Probabilistic and Topological Semantics for Timed Automata [chapter]

Christel Baier, Nathalie Bertrand, Patricia Bouyer, Thomas Brihaye, Marcus Größer
<span title="">2007</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Like most models used in model-checking, timed automata are an idealized mathematical model used for representing systems with strong timing requirements. In such mathematical models, properties can be violated, due to unlikely (sequences of) events. We propose two new semantics for the satisfaction of LTL formulas, one based on probabilities, and the other one based on topology, to rule out these sequences. We prove that the two semantics are equivalent and lead to a PSPACE-Complete
more &raquo; ... ing problem for LTL over finite executions. Idealization of mathematical models. Timed automata are an idealized mathematical model, in which several assumptions are implicitely made: it has infinite precision, instantaneous events, etc. Several ideas have been explored to overcome the fact that these hypotheses are in practice unrealistic. The model of implementable controllers has been proposed, where constraints and precision of clocks are somewhat relaxed [8] . In this framework, if the model satisfies a safety property, then, on a simple model of processor, its implementation will also satisfy this property. This implementation model has been considered in [15, 7, 4, 6] . However, it induces a very strong notion of robustness, suitable for really critical systems (like rockets or X-by-wire systems in cars), but maybe too strong for less critical systems (like mobile phones or network applications). ⋆ Partly supported by a Lavoisier fellowship. ⋆⋆ Partly supported by a Marie Curie fellowship.
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