On Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Simon Guilloud; Viktor Kunčak

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arXiv · 2110.03315

On Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Simon Guilloud·Viktor Kunčak

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Abstract

We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of boolean algebra. We use as a base a variation of Hopcroft, Ullman and Aho algorithm for tree isomorphism which we combine with a term rewriting system to decide equivalence of two terms. We prove that the rewriting system is terminating and confluent and hence the existence of a normal form, and that our algorithm is computing it. We also discuss applications and present an effective implementation in Scala.

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Simon Guilloud, Viktor Kunčak. 2021-10-07. On Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time. https://arxiv.org/abs/2110.03315

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