Better is better than well: on efficient verification of infinite-state systems

Abstract. We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a linear-time timed temporal logic which extends LTL with timing constraints on modalities, and recently, its model-checking has been proved decidable in several cases. We investigate these decidable fragments of MTL (full MTL when interpreted over finite timed words, and Safety-MTL when interpreted over infinite timed words), and prove two kinds of results.(1) We first prove that, contrary to model-checking, the control problem is undecidable. Roughly, the computation of a lossy channel system could be encoded as a model-checking problem, and we prove here that a perfect channel system can be encoded as a control problem. (2) We then prove that if we fix the resources of the controller (by resources we mean clocks and constants that the controller can use), the control problem becomes decidable. This decidability result relies on properties of well (and better) quasi-orderings.

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“…see [2]). Instead we recall some properties of bqo (see [2,3]), which will be used in the following.…”

Section: Well Quasi-orderings and Better Quasi-orderingsmentioning

confidence: 96%

“…2 A timed automaton (TA, for short) [5] is an STS with finitely many states. In the sequel, if A is a TA, then we will write T (A) for the STS corresponding to A where all states are considered accepting.…”

Section: Symbolic Transition Systems and Timed Automatamentioning

confidence: 99%

Controller Synthesis for MTL Specifications

Bouyer

Bozzelli

Chevalier

2006

CONCUR 2006 – Concurrency Theory

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“…Assume that the clocks x 1 , x 2 and x 3 are associated to the transitions t 1 , t 2 and t 3 , respectively. In the initial marking the clock x 1 gets initialized to the value 0 and as the firing interval of t 1 is [2,4], the only possible behaviour of the net is to delay any time between 2 and 4 time units and then fire the transition t 1 . This produces two new tokens into p 2 and p 3 and the clocks x 2 and x 3 get initialized at the same time.…”

Section: Time Petri Netsmentioning

confidence: 99%

“…This implies that t 3 is never firable and unlike the underlying untimed net, the TPN in our example is bounded and even 1-safe. Assume now that the time interval [5,7] associated with t 3 is replaced by [2,8]. Now after firing t 1 and starting the clocks x 2 and x 3 , the transition t 3 is ready to fire already after two time units, and after another 1 time unit both t 2 and t 3 are enabled.…”

Section: Time Petri Netsmentioning

confidence: 99%

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Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

Srba

Lecture Notes in Computer Science

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Abstract. Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semiformally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.

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