Recently, a characterization of the class of nondeterministic finite automata (NFAs) for which determinization results in a minimal deterministic finite automaton (DFA), was given in [2]. We present a similar result for the case of symmetric difference NFAs. Also, we show that determinization of any minimal symmetric difference NFA produces a minimal DFA.

Inoue et al. introduced an automaton on a twodimensional tape, which decides acceptance or rejection of an input tape by scanning the tape from various sides by various automata which move one way, and investigated the accepting power of such an automaton. This paper continues the investigation of this type of automata, especially, ∨-type automata (obtained by combining four three-way two-dimen...

Let β > 1, d a positive integer, and Zβ,d = {z1z2 · · · | ∑ i>1 ziβ −i = 0, zi ∈ {−d, . . . , d}} be the set of infinite words having value 0 in base β on the alphabet {−d, . . . , d}. Based on a recent result of Feng on spectra of numbers, we prove that if the set Zβ,⌈β⌉−1 is recognizable by a finite Büchi automaton then β is a Pisot number. As a consequence of previous results, the set Zβ,d i...

Let β > 1, d a positive integer, and Zβ,d = {z1z2 · · · | ∑ i>1 ziβ −i = 0, zi ∈ {−d, . . . , d}} be the set of infinite words having value 0 in base β on the alphabet {−d, . . . , d} ⊂ Z. Based on a result of Feng on spectra of numbers, we prove that if the set Zβ,⌈β⌉−1 is recognizable by a finite Büchi automaton then β must be a Pisot number. As a consequence of previous results, the set Zβ,d...

We introduce a notion of partial derivative of a regular expression and apply it to finite automaton constructions. The notion is a generalization of the known notion of word derivative due to Brzozowski: partial derivatives are related to non-deterministic finite automata (NFA’s) in the same natural way as derivatives are related to deterministic ones (DFA’s). We give a constructive definition...

The partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptoti...

This paper addresses the problem of turning a rational (ie regular) expression into a finite automaton. We formalize and generalize the idea of “partial derivatives” introduced in 1995 by V. Antimirov, in order to obtain a construction of an automaton with multiplicity from a rational expression describing a formal power series with coefficients in a semiring. We first define precisely what is ...

A model of computation dealing with infinite alphabets is proposed. This model is based on replacing the equality test by unijication. It appears to be a natural generalization of the classical Rabin-Scott finiteThe basic idea is to equip the automaton with a finite set of proper stam (like in the classic model), in which the “real computation” is done. In addition, the automaton is equipped wi...

Many fuzzy automaton models have been introduced in the past. Here, we discuss two basic nite fuzzy automaton models, the Mealy and Moore types, for lexical analysis. We show that there is a remarkable di erence between the two types. We consider that the latter is a suitable model for implementing lexical analysers. Various properties of fuzzy regular languages are reviewed and studied. A fuzz...

In recent years much attention has been paid to parallelism and concurrent systems. Petri nets are a formalism which is commonly used for these studies [8]. The theory of Petri nets can be described in the mathematical frame of vector addition systems (VAS). Although these two approaches are equivalent, we formulate our results here in the VAS formalism. Karp and Miller provided in [5] a tool w...