The use of Time-Interval Automata in the Modeling of Timed Discrete Event Systems and its Application to Opacity

Abstract

This paper addresses the problem of language opacity for a class of discrete-event systems whose transitions occur within some known time interval after the event becomes enabled. For this purpose, a new class of timed automata is proposed, time-interval automata (TIA), in which the time elapsed is associated with a unique clock, allowing each transition to be associated with a time interval of occurrence. We present new procedures to compute complement, projection of TIA, complete synchronous composition between TIA, which, differently from existing approaches, do not require refinement by partition. We extend the usual language-based definition of opacity to this class of timed automata, present necessary and sufficient conditions for timed language-based opacity, and propose an algorithm for its verification.