Concurrent Conciseness of Degree, Probabilistic, Nondeterministic and Deterministic Finite Automata (Extended Abstract)

The conciseness of degree automata (nondeterministic finite automata with a specified acceptance degree) and probabilistic automata over both nondeterministic and deterministic finite automata is investigated. In particular, we exhibit a class of languages for which degree automata are at least polynomially more concise than the equivalent nondeterministic automata. We show that there is no function which bounds the conciseness of probabilistic automata with isolated cutpoints over nondeterministic or degree automata. The concurrent conciseness of probabilistic automata and degree automata over nondeterministic and deterministic automata is also studied.