Finite automata are one of the oldest and most intensely investigated computational models. Historically, the theory of finite automata counts among the oldest topics in computer science, and is one of the basic building blocks of the theory of formal languages. Its origins can be tracked back to the 1940’s, when finite automata were used to model nerve nets [6]. Since its original discovery, f...

A method for the determination of all cycles of deterministic finite state automata is presented. Using a finite field description GF(2) these automata are shown to correspond to multilinear state equations. Basic results from feedback shift register theory are recalled and developed towards a complete analysis tool for affine-linear automata. The multilinear case is reduced to the affine-linea...

This paper is a self-contained introduction to the theory of finite-state automata on infinite words. The study of automata on infinite inputs was initiated by Büchi in order to settle certain decision problems arising in logic. Subsequently, there has been a lot of fundamental work in this area, resulting in a rich and elegant mathematical theory. In recent years, there has been renewed intere...

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 ...

The theory of finite-state automata (FSA) is rich and finite-state automata techniques have been used in a wide range of domains, such as switching theory, pattern matching, pattern recognition, speech processing, hand writing recognition, optical character recognition, encryption algorithm, data compression, indexing and operating system analysis (Petri-net). In this chapter, we describe the b...

Euclidean Automata (EA) are finite state computational devices that take continuous parameter vectors as input. We investigate decompositions of EA into simpler Euclidean and classical finite state automata, relate them to better known computational devices such as artificial neural nets and electronic devices, and show that they are plausible Big Mechanism candidates.

We are interested in identifying a model for discrete event systems from observations. A common way to model discrete event systems is by using deterministic finite state automata (DFA). When observing a system, however, there often is information in addition to the system events, namely, their times of occurrence. If this time information is important, a DFA is too limited. For example, it is ...

Nominal sets, presheaf categories, and named sets have successfully served as models of the state space of process calculi featuring resource generation. More recently, automata built in such categories have been studied as acceptors of languages of finite words over infinite alphabets. In this paper we investigate automata whose state spaces are nominal sets, and that accept infinite words. Th...

This paper reviews some works on finite automaton one-key cryptosystems and related topics such as autonomous finite automata and Latin arrays. It is well known that shift registers are important sequence generators in stream ciphers. But shift registers are merely a special kind of autonomous finite automata. Finite automata were considered as suitable mathematical models of cryptosystems from...

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for ...