and if) a safe complete unfolding has been found. For a detailed presentation of the emptiness procedure, we refer to [11].…”

Section: The Emptiness Problemmentioning

confidence: 99%

“…For reasons of space, all proofs of technical results in this paper are given in [12]. Related Work The first order alternating automata model presented in this paper stems from our previous work on boolean alternating automata extended with variables ranging over infinite data [11]. There we considered states to be propositional variables, as in the classical textbook alternating automata model, and all variables of the automaton to be observable in the input.…”

Section: Introductionmentioning

confidence: 99%

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First Order Alternation

Iosif¹,

Xu²

2018

Preprint

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We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted predicate terms. The model is closed under union, intersection and complement, and its emptiness problem is undecidable, even for the simplest data theory of equality. To cope with this limitation, we develop an abstraction refinement semi-algorithm based on lazy annotation of the symbolic execution paths with interpolants, obtained by applying (i) quantifier elimination with witness term generation and (ii) Lyndon interpolation in the quantifier-free data theory with uninterpreted predicate symbols. This provides a method for checking inclusion of timed and finitememory register automata, and emptiness of quantified predicate automata, previously used in the verification of parameterized concurrent programs, composed of replicated threads, with a shared-memory communication model. − −−−−−− → φ, where φ is any formula in the first-order theory of the data domain, in which each state predicate occurs under an even number of negations. In this model, the arguments of a predicate atom q(y 1 , . . ., y k ) track the values of the internal variables associated with the state. Together with the input values x 1 , . . . , x n , these values are used to compute the successor states and are invisible in the input sequence.

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Section: The Emptiness Problemmentioning

confidence: 99%

“…The semi-algorithm stops when (and if) a safe complete unfolding has been found. For a detailed presentation of the emptiness procedure, we refer to [11].…”

Section: The Emptiness Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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First Order Alternation

Iosif¹,

Xu²

2018

Preprint

Self Cite

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“…The alternating automata model presented in this paper extends the alternating automata with variables ranging over infinite data considered in [14]. There all variables were required to be observable in the input.…”

Section: Introductionmentioning

confidence: 99%

Alternating Automata Modulo First Order Theories

Iosif¹,

Xu²

2019

Computer Aided Verification

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We introduce first-order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first-order formulae, with states and internal variables given by uninterpreted predicate terms. The model is closed under union, intersection and complement, and its emptiness problem is undecidable, even for the simplest data theory of equality. To cope with the undecidability problem, we develop an abstraction refinement semi-algorithm based on lazy annotation of the symbolic execution paths with interpolants, obtained by applying (i) quantifier elimination with witness term generation and (ii) Lyndon interpolation in the quantifierfree theory of the data domain, with uninterpreted predicate symbols. This provides a method for checking inclusion of timed and finite-memory register automata, and emptiness of quantified predicate automata, previously used in the verification of parameterized concurrent programs, composed of replicated threads, with shared memory.

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“…Interpolants are commonly used as a means of abstraction. Since McMillan's first application of interpolants in formal verification [26], interpolation has been applied in algorithms with various extensions in model checking [11,27,34,20,2,31,1,28,16,35,15,14,24]. Model checkers CPAchecker [8], SeaHorn [17], Ultimate Automizer [19] and others leverage interpolants in some form.…”

Section: Related Workmentioning

confidence: 99%

Function Summarization Modulo Theories

Asadi

Blicha

Fedyukovich

et al.

EPiC Series in Computing

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SMT-based program verification can achieve high precision using bit-precise models or combinations of different theories. Often such approaches suffer from problems related to scalability due to the complexity of the underlying decision procedures. Precision is traded for performance by increasing the abstraction level of the model. As the level of abstraction increases, missing important details of the program model becomes problematic. In this paper we address this problem with an incremental verification approach that alternates precision of the program modules on demand. The idea is to model a program using the lightest possible (i.e., less expensive) theories that suffice to verify the desired property. To this end, we employ safe over-approximations for the program based on both function summaries and light-weight SMT theories. If during verification it turns out that the precision is too low, our approach lazily strengthens all affected summaries or the theory through an iterative refinement procedure. The resulting summarization framework provides a natural and light-weight approach for carrying information between different theories. An experimental evaluation with a bounded model checker for C on a wide range of benchmarks demonstrates that our approach scales well, often effortlessly solving instances where the state-of-the-art model checker CBMC runs out of time or memory.

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Abstraction Refinement for Emptiness Checking of Alternating Data Automata

Cited by 10 publications

References 26 publications

First Order Alternation

First Order Alternation

Alternating Automata Modulo First Order Theories

Function Summarization Modulo Theories

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