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- W3162701640 abstract "In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ( ({mathcal {L}_{vert {cdot }vert }} ) ) to a decision procedure for ({mathcal {L}_{vert {cdot }vert }} ) extended with set terms denoting finite integer intervals ( ({mathcal {L}_{[,]}} ) ). In ({mathcal {L}_{[,]}} ) interval limits can be integer linear terms including 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 } (‘setlog’) 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.
- W3162701640 created "2021-05-24" @default.
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- W3162701640 date "2023-09-22" @default.
- W3162701640 modified "2023-09-24" @default.
- W3162701640 title "A Decision Procedure for a Theory of Finite Sets with Finite Integer Intervals" @default.
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- W3162701640 doi "https://doi.org/10.1145/3625230" @default.
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