Inspired by failure functions found in classical pattern matching algorithms, a failure deterministic finite automaton (FDFA) is defined as a formalism to recognise a regular language. An algorithm, based on formal concept analysis, is proposed for deriving from a given deterministic finite automaton (DFA) a language-equivalent FDFA. The FDFA’s transition diagram has fewer arcs than that of the...

Measure Many Quantum Finite Automaton is not the strongest known model of quantum automaton but, it is still an open question what is the class of languages recognized by it when only bounded error probability is allowed. In this paper a natural class of ”word set” regular languages are studied. A proof that in general case the class can not be recognized by One-way model of Measure Many Quantu...

We consider finite and polynomial ambiguity of weighted tree automata. Concerning finite ambiguity, we show that a finitely ambiguous weighted tree automaton can be decomposed into a sum of unambiguous automata. For polynomial ambiguity, we show how to decompose a polynomially ambiguous weighted tree automaton into simpler polynomially ambiguous automata and then analyze the structure of these ...

We deene the nondeterministic complexity of a nite automaton and show that there exist, for any integer p 1, automata which need (k 1=p) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable M-subsets of a free monoid into a hierarchy whose members are indexed by polynomials, where M denotes the Min{Plus semiring.

A locally threshold testable language L is a language with the property that for some nonnegative integers k and l and for some word u from L, a word v belongs to L iff (1) the prefixes [suffixes] of length k − 1 of words u and v coincide, (2) the numbers of occurrences of every factor of length k in both words u and v are either the same or greater than l − 1. A deterministic finite automaton ...

The suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata.We also characteri...

We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call “átomaton”, whose states are the “atoms” of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the átomaton, and prove that it is isomorphic to the normal automaton of Sengoku, and to an auto...

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, i...

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ǫtransitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(|A|2E), and finite or polynomial ambiguity in time O(|A|3E), where |A|E denotes the number of transitions of A. These complexities significantly improve over the previo...

Visualization has become an integral part in a wide array of application areas, and papers are solicited both for original visualization research and for the application of visualization towards the understanding of domain-specific data. Our main objective is the visual representation of a directed finite graph with labels attached to edges based on the structure properties of the graph. In par...