Minimizable timed automata

Abstract

We present a generalization of the classical theory of testing for Mealy machines to a setting of dense real-time systems. A model of timed I O automata is introduced, inspired by the timed automaton model of Alur and Dill, together with a notion of test sequence for this model. Our main contribution is a test generation algorithm for black-box conformance testing of timed I O automata. Although it is highly exponential and cannot be claimed to be of practical value, it is the rst algorithm that yields a nite and complete set of tests for dense real-time systems.

Real Time Temporal Logic: Past, Present, Future

“…The last three features do not change the expressive power of timed automata, see [SV96], but allow us to treat clocks in a more "dynamic" fashion. Note that clock inactivity in a state can be encoded implicitly by the fact that in all paths emanating from the state, the clock is reset to zero before being tested [DY96].…”

On Recognizable Timed Languages

“…To facilitate the construction we will use an extended form of timed automata, proposed in [SV96], where transitions can be be labelled by assignments of the form x := 0 and x := y (clock renaming). As shown in [SV96] such automata can be transformed into standard timed automata (see also [BDFP00]). …”

“…The closest work to ours, in the sense of trying to establish a semantic inputoutput definition of a state in a timed system, is [SV96], motivated by testing of…”

A Machine-Independent Characterization of Timed Languages

“…Existing approaches to this problem explicitly minimize various resources used by an automaton, such a locations or clocks, see [1,8,[14][15][16]. We take a different approach, which abstracts away from the syntax of a timed automaton, and focuses on the recognized language, and specifically its Myhill-Nerode equivalence relation.…”

“…We only mention here a few related papers we are aware of. Minimization of (nondeterminstic) timed automata has been studied in particular in [1,14,16], with respect to bisimulation equivalence. As we mention later, our approach extends easily to bisimulation.…”