A Decision Procedure for a Theory of Finite Sets with Finite Integer Intervals

05/06/2021
by   Maximiliano Cristiá, et al.
0

In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints (ℒ_|·|) to a decision procedure for ℒ_|·| extended with set terms denoting finite integer intervals (ℒ_[ ]). In 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 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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset