Abstract
Linear arithmetic with stars, \(\mathrm {LIA} ^\star \), is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. \(\mathrm {LIA} ^\star \) formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for \(\mathrm {LIA} ^\star \) that checks satisfiability of \(\mathrm {LIA} ^\star \) formulas. By refining on-demand under and over-approximations of \(\mathrm {LIA} ^\star \) formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that \(\mathrm {LIA} ^\star \) formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.
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Levatich, M., Bjørner, N., Piskac, R., Shoham, S. (2020). Solving \(\mathrm {LIA} ^\star \) Using Approximations. In: Beyer, D., Zufferey, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2020. Lecture Notes in Computer Science(), vol 11990. Springer, Cham. https://doi.org/10.1007/978-3-030-39322-9_17
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