Higher-Dimensional Timed Automata for Real-Time Concurrency

Amazigh Amrane; Hugo Bazille; Emily Clement; Uli Fahrenberg; Philipp Schlehuber-Caissier

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arXiv · 2401.17444

Higher-Dimensional Timed Automata for Real-Time Concurrency

Amazigh Amrane·Hugo Bazille·Emily Clement·Uli Fahrenberg·Philipp Schlehuber-Caissier

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Abstract

We present a new language semantics for real-time concurrency. Its operational models are higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional automata and timed automata. In real-time concurrent systems, both concurrency of events and timing and duration of events are of interest. Thus, HDTAs combine the non-interleaving concurrency model of higher-dimensional automata with the real-time modeling, using clocks, of timed automata. We define languages of HDTAs as sets of interval-timed pomsets with interfaces. We show that language inclusion of HDTAs is undecidable. On the other hand, using a region construction we can show that untimings of HDTA languages have enough regularity so that untimed language inclusion is decidable. On a more practical note, we give new insights on when practical applications, like checking reachability, might benefit from using HDTAs instead of classical timed automata.

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Amazigh Amrane, Hugo Bazille, Emily Clement, Uli Fahrenberg, Philipp Schlehuber-Caissier. 2024-01-30. Higher-Dimensional Timed Automata for Real-Time Concurrency. https://arxiv.org/abs/2401.17444

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