## Abstract

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 (∧_{i}p_{i}=q_{i}→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.

Original language | English |
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Pages (from-to) | 595-616 |

Number of pages | 22 |

Journal | Journal of Logical and Algebraic Methods in Programming |

Volume | 85 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jun 2016 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

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