Algebras for Deterministic Computation Are Inherently Incomplete

Fuente: arXiv
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Autori principali: Cate, Balder ten, Kappé, Tobias
Natura: Preprint
Pubblicazione: 2024
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author Cate, Balder ten
Kappé, Tobias
author_facet Cate, Balder ten
Kappé, Tobias
contents Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice, and iteration) it is able to express all non-deterministic finite state control flow over a finite set of primitives. It is natural to ask whether there exists a similar finite set of constructs that can capture all deterministic computation. We show that this is not the case. More precisely, the deterministic fragment of KAT is not generated by any finite set of regular control flow operations. This generalizes earlier results about the expressivity of the traditional control flow operations, i.e., sequential composition, if-then-else and while.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14284
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Algebras for Deterministic Computation Are Inherently Incomplete
Cate, Balder ten
Kappé, Tobias
Programming Languages
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice, and iteration) it is able to express all non-deterministic finite state control flow over a finite set of primitives. It is natural to ask whether there exists a similar finite set of constructs that can capture all deterministic computation. We show that this is not the case. More precisely, the deterministic fragment of KAT is not generated by any finite set of regular control flow operations. This generalizes earlier results about the expressivity of the traditional control flow operations, i.e., sequential composition, if-then-else and while.
title Algebras for Deterministic Computation Are Inherently Incomplete
topic Programming Languages
url https://arxiv.org/abs/2411.14284