Exact Generation of Acyclic Deterministic Finite Automata

Exact Generation of Minimal Acyclic Deterministic Finite Automata

We give a canonical representation for minimal acyclic deterministic finite automata (MADFA) with n states over an alphabet of k symbols. Using this normal form, we present a method for the exact generation of MADFAs. This method avoids a rejection phase, that would be needed if a generation algorithm for a larger class of objects that contains the MADFAs were used. We give an upper bound for M...

On the Representation of Finite Automata

We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFA’s) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its enumeration provides an alternative way to obtain the exact number of ICDFA’s. 1 Motivation In symbolic manipulation environments for finite automata, it is...

Exact enumeration of acyclic deterministic automata

A linear recurrence relation is derived for the number of unlabelled initially connected acyclic automata. The coefficients of this relation are determined by another, alternating, recurrence relation. The latter determines, in particular, the number of acyclic automata with labelled states. Certain simple enumerative techniques developed by the author for counting initially connected automata ...

A Fast and Simple Algorithm for Constructing Minimal Acyclic Deterministic Finite Automata

In this paper, we present a fast and simple algorithm for constructing a minimal acyclic deterministic finite automaton from a finite set of words. Such automata are useful in a wide variety of applications, including computer virus detection, computational linguistics and computational genetics. There are several known algorithms that solve the same problem, though most of the alternative algo...

A Taxonomy of Algorithms for Constructing Minimal Acyclic Deterministic Finite Automata