History-Dependent Automata

In this paper we present history-dependent automata (HD-automata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with history-dependent formalisms. In a history-dependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is -calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the history-preserving semantics of Petri nets. Ordinary automata are an unsatisfactory operational model for these formalisms: infinite automata are obtained for all the systems with infinite computations, even for very simple ones; moreover, the ordinary definition of bisimulation does not apply in these cases, thus preventing the reusage of standard theories and algorithms. In this paper we show that HD-automata are an adequate model for the history-dependent formalisms. We present translations of -calculus, CCS with localities and Petri nets into HD-automata; and we show that finite HD-automata are obtained for significant classes of systems with infinite computations. We also define HD-bisimulation and show that it captures the standard equivalences of the considered history-dependent formalisms. Moreover, we prove that HD-automata can be minimized, and that the same minimal HD-automaton is associated to each class of bisimilar HDautomata. Finally, we provide a categorical definition of HD-automata and of HD-bisimulation (by exploiting open maps).