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- W4386983851 abstract "In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($mathcal{L}_{lvertcdotrvert}$) to a decision procedure for $mathcal{L}_{lvertcdotrvert}$ extended with set terms denoting finite integer intervals ($mathcal{L}_{[,]}$). In $mathcal{L}_{[,]}$ interval limits can be integer linear terms including emph{unbounded variables}. These intervals are a useful extension because they allow to express non-trivial set operators such as the minimum and maximum of a set, still in a quantifier-free logic. Hence, by providing a decision procedure for $mathcal{L}_{[,]}$ it is possible to automatically reason about a new class of quantifier-free formulas. The decision procedure is implemented as part of the ${log}$ tool. The paper includes a case study based on the elevator algorithm showing that ${log}$ can automatically discharge all its invariance lemmas some of which involve intervals." @default.
- W4386983851 created "2023-09-24" @default.
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- W4386983851 date "2021-05-06" @default.
- W4386983851 modified "2023-10-18" @default.
- W4386983851 title "A Decision Procedure for a Theory of Finite Sets with Finite Integer Intervals" @default.
- W4386983851 doi "https://doi.org/10.48550/arxiv.2105.03005" @default.
- W4386983851 hasPublicationYear "2021" @default.
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