Limitedness theorem on finite automata with distance functions

Limitedness Theorem on Finite Automata with Distance Functions: An Algebraic Proof

A finite automaton .d with a distance function d is a sextuple, (C, Q, M, S, F, d), such that C is the input alphabet, Q is the finite set of states, M: Q x C -+ 2Q is the transition function, S c Q and F c Q are the sets of initial and final states, respectively, d: Q x C x Q -+ (0, 1, co } is the distance function, where co denotes infinity, and d satisfies the following: for any (q,a,q’)E Q ...

The limitedness problem on distance automata: Hashiguchi's method revisited

Hashiguchi has studied the limitedness problem of distance automata (DA) in a series of paper ([3], [6] and [7]). The distance of a DA can be limited or unbounded. Given that the distance of a DA is limited, Hashiguchi has proved in [7] that the distance of the automaton is bounded by 2 3+n , where n is the number of states. In this paper, we study again Hashiguchi’s solution to the limitedness...

Finite Tree Automata with Cost Functions

Cost functions for tree automata are mappings from transitions to (tuples o0 polynomials over some semiring. We consider four semirings, namely N the semiring of nonnegative integers, A the "arctical semiring", T the tropical semiring and F the semiring of finite subsets of nonnegative integers. We show: for semirings N and A it is decidable in polynomial time whether or not the costs of accept...

Towards a Cardinality Theorem for Finite Automata

Kummer’s cardinality theorem states that a language is recursive if a Turing machine can exclude for any n words one of the n + 1 possibilities for the number of words in the language. This paper gathers evidence that the cardinality theorem might also hold for finite automata. Three reasons are given. First, Beigel’s nonspeedup theorem also holds for finite automata. Second, the cardinality th...

Decision Issues on Functions Realized by Finite Automata