A cyclic proof system for Guarded Kleene Algebra with Tests (full version)
Logic in Computer Science
2024-05-14 v1 Formal Languages and Automata Theory
Logic
Abstract
Guarded Kleene Algebra with Tests (GKAT for short) is an efficient fragment of Kleene Algebra with Tests, suitable for reasoning about simple imperative while-programs. Following earlier work by Das and Pous on Kleene Algebra, we study GKAT from a proof-theoretical perspective. The deterministic nature of GKAT allows for a non-well-founded sequent system whose set of regular proofs is complete with respect to the guarded language model. This is unlike the situation with Kleene Algebra, where hypersequents are required. Moreover, the decision procedure induced by proof search runs in NLOGSPACE, whereas that of Kleene Algebra is in PSPACE.
Cite
@article{arxiv.2405.07505,
title = {A cyclic proof system for Guarded Kleene Algebra with Tests (full version)},
author = {Jan Rooduijn and Dexter Kozen and Alexandra Silva},
journal= {arXiv preprint arXiv:2405.07505},
year = {2024}
}
Comments
Full version of paper accepted at IJCAR 2024