On regions and zones for event-clock automata

Abstract

Event clock automata (ECA) are a model for timed languages that has been introduced by Alur, Fix and Henzinger as an alternative to timed automata, with better theoretical properties (for instance, ECA are determinizable while timed automata are not). In this paper, we revisit and extend the theory of ECA. We first prove that no finite time abstract language equivalence exists for ECA, thereby disproving a claim in the original work on ECA. This means in particular that regions do not form a time abstract bisimulation. Nevertheless, we show that regions can still be used to build a finite automaton recognizing the untimed language of an ECA. Then, we extend the classical notions of zones and DBMs to let them handle event clocks instead of plain clocks (as in timed automata) by introducing event zones and Event DBMs (EDBMs). We discuss algorithms to handle event zones represented as EDBMs, as well as (semi-) algorithms based on EDBMs to decide language emptiness of ECA.

Simulations for Event-Clock Automata

“…In the earlier works on ECA [4,19], prophecy clocks assumed non-negative values and decreased along with time. This allowed to write guards on prophecy clocks with non-negative constants, e.g., − → a ≤ 5 means that the next a occurs in at most 5 time units.…”

“…A main reason for this is the difficulty in adapting zone-based algorithms, critical in the timed automata setting, to the event-clock automata setting. This difficulty was recently studied in [18,19], where the authors also proposed a solution using zone extrapolations.In this paper, we propose an alternative zone-based algorithm, using simulations for finiteness, to solve the reachability problem for event-clock automata. Our algorithm exploits the G-simulation framework, which is the coarsest known simulation relation for reachability, and has been recently used for advances in other extensions of timed automata.…”

“…A main reason for this is the difficulty in adapting zone-based algorithms, critical in the timed automata setting, to the event-clock automata setting. This difficulty was recently studied in [18,19], where the authors also proposed a solution using zone extrapolations.…”

Timed Systems through the Lens of Logic

“…Let us illustrate this template in action via another example of a well-studied model, namely, event predicting clocks [8,23], which can be simulated by ordinary (non-deterministic) timed automata. We fix a set AP of atomic propositions (events) arising from the system.…”

On the determinization of event-clock input-driven pushdown automata

“…As an alternative timed device, the class of event-clock automata (ECA) was introduced by Alur et al [3] and further studied by Geeraerts et al [11]: this class allows determinization and complementation, and hence it enjoys decidable inclusion problem. An ECA is defined with a "prophecy clock" and a "history clock" bound to each input symbol.…”