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Register a new userTrace Expressiveness of Timed and Probabilistic Automata
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Added by
Valentin Bura
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting probabilistic behavior and their expressiveness has been studied relative to non-probabilistic transition systems and Markov chains. In this paper, we consider previous formalisms of Timed, Probabilistic and Stochastic Timed Automata, we present our new model of Timed Automata with Polynomial Delay, we introduce a measure of expressiveness for automata we call trace expressiveness and we characterize the expressiveness of these models relative to each other under this new measure.
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We consider previous models of Timed, Probabilistic and Stochastic Timed Automata, we introduce our model of Timed Automata with Polynomial Delay and we characterize the expressiveness of these models relative to each other.
Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one-clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that, for one-clock probabilistic timed automata, the model-checking problem for the probabilistic timed temporal logic PCTL is EXPTIME-complete. However, the model-checking problem for the subclass of PCTL which does not permit both punctual timing bounds, which require the occurrence of an event at an exact time point, and comparisons with probability bounds other than 0 or 1, is PTIME-complete for one-clock probabilistic timed automata.
We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS2003, LNCS, Volume 2791, p. 182-188, 2004 ] and by E. Asarin in [ Challenges in Timed Languages, From Applied Theory to Basic Theory, Bulletin of the EATCS, Volume 83, p. 106-120, 2004 ]. In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular. We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular. We show that in the case of timed Buchi automata accepting infinite timed words some of these problems are Pi^1_1-hard, hence highly undecidable (located beyond the arithmetical hierarchy).
Timed Automata (TA) are a very popular modeling formalism for systems with time-sensitive properties. A common task is to verify if a network of TA satisfies a given property, usually expressed in Linear Temporal Logic (LTL), or in a subset of Timed Computation Tree Logic (TCTL). In this paper, we build upon the TACK bounded model checker for TA, which supports a signal-based semantics of TA and the richer Metric Interval Temporal Logic (MITL). TACK encodes both the TA network and property into a variant of LTL, Constraint LTL over clocks (CLTLoc). The produced CLTLoc formula can then be solved by tools such as Zot, which transforms CLTLoc properties into the input logics of Satisfiability Modulo Theories (SMT) solvers. We present a novel method that preserves TACKs encoding of MITL properties while encoding the TA network directly into the SMT solver language, making use of both the BitVector logic and the logic of real arithmetics. We also introduce several optimizations that allow us to significantly outperform the CLTLoc encoding in many practical scenarios.
Active learning of timed languages is concerned with the inference of timed automata from observed timed words. The agent can query for the membership of words in the target language, or propose a candidate model and verify its equivalence to the target. The major difficulty of this framework is the inference of clock resets, central to the dynamics of timed automata, but not directly observable. Interesting first steps have already been made by restricting to the subclass of event-recording automata, where clock resets are tied to observations. In order to advance towards learning of general timed automata, we generalize this method to a new class, called reset-free event-recording automata, where some transitions may reset no clocks. This offers the same challenges as generic timed automata while keeping the simpler framework of event-recording automata for the sake of readability. Central to our contribution is the notion of invalidity, and the algorithm and data structures to deal with it, allowing on-the-fly detection and pruning of reset hypotheses that contradict observations, a key to any efficient active-learning procedure for generic timed automata.
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