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...

In order to study precisely the growth of timed languages, we associate to such a language a generating function. These functions (tightly related to volume and entropy of timed languages) satisfy compositionality properties and, for deterministic timed regular languages, can be characterized by integral equations. We provide procedures for closed-form computation of generating functions for so...

The timed modal logic Lν has been proposed in order to express timed properties over real-time systems modeled as (compositions of) timed automata. In this paper, we present a short survey of results about Lν : complexity of model checking, expressivity, compositional methods, relationship with strong timed bisimulation etc. We also show how Lν can be extended in order to express new properties.

The algorithmic analysis of timed automata is fundamentally limited by the undecidability of the universality problem. For this reason and others, there has been considerable interest in restricted classes of timed automata. In this paper we study the universality problem for two prominent such subclasses: open and closed timed automata. This problem is described as open in [6, 8] in the case o...

Recently, the model of weighted timed automata has gained interest within the real-time community. In a previous work, we built a bridge to the theory of weighted automata and introduced a general model of weighted timed automata defined over a semiring and a family of cost functions. In this model, a weighted timed automaton recognizes a timed series, i.e., a function mapping to each timed wor...

Parametric timed automata extend timed automata (Alur and Dill, 1991) in that they allow the specification of parametric bounds on the clock values. Since their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the emptiness problem for parametric timed automata with one clock is decidable, whereas it is undecidable if the automaton uses three or more parametric clocks. The p...

We develop theory on the efficiency of identifying (learning) timed automata. In particular, we show that: i) deterministic timed automata cannot be identified efficiently in the limit from labeled data, and ii) that one-clock deterministic timed automata can be identified efficiently in the limit from labeled data. We prove these results based on the distinguishability of these classes of time...