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arXiv · 2407.18131

Reachability for Multi-Priced Timed Automata with Positive and Negative Rates

Andrew Scoones·Mahsa Shirmohammadi·James Worrell
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Abstract

Multi-priced timed automata (MPTA) are timed automata with observer variables whose derivatives can change from one location to another. Observers are write-only variables, that is, they do not affect the control flow of the automaton; thus MPTA lie between timed and hybrid automata in expressiveness. Previous work considered observers with non-negative slope in every location. In this paper we treat observers that have both positive and negative rates. Our main result is an algorithm to decide a gap version of the reachability problem for this variant of MPTA. We translate the gap reachability problem into a gap satisfiability problem for mixed integer-real systems of nonlinear constraints. Our main technical contribution -- a result of independent interest -- is a procedure to solve such contraints via a combination of branch-and-bound and relaxation-and-rounding.

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Andrew Scoones, Mahsa Shirmohammadi, James Worrell. 2024-07-25. Reachability for Multi-Priced Timed Automata with Positive and Negative Rates. https://arxiv.org/abs/2407.18131

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