Revisiting timed logics with automata modalities

Abstract

It is well known that (timed) ω-regular properties such as 'p holds at every even position' and 'p occurs at least three times within the next 10 time units' cannot be expressed in Metric Interval Temporal Logic (MITL) and Event Clock Logic (ECL). A standard remedy to this de ciency is to extend these with modalities de ned in terms of automata. In this paper, we show that the logics EMITL 0,∞ (adding non-deterministic nite automata modalities into the fragment of MITL with only lower-and upper-bound constraints) and EECL (adding automata modalities into ECL) are already as expressive as EMITL (full MITL with automata modalities). In particular, the satis ability and model-checking problems for EMITL 0,∞ and EECL are PSPACE-complete, whereas the same problems for EMITL are EXPSPACE-complete. We also provide a simple translation from EMITL 0,∞ to diagonal-free timed automata, which enables practical satis ability and model checking based on o -the-shelf tools. CCS CONCEPTS• eory of computation → Timed and hybrid models; Logic and veri cation; Veri cation by model checking; KEYWORDS metric interval temporal logic, timed automata, model checking

Fast Algorithms for Handling Diagonal Constraints in Timed Automata

“…Diagonal constraints are a useful modeling feature and occur naturally in certain problems, especially scheduling [16] and logic-automata translations [15,22]. It is however known that they do not add any expressive power: every timed automaton can be converted into a diagonal-free timed automaton [6].…”