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On the language inclusion problem for timed automata: Closing a decidability gap
- in Proc. LICS’04. IEEE
"... We consider the language inclusion problem for timed automata: given two timed automata A and B, are all the timed traces accepted by B also accepted by A? While this problem is known to be undecidable, we show here that it becomes decidable if A is restricted to having at most one clock. This is so ..."
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We consider the language inclusion problem for timed automata: given two timed automata A and B, are all the timed traces accepted by B also accepted by A? While this problem is known to be undecidable, we show here that it becomes decidable if A is restricted to having at most one clock. This is somewhat surprising, since it is well-known that there exist timed automata with a single clock that cannot be complemented. The crux of our proof consists in reducing the language inclusion problem to a reachability question on an infinite graph; we then construct a suitable well-quasi-order on the nodes of this graph, which ensures the termination of our search algorithm. We also show that the language inclusion problem is decidable if the only constant appearing among the clock constraints of A is zero. Moreover, these two cases are essentially the only decidable instances of language inclusion, in terms of restricting the various resources of timed automata. 1.
On recognizable timed languages
- In Proc. FOSSACS04, Conf. on Foundations of Software Science and Computation Structures, LNCS
, 2004
"... Abstract. In this work we generalize the fundamental notion of recognizability from untimed to timed languages. The essence of our definition is the existence of a right-morphism from the monoid of timed words into a bounded subset of itself. We show that the recognizable languages are exactly those ..."
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Abstract. In this work we generalize the fundamental notion of recognizability from untimed to timed languages. The essence of our definition is the existence of a right-morphism from the monoid of timed words into a bounded subset of itself. We show that the recognizable languages are exactly those accepted by deterministic timed automata and argue that this is, perhaps, the right class of timed languages, and that the closure of untimed regular languages under projection is a positive accident that cannot be expected to hold beyond the finite-state case. 1
A machine-independent characterization of timed languages
"... We introduce a variant of Fraenkel-Mostowski sets (known also as nominal sets) that is well-suited for languages recognized by timed automata. We state and prove a machine-independent characterization of languages recognized by deterministic timed automata. Finally, in the setting of Fraenkel-Mosto ..."
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Cited by 9 (3 self)
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We introduce a variant of Fraenkel-Mostowski sets (known also as nominal sets) that is well-suited for languages recognized by timed automata. We state and prove a machine-independent characterization of languages recognized by deterministic timed automata. Finally, in the setting of Fraenkel-Mostowski sets we define a class of automata, called timed register automata, that extends timed automata and is effectively closed under minimization.
A Game Approach to Determinize Timed Automata
, 2011
"... Timed automata are frequently used to model real-time systems. Their determinization is a key issue for several validation problems. However, not all timed automata can be determinized, and determinizability itself is undecidable. In this paper, we propose a game-based algorithm which, given a time ..."
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Cited by 7 (1 self)
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Timed automata are frequently used to model real-time systems. Their determinization is a key issue for several validation problems. However, not all timed automata can be determinized, and determinizability itself is undecidable. In this paper, we propose a game-based algorithm which, given a timed automaton with ε-transitions and invariants, tries to produce a language-equivalent deterministic timed automaton, otherwise a deterministic over-approximation. Our method subsumes two recent contributions: it is at once more general than the determinization procedure of [4] and more precise than the approximation algorithm of [11].
Extending PSL for Analog Circuits
- PROSYD DELIVERABLE D1.3/1
, 2005
"... This document is a first proposal for an extension of PSL toward real-time and analog properties. It represents mainly the work of Verimag and Weizmann with a participation of ST in giving insights about the the design and validation of such circuits. ..."
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Cited by 7 (2 self)
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This document is a first proposal for an extension of PSL toward real-time and analog properties. It represents mainly the work of Verimag and Weizmann with a participation of ST in giving insights about the the design and validation of such circuits.
Off-Line Test Selection with Test Purposes for Non-deterministic Timed Automata
- VOL. 8(4:8)2012, PP. 1–33
, 2012
"... ..."
On decision problems for timed automata
"... We solve some decision problems for timed automata which were raised by Tripakis in [9] and by Asarin in [3]. 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. ..."
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We solve some decision problems for timed automata which were raised by Tripakis in [9] and by Asarin in [3]. 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.
Timed Automata for the Development of Real-Time Systems
, 2011
"... Timed automata are a popular formalism to model real-time systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of real-time ..."
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Timed automata are a popular formalism to model real-time systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of real-time system. This paper presents a fairly comprehensive survey, comprised of eighty variants of timed automata. The paper classifies all these eighty variants of timed automata in an effort to determine current developments. It uses analysis techniques, formal properties, and decision problems to draw distinctions between different versions. Moreover, the paper discusses the challenges behind using a timed automata specification to derive an implementation of a working real-time system and presents some solutions. Finally, the paper lists and classifies forty tools supporting timed automata. The paper does not only discuss many variants and their supporting concepts (e.g., closure properties, decision problems), techniques (e.g., for analysis), and tools, but it also attempts to help the reader navigate the vast literature in the field, to highlight differences and similarities between variants, and to reveal research trends and promising avenues for future exploration.
Dynamic Observers for Fault Diagnosis of Timed Systems
"... Abstract — In this paper we extend the work on dynamic observers for fault diagnosis [1], [2], [3] to timed automata. We study sensor minimization problems with static observers and then address the problem of computing the most permissive dynamic observer for a system given by a timed automaton. I. ..."
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Abstract — In this paper we extend the work on dynamic observers for fault diagnosis [1], [2], [3] to timed automata. We study sensor minimization problems with static observers and then address the problem of computing the most permissive dynamic observer for a system given by a timed automaton. I.
Modeling, Verification and Testing using Timed and Hybrid Automata
"... 1.2 Modeling with timed and hybrid automata................... 3 ..."
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1.2 Modeling with timed and hybrid automata................... 3
