Once More on the Edge-Minimization of Nondeterministic Finite Automata and the Connected Problems

Abstract

We consider in this paper the problem of edge-minimization for nondeterministic finite automata and some connected questions. We shall formulate a new algorithm solving this problem; this algorithm is a simplification of two ones published before. The connected problems include at first algorithms of combining states. We formulate some new sufficient conditions for the possibility of such combining.

Some more algorithms for Conway’s universal automaton

“…is a pseudo-grid (or a grid, see [6]), and for B, we obtain a contradiction with the definition of the grid. Vice versa, let (X , Y) be a state of automaton U L .…”

“…For some states A ∈ Q π and X ∈ Q ρ , condition A#X holds if and only if there exist some words u ∈ L in L (A) and v ∈ L out L R (X), such that uv R ∈ L(K). In [6], we considered a simple algorithm for constructing this relation.…”

“…In [6], we considered a possible algorithm of constructing automaton L R ; using this algorithm, we obtained at the same time values of functions ϕ in and ϕ out and binary relation #. In this section, we shall obtain automaton U L using the same algorithm.…”

“…In Section 2 we introduce some notions: binary relation #, pseudo-grid, grid, covering subset of the grids. This notions appeared in [5,6].…”

“…In Section 5 we give two algorithms of constructing automaton U L , the second of them being "the mirror image" of the first. This algorithms rely on the algorithm, described in [6]. Also we give a simplified version of the first algorithm.…”