Decidable $${\exists }^*{\forall }^*$$ First-Order Fragments of Linear Rational Arithmetic with Uninterpreted Predicates

Voigt, Marco

doi:10.1007/s10817-020-09567-8

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2022

2024

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Cited by 2 publications

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“…Form an application perspective, the BS(LRA) fragment already encompasses a number of used (sub)languages. For example, timed automata [3] and a number of extensions thereof are contained in the BS(LRA) fragment [60].…”

Section: Discussionmentioning

confidence: 99%

An Efficient Subsumption Test Pipeline for BS(LRA) Clauses

Bromberger

Leutgeb

Weidenbach

2022

Automated Reasoning

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The importance of subsumption testing for redundancy elimination in first-order logic automatic reasoning is well-known. Although the problem is already NP-complete for first-order clauses, the meanwhile developed test pipelines efficiently decide subsumption in almost all practical cases. We consider subsumption between first-oder clauses of the Bernays-Schönfinkel fragment over linear real arithmetic constraints: BS(LRA). The bottleneck in this setup is deciding implication between the LRA constraints of two clauses. Our new sample point heuristic preempts expensive implication decisions in about 94% of all cases in benchmarks. Combined with filtering techniques for the first-order BS part of clauses, it results again in an efficient subsumption test pipeline for BS(LRA) clauses.

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Section: Discussionmentioning

confidence: 99%