We study the cost-optimal reachability problem for weighte d imed automata such that positive and negative costs are allowed on edges and locations. By optima lity, we mean an infimum cost as well as… (More)

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce finite automata and rational expressions for these words. We prove that for… (More)

We survey the properties of sets of integers recognizable by automata when they are written in p-ary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different… (More)

We study the model-checking problem for weighted timed automata and the weighted CTL logic by the bisimulation approach. Weighted timed automata are timed automata extended with costs on both edges… (More)

There exist various well-known characterizations of sets of numbers recognizable by a nite automaton, when they are represented in some integer base p 2. We show how to modify these… (More)

The classical LTL synthesis problem is purely qualitative: the given LTL specification is realized or not by a reactive system. LTL is not expressive enough to formalize the correctness of reactive… (More)

In this paper we study the model-checking problem for weighted timed automata and the weighted CTL logic ; we also study the finiteness of bisimulations of weighted timed automata. Weighted timed… (More)

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce automata and rational expressions for words on linear orderings.