Showing papers on "Büchi automaton published in 1980"

Amounts of nondeterminism in finite automata

Abstract: The amount of nondeterminism in a nondeterministic finite automaton (NFA) is measured by counting the minimal number of "guessing points" a string w has to pass through on its way to an accepting state. NFA's with more nondeterminism can achieve greater savings in the number of states over their deterministic counterparts than NFA's with less nondeterminism. On the other hand, for some nontrivial infinite regular languages a deterministic finite automaton (DFA) can already be quite succinct in the sense that NFA's need as many states (and even context-free grammars need as many nonterminals) as the minimal DFA has states.

Constructing a finite automaton for a given regular expression

Abstract: Regular expressions have a number of applications in computer science; the most important one is probably the lexical analysis of programs (see for instance [3]). Other applications are pattern recognition and pattern matching (including text editing and bibliographical search systems). Common to all these approaches is that the regular expression must be converted into a finite automaton; in most cases it is to be a deterministic automaton. This is usually achieved by first constructing a nondeterministic automaton accepting the language denoted by the expression and then applying the subset construction to it, possibly reducing the resulting deterministic automaton afterwards. A closer look at the algorithms involved in this process reveals that as far as its computational complexity is concerned the most crucial step is the construction of the nondeterminJstic automaton. For if we can construct a nondetermJnlstic automaton with n states corresponding to a given regular expression, then the equivalent deterministic automaton may have up to 2 n states and since reducing of an m-state deterministic automaton Js of time complexity O(m log m) the complete process may therefore be of time complexity O(n 2n). However, suppose that in the first step we obtain a nondeterminlstic automaton with 2n states :for the same expression, then the

Semi-group, group quotient and homogeneous automata

Abstract: Every cyclic automaton is isomorphic to a semi-group quotient automaton, while for a homogeneous automaton the semi-group may be replaced by a group. The connection between this isomorphism and the inertial relation on the state-space is explored, leading to more general statements. For example, a pseudo-homogeneous automaton is pseudo-isomorphic to a group-quotient automaton.

Good state transition policies for nondeterministic and stochastic automata

Abstract: If the state transitions of a nondeterministic or stochastic automaton are rewarded, the question arises whether or not the automaton can adopt a policy which makes sure that this return is maximal or nearly maximal. This problem is of interest, e.g., if one wants to find an optimal prediction for the next state of a stochastic automaton, or if optimal learning strategies are looked for, when optimality is measured in terms of a given goal of learning. It is shown in this paper that under some mildly restricted conditions such optimal or nearly optimal state transition policies exist. This is done for stochastic automata. By means of a representation of nondeterministic by stochastic automata—a result which seems to be of interest by itself—this carries over to the non-deterministic case. The methods and main auxiliary results come from the theory of set valued maps.