Showing papers on "ω-automaton published in 1974"

On the Determinization of Weighted Automata.

Abstract: In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings We define a class of semirings in which we can show that the twins property is sufficient for the termination of the algorithm We also introduce single-valued WFA and give a partial correction of a claim by Mohri [25] by showing several characterizations of single-valued WFA, eg, the formal power series computed by a single-valued WFA is subsequential iff it has bounded variation Also, it is decidable in polynomial time whether a given WFA over the tropical semiring is single-valued

Bounded-reversal multihead finite automata languages

Abstract: A well-known open problem in computational complexity is to find an easily specified language not recognized by any log2 n tape-bounded Turing machine. It is known that the log2 n family is identical to the family of languages recognized by two-way multihead finite automata. Attention here is restricted to those multihead automata which may only reverse each head a fixed constant number of times. It is shown that every bounded language recognized by an automaton from this family satisfies the semilinear property. Thus, easily specified languages which are too complex to be recognized by these restricted multihead automata are obtained.

Errors in Regular Languages

Abstract: Random occurrences of three types of errors in the input to a finite automaton are considered: an α error is a deletion of one symbol from the input string; a β error is an insertion of one extra symbol; and a δ error is a change of one symbol into another symbol. A method using operators for determining regular expressions defining error-corrupted strings is developed and is employed in the construction of a finite automaton, the outputs of which are stochastically generated by Bayes' Rule (with certain approximations) to take into account the frequencies with which strings appear as inputs and the probabilities of errors.

Some results concerning automata on two-dimensional tapes

Abstract: Hierarchies of automata operating on two-dimensional tapes are investigated. In particular, it is shown that finite automata with n+3 markers (n+2 heads) are strictly more powerful than those with n markers (n heads)

Automata theory motivated by problem solving

Abstract: The state-space search methods are well-known techniques in problem solving [1]. In general, a sequence of elementary operators is constructed, leading from a given initial state to one of the goal states of a particular problem domain. Let us call any such sequence a plan (it is a plan how to reach the goal). Consider the usual case of a finite state space. The concept of a finite automaton is a natural and obvious abstraction of such a state space. The set of all plans is just the regular language recognized by the corresponding finite automaton -and this seems to be all in which one field can contribute to the other. However, there exists a radical generalization of the concept of a plan ([2], [3]) which is important in problem solving and quite appealing from the automata-theoretic point of view. It is the case of so called \"branching\" or \"conditional\" plans: roughly speaking, a lack of prior information about a particular state makes it necessary to consider two or more outgoing operators in parallel , thus yielding a plan consisting of a set of sequences instead of a single sequence. Moreover, for the same reason, there are no goal states but only \"goal opportunities\", so that a plan may contain also prefixes of its elements. (This approach Is related to the logical framework of [2]; alternatively, one can consider operators with multiple outcomes [3]0

Structure Theory of Automata

Abstract: The aim of this chapter is to study the structural properties of automata which are mentioned in 2.9: The construction and characterization of isomorphisms, subautomata, equalizers, products, coequalizers, coproducts, image-factorizations and free automata respectively. This is already done in [33] for deterministic automata, and, similar to that case, it will be shown for automata in monoidal categories (K,⊗) that most of the constructions can be “lifted” from K, which means that they can be constructed componentwise in the category K. On the other hand the constructions of coproducts and free automata in the category of automata with variable input and output is more difficult and the proofs are rather long.

On tests with finite memory in finite time (Corresp.)

Abstract: The purpose of this correspondence is to display an inductive proof of an optimality result for testing symmetric simple hypotheses concerning a binomial parameter with a three-state memory and n observations. Specifically, it is shown that if one restricts attention to three-state automata allowing transitions only between adjacent states, then no artificial randomization is required in the middle state of the optimal machine. The success in this problem of what will be called simultaneous induction suggests the possibility of obtaining characterizations of optimal automata in more general problems by similar techniques.

The dimension of stability of stochastic automata

Abstract: The concept of the dimension of stability of stochastic automata is introduced and examined. We are concerned with the minimal-state form of the automaton and the dimension of stability. Natural automata are defined, for which the dimension of stability is not less than the difference between the number of states and the number of states of its minimal-state equivalent. For minimal state automata, the upper bound on the dimension of stability is given, and we demonstrate minimal-state automata for which the dimension of stability reaches this upper bound. An estimate of the dimension of stability of automata that are not necessarily minimal state is based on this result for minimal-state automata.

A general definition of stochastic automata

Abstract: A new class of stochastic automata is defined. Its elements, called dependent automata, are characterized by a partition on the set of states such that the transition between the blocks is defined deterministicly. The definitions of isomorphism and equivalence are adapted. Some relations with other classes of stochastic automata and subclasses of dependent automata are defined.

On the output structure of certain finite automata

Abstract: The output structure of certain composite automata is studied. The components are cyclic group-type automata with a group homomorphism as output function associated with each state. Properties of the output sequence such as frequencies and periods of symbols are expressed by properties of the component automata and their connections.

Channel capacity of a finite-state linear automation (Corresp.)

Abstract: A finite-state deterministic linear automaton is viewed as a communication channel from a source to a receiver, accepting source symbols as inputs and generating outputs for a receiver. The automaton is assumed to be composed of two subautomata, one representing the next-state function and one the output function. With the use of Shannon's theorem for capacities of discrete channels, it is demonstrated that the channel capacities of the linear automaton and its subautomata can be readily determined by an analytical procedure rather than by applying an iterative algorithm as required for general finite-state automata.