We show that for all n and α such that 1 ≤ n ≤ α ≤ 2 there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to const...

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be...

For each positive integer r ≥ 1, a nondeterministic machine M is r path-bounded if for any input word x, there are r computation paths of M on x. This paper investigates the accepting powers of pathbounded one-way (simple) multihead nondeterministic finite automata. It is shown that for each k ≥ 2 and r ≥ 1, there is a language accepted by an (r+1) path-bounded one-way nondeterministic k head f...

We have implemented a package that transforms concise algebraic descriptions of linear block codes into finite automata representations, and also generates decoders from such representations. The transformation takes a description of the code in the form of a k × n generator matrix over a field with q elements, representing a finite language containing q strings, and constructs a minimal automa...

We investigate the conversion of nondeterministic finite automata and context-free grammars into Parikh equivalent deterministic finite automata, from a descriptional complexity point of view. We prove that for each nondeterministic automaton with n states there exists a Parikh equivalent deterministic automaton with e √ n·lnn) states. Furthermore, this cost is tight. In contrast, if all the st...

A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, Dtrivial, monotonic, partially monotonic automata and automata with a zero state. For these subcla...

Iterated Finite Automaton (IFA) is invented by Wolfram for studying the conventional Finite State Automata(FSA) by means of A New Kind of Science (NKS) methodology. An IFA is a composition of a finite state automaton and a tape with limited cells. The complexity of behaviors generated by various FSA operating on different tapes can be visualized by two dimensional patterns. Through enumerating ...

Partial words, that is, finite words with holes, were introduced in the 70s by Fischer and Paterson, with respect to bioinformatics applications. Infinite partial words were introduced later. Recently, Dassow et al.’s connected partial words and regular languages. In this paper, we extend the local partial languages to local ω-partial languages and study their closure properties. We introduce t...

We prove that the limit dynamics of any finite automata network under parallel update schedule correspond exactly to fixed points a so-called strictly one-way cellular automaton. This correspondence is proven be exact, as automaton can transformed into corresponding network, latter former. transformation operated using output functions, which have been developed in author’s previous works.