Multi-aspect minimization non-deterministic finite automata (Part I. Supporting facts and algorithms)

In the first part of the article, the authors consider some auxiliary algorithms for two problems of minimization of nondeterministic finite automata: vertex-minimization and edge-minimization. The researchers give a simple algorithm for minimization of deterministic automata, which also enables simultaneous construction of state-marking functions. The article proves some auxiliary propositions about input languages of the basis automaton states, necessary for algorithms of equivalent transformation of nondeterministic finite automata.