Various kinds of automata with weights

摘要

By extracting the basic properties common to the automata appeared in existing literatures, we develop a general formulation of automata with “weights”. We define a pseudoautomaton and derive from it the well-known deterministic automaton, nondeterministic automaton, probabilistic automaton, fuzzy automaton, and so on. Moreover, several interesting automata such as l-semigroup automaton, lattice automaton, dual lattice automaton, mixed boolean automaton, semiring automaton, ring automaton and field automaton which have never appeared in any other paper before are derived.