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It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a…
An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is…
We show that counting Euler tours in undirected bounded tree-width graphs is tractable even in parallel - by proving a $\#SAC^1$ upper bound. This is in stark contrast to #P-completeness of the same problem in general graphs. Our main…
We consider recognizable trace rewriting systems with level-regular contexts (RTL). A trace language is level-regular if the set of Foata normal forms of its elements is regular. We prove that the rewriting graph of a RTL is word-automatic.…
Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against \omega-regular specifications…
Updatable timed automata (UTA) are extensions of classic timed automata that allow special updates to clock variables, like x:= x - 1, x := y + 2, etc., on transitions. Reachability for UTA is undecidable in general. Various subclasses with…
We consider systems composed of an unbounded number of uniformly designed linear hybrid automata, whose dynamic behavior is determined by their relation to neighboring systems. We present a class of such systems and a class of safety…
Specifying properties can be challenging work. In this paper, we propose an automated approach to exemplify properties given in the form of automata extended with timing constraints and timing parameters, and that can also encode…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
ELAN is a powerful language and environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. Timed automata is a class of continuous real-time models of reactive systems for…
ELAN is a powerful language and environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. Timed automata is a class of continuous real-time models of reactive systems for…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.