Superposition as a Decision Procedure for Timed Automata

Fietzke, Arnaud; Weidenbach, Christoph

doi:10.1007/s11786-012-0134-5

Cited by 18 publications

(34 citation statements)

References 39 publications

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“…Nevertheless, the SUP(LA) calculus is a decision procedure for the FOL(LA) ground case [21] and for the FOL(LA) fragment resulting from the translation of timed automata [15]. In this paper we extend the latter result to the fragment corresponding to the translation of timed automata extended with unbounded integer variables.…”

Section: Introductionmentioning

confidence: 90%

“…The encoding of reachability for extended timed automata is analogous to that for classical timed automata [15], except that clauses encoding discrete transitions now also include integer guards and assignments. We use a reachability predicate Reach, and constant symbols l ∈ L for every location 1 .…”

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

“…In [15], we show how to ensure that the positive literals of such clauses are always strictly maximal in the clause. This guarantees that starting from the encoding of an extended timed automaton and one (or more) reachability conjecture, only negative unit clauses can be derived (that's why we don't need factoring).…”

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

“…Since there are only finitely many locations, there must be infinitely many clauses in the derivation referring to the same location, say l, (those are clauses of the form Λ Reach(x, z, l) →) and hence l must lie on a cycle. If no path from l back to itself involves any integer operations, then l can only repeat finitely often (see [15] for details). Hence l must lie on an integer cycle, which by assumption is unique and acceleratable, and at least one of its locations is a reset location, say l r .…”

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

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Automatic Generation of Invariants for Circular Derivations in SUP(LA)

Fietzke

Kruglov

Weidenbach

2012

Logic for Programming, Artificial Intelligence, and Reasoning

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The hierarchic combination of linear arithmetic and first-order logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant problems.

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Section: Introductionmentioning

confidence: 90%

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

Section: Finite Saturation Of Extended Timed Automatamentioning

confidence: 99%

See 2 more Smart Citations

Automatic Generation of Invariants for Circular Derivations in SUP(LA)

Fietzke

Kruglov

Weidenbach

2012

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

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show abstract

“…Yet, to our knowledge, specific extensions or applications for timed systems are rather limited. As an exception, the papers [5,17] propose a monolithic, non-compositional method for finding invariants in the case of systems represented as a single timed automaton.…”

Section: Fig 2 a Timed Systemmentioning

confidence: 99%

Compositional Invariant Generation for Timed Systems

Aştefănoaei

Rayana

Bensalem

et al. 2014

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. In this paper we address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints induced by the synchronisations between components. The method has been implemented as an extension of the D-Finder tool and successfully experimented on several benchmarks.

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Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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Satisfiability is the problem of deciding whether a formula has a model. Although it is not even semidecidable in first-order logic, it is decidable in some first-order theories or fragments thereof (e.g., the quantifier-free fragment). Satisfiability modulo a theory is the problem of determining whether a quantifier-free formula admits a model that is a model of a given theory. If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union. A standard solution is the equality-sharing method by Nelson and Oppen, which requires the theories to be disjoint and stably infinite. This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where some theories are unrestricted, while others must satisfy stronger requirements than stable infiniteness; superposition-based decision procedures; and current work on conflict-driven satisfiability (CDSAT).

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Superposition as a Decision Procedure for Timed Automata

Cited by 18 publications

References 39 publications

Automatic Generation of Invariants for Circular Derivations in SUP(LA)

Automatic Generation of Invariants for Circular Derivations in SUP(LA)

Compositional Invariant Generation for Timed Systems

Theory Combination: Beyond Equality Sharing

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