# Canonical finite models of Kleene algebra with tests

## 抄録

Kleene algebra with tests (KAT) was introduced by Kozen as an extension of Kleene algebra (KA). So far, the decidability of equational formulas (p=q) and Horn formulas (∧ipi=qi→p=q) in KAT has been investigated by several authors. Continuing this line of research, the current paper studies the decidability of existentially quantified equational formulas ∃q∈P.(p=q) in KAT, where P is a fixed collection of KAT terms and plays a role as a parameter of this decision problem. To design a systematic strategy of deciding problems of this form, given in this paper is an effective procedure of constructing from each KAT term p a finite KAT model K(p) that will be called the canonical finite model of the KAT term p. Applications of this construction are presented, proving the decidability of ∃q∈P.(p=q) for several non-trivial P.

本文言語 英語 595-616 22 Journal of Logical and Algebraic Methods in Programming 85 4 https://doi.org/10.1016/j.jlamp.2015.11.001 出版済み - 6 2016 はい

## All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Software
• Logic
• Computational Theory and Mathematics