Abstract
In this work, we study properties of deterministic finite-state automata with timers, a subclass of timed automata proposed by Vaandrager et al. as a candidate for an efficiently learnable timed model. We first study the complexity of the configuration reachability problem for such automata and establish that it is \(\textsf{PSPACE}\)-complete. Then, as simultaneous timeouts (we call these, races) can occur in timed runs of such automata, we study the problem of determining whether it is possible to modify the delays between the actions in a run, in a way to avoid such races. The absence of races is important for modelling purposes and to streamline learning of automata with timers. We provide an effective characterization of when an automaton is race-avoiding and establish that the related decision problem is in \(\textsf{3EXP}\) and \(\textsf{PSPACE}\)-hard.
This work was supported by the Belgian FWO “SAILor” project (G030020N). Gaëtan Staquet is a research fellow (Aspirant) of the Belgian F.R.S.-FNRS. The research of Frits Vaandrager was supported by NWO TOP project 612.001.852 “Grey-box learning of Interfaces for Refactoring Legacy Software (GIRLS)”.
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Notes
- 1.
Notation \({\textsf {dom}}(f)\) means the domain of the partial function f.
- 2.
The reason for this choice will be clarified at the end of this section.
- 3.
When using the action indices in the blocks, we have \(B_1 = (1 ~3, \bot )\) and \(B_2 = (2 ~ 4, \bot )\).
- 4.
Recall that the sequence of a block can be composed of a single action.
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Bruyère, V., Pérez, G.A., Staquet, G., Vaandrager, F.W. (2023). Automata with Timers. In: Petrucci, L., Sproston, J. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2023. Lecture Notes in Computer Science, vol 14138. Springer, Cham. https://doi.org/10.1007/978-3-031-42626-1_3
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