LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals

Becker, Bernd; Dax, Christian; Eisinger, Jochen; Klaedtke, Felix

doi:10.1007/978-3-540-73368-3_36

Cited by 26 publications

(28 citation statements)

References 12 publications

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“…, x n ), we can check if an initial configuration verifies the existence of an infinite run satisfying a temporal formula. This can be done with a solver for Presburger arithmetic (tools handling first-order logics with linear arithmetic are for instance LIRA [3], TAPAS [23], CVC3 [2] and Z3 [26]). Hence, Theorem 5 is the final step in our investigations since verification problems are then reduced effectively to satisfiability in Presburger arithmetic.…”

Section: ])mentioning

confidence: 99%

The Complexity of Reversal-Bounded Model-Checking

Bersani

Demri

2011

Frontiers of Combining Systems

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Abstract. We study model-checking problems on counter systems when guards are quantifier-free Presburger formulae, the specification languages are LTL-like dialects with arithmetical constraints and the runs are restricted to reversal-bounded ones. We introduce a generalization of reversal-boundedness and we show the NExpTime-completeness of the reversal-bounded model-checking problem as well as for related reversalbounded reachability problems. As a by-product, we show the effective Presburger definability for sets of configurations for which there is a reversal-bounded run verifying a given temporal formula. Our results generalize existing results about reversal-bounded counter automata and provides a uniform and more general framework.

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Section: ])mentioning

confidence: 99%

The Complexity of Reversal-Bounded Model-Checking

Bersani

Demri

2011

Frontiers of Combining Systems

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“…This characterization shows that arithmetic automata can symbolically represent sets of solutions of complex linear constraints combining both integral and real values. Recall that the construction of arithmetic automata from formulae in FO (R, Z, +, ≤, X r ) is effective and tools Lash and Lira [BDEK07] implement efficient algorithms for the restricted logic FO (R, Z, +, ≤). The predicate X r is discarded in these tools in order to obtain arithmetic automata that are deterministic weak Buchi automata [BJW05].…”

Section: Arithmetic Automatamentioning

confidence: 99%

“…In particular arithmetic automata are adapted to the symbolic model checking approach computing inductively reachability sets of systems manipulating counters [BLP06] and/or clocks [BH06]. In practice algorithms for effectively computing an arithmetic automaton encoding the solutions of formulas in FO (R, Z, +, ≤) have been recently successfully implemented in tools Lash and Lira [BDEK07]. Unfortunately, interesting qualitative properties are difficult to extract from arithmetic automata.…”

Section: Introductionmentioning

confidence: 99%

Convex Hull of Arithmetic Automata

Leroux¹

2008

Static Analysis

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Abstract. Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata.

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“…We implemented both constructions in our tool lira [2] and evaluated them. The savings in terms of number of states range from 15% to 20%.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…Automata over infinite objects have emerged as a powerful tool for specification and verification of nonterminating programs [23,32], and for implementation of decision procedures for logical theories [2,4,9,18]. For instance, the automata-theoretic approach to model checking is easy to understand, automatic, and thus attractive to practitioners.…”

Section: Introductionmentioning

confidence: 99%

Mechanizing the Powerset Construction for Restricted Classes of ω-Automata

Dax

Eisinger

Klaedtke

Automated Technology for Verification and Analysis

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Abstract. Automata over infinite words provide a powerful framework to solve various decision problems. However, the mechanized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Büchi automata (wdbas) can be handled algorithmically almost as efficient as deterministic automata over finite words. In this paper, we show how and when the standard powerset construction for automata over finite words can be used to determinize automata over infinite words. An instance is the class of automata that accept wdba-recognizable languages. Furthermore, we present applications of this new determinization construction. Namely, we apply it to improve the automata-based approach for the mixed firstorder linear arithmetic over the reals and the integers, and we utilize it to accelerate finite state model checking. We report on experimental results for these two applications.

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LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals

Cited by 26 publications

References 12 publications

The Complexity of Reversal-Bounded Model-Checking

The Complexity of Reversal-Bounded Model-Checking

Convex Hull of Arithmetic Automata

Mechanizing the Powerset Construction for Restricted Classes of ω-Automata

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