Finite Automata and Their Decision Problems

Abstract

Finite automata are considered in this paper a s instruments for classifying finite tapes. Each onetape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms. 7. J. C. Shepherdson, "The reduction of two-way automata to one-way automata,"

Decidability of second-order theories and automata on infinite trees.

“…A (nondeterministic) finite automaton (see [13]) is a system 2Í = <S, M, S0, F>, where (S, M> is as above, S0^S, F£5. Following Biichi [1], we say that 21 accepts v e S™ if for some 2i-run r on v, r(0) e S0 and In (r) n F=£ 0.…”

The Unmet Challenge of Timed Systems

“…For ODE models, the reduced system should produce behaviors (trajectories) which are close to the detailed one in some metric. In the Computer Science tradition, projecting away variables renders the system non-deterministic in a set-theoretic sense, first introduced in [26]. 5 Hence the abstract system may have several behaviors emanating from the same initial state and the relation between the two levels is typically a conservative approximation: the set of behaviors of the abstract model is a superset of those of the concrete system.…”

From Nondeterministic B\"uchi and Streett Automata to Deterministic Parity Automata

“…We can use deterministic automata also as monitors in games (see below). Determinization for automata on finite words is relatively simple [RS59]. For automata on infinite words this is not the case.…”

“…We know that there exists an efficient procedure that gets a nondeterministic automaton with n states and constructs a deterministic automaton with 2 n states accepting the same language [RS59]. This construction is tight [HMU00].…”