Kamp Theorem for Pomset Languages of Higher Dimensional Automata

Fuente: arXiv
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Main Authors: Clement, Emily, Erlich, Enzo, Ledent, Jérémy
Format: Preprint
Published: 2024
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author Clement, Emily
Erlich, Enzo
Ledent, Jérémy
author_facet Clement, Emily
Erlich, Enzo
Ledent, Jérémy
contents Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp's theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets, and show that it is equivalent to FO.
format Preprint
id arxiv_https___arxiv_org_abs_2410_12493
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Kamp Theorem for Pomset Languages of Higher Dimensional Automata
Clement, Emily
Erlich, Enzo
Ledent, Jérémy
Formal Languages and Automata Theory
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp's theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets, and show that it is equivalent to FO.
title Kamp Theorem for Pomset Languages of Higher Dimensional Automata
topic Formal Languages and Automata Theory
url https://arxiv.org/abs/2410.12493