Composability of infinite-state activity automata

Abstract

Let ℳ be a class of (possibly nondeterministic) language acceptors with a one-way input tape. A system (.A; A1,..., Ar) of automata in ℳ, is composable if for every string w = a1...a n of symbols accepted by A, there is an assignment of each symbol in w to one of the Ai's such that if wi is the subsequence assigned to Ai, then wi is accepted by Ai. For a nonnegative integer k, a k-lookahead delegator for (A; A1,..., Ar) is a deterministic machine D in ℳ. which, knowing (a) the current states of A, A1,..., Ar and the accessible "local" information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the k lookahead symbols to the right of the current input symbol being processed, can uniquely determine the Ai to assign the current symbol. Moreover, every string w accepted by A is also accepted by D, i.e., the subsequence of string w delegated by D to each Ai is accepted by Ai. Thus, k-lookahead delegation is a stronger requirement than composability, since the delegator D must be deterministic. A system that is composable may not have a k-delegator for any k. We look at the decidability of composability and existence of k-delegators for various classes of machines ℳ. Our results have applications to automated composition of e-services. When e-services are modeled by automata whose alphabet represents a set of activities or tasks to be performed (namely, activity automata), automated design is the problem of "delegating" activities of the composite e-service to existing e-services so that each word accepted by the composite e-service can be accepted by those e-scrvices collectively with each accepting a subsequence of the word, under possibly some Presburger constraints on the numbers and types of activities that can be delegated to the different e-services. Our results generalize earlier ones (and resolve some open questions) concerning composability of deterministic finite automata as e-services to finite automata that are augmented with unbounded storage (e.g., counters and pushdown stacks) and finite automata with discrete clocks (i.e., discrete timed automata). © Springer-Verlag 2004.