• DOI:10.1007/978-3-319-06251-8_6
• Corpus ID: 38866270

A Modified Completeness Theorem of KAT and Decidability of Term Reducibility

@inproceedings{Uramoto2014AMC,
  title={A Modified Completeness Theorem of KAT and Decidability of Term Reducibility},
  author={Takeo Uramoto},
  booktitle={RAMiCS},
  year={2014}
}

• Takeo Uramoto
• Published in RAMiCS 28 April 2014
• Mathematics

Kleene algebra with tests (KAT) was introduced by Kozen as an extension of Kleene algebra (KA). The decidability of equational formulas p = q and Horn formulas ∧ i p i = q i → p = q in KAT has been studied so far by several researchers. Continuing this line of research, this paper studies the decidability of existentially quantified equational formulas ∃ q ∈ P. (p = q) in KAT, where P is a fixed collection of KAT terms. A new completeness theorem of KAT is proved, and via the completeness theorem, the decision problem of ∃ q ∈ P. (p = q) is reduced to a certain membership problem of regular languages, to which a pseudo-identity-based decision method is applicable. Based on this reduction, an instance of the problem is studied and shown to be decidable.