The construction of minimal acyclic deterministic partial nite automata to represent large natural language vocabularies is described. Applications of such automata include: spelling checkers and advisers, multilanguage dictionaries, thesauri, minimal perfect hashing and text compression. Part of this research was supported by a grant awarded by the Brazilian National Council for Scienti c and ...

Quite often, trivial problems stated for Deterministic Finite Automata (DFA) are surprisingly difficult for the nondeterministic case (NFA). In any non-minimal DFA for a given regular language, we can find two equivalent states wich can be “merged” without changing the accepted language. This is not the case for NFA, where we can have non-minimal automata with no “mergible” states. In this pape...

We investigate unary regular languages and compare deterministic finite automata (DFA’s), nondeterministic finite automata (NFA’s) and probabilistic finite automata (PFA’s) with respect to their size. Given a unary PFA with n states and an -isolated cutpoint, we show that the minimal equivalent DFA has at most n 1 2 states in its cycle. This result is almost optimal, since for any α < 1 a famil...

This work considers weak deterministic Büchi automata reading encodings of non-negative d-vectors of reals in a fixed base. A saturated language is a language which contains all encoding of elements belonging to a set of d-vectors of reals. A Real Vector Automaton is an automaton which recognizes a saturated language. It is explained how to decide in quasi-linear time whether a minimal weak det...

Constraint automaton is a formalism to capture the operational semantics of the channel based coordination language Reo. In general constraint automaton can be used as a formalism for modeling coordination of some components. In this paper we introduce a standard linear temporal logic and two fragments of it for expressing the properties of the systems modeled by constraint automata and show th...

Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that Černy’s conjecture holds true, if and only if, it holds true for planar automata. In this paper we have gathered some evidence concerning this conjecture. This evidence amounts to show that the class of planar automata is representative of the algorithmic hardness ...

Sets of finite words, as well as some infinite ones, can be described using finite systems, e.g. automata. On the other hand, some automata may be constructed with use of even more compact systems, like Petri nets. We call such automata Petri net solvable. In this paper we consider the solvability of singleton languages over a binary alphabet (i.e. binary words). An unsolvable (i.e. not solvabl...

In the 1980’s Stallings [35] showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This allows for the deep algorithmic theory of finite automata and finite inverse monoids to be used to answer questions about finitely generate...

Finite (nondeterministic) automata are very useful building blocks in the field of string matching. This is particularly true in the case of multiple pattern matching, where the use of factor-based automata can reduce substantially the number of computational steps when the patterns have large common factors. Direct simulation of nondeterministic automata can be performed very efficiently using...