Converting two-way nondeterministic unary automata into simpler automata

Converting Two-Way Nondeterministic Unary Automata into Simpler Automata

We show that, on inputs of length exceeding 5n, any n-state unary two-way nondeterministic 4nite automaton (2nfa) can be simulated by a (2n+2)-state quasi-sweeping 2nfa. Such a result, besides providing a “normal form” for 2nfa’s, enables us to get a subexponential simulation of unary 2nfa’s by two-way deterministic 4nite automata (2dfa’s). In fact, we prove that any n-state unary 2nfa can be s...

Complementing Unary Nondeterministic Automata

Probabilistic and Nondeterministic Unary Automata

We investigate unary regular languages and compare deterministic finite automata (DFA’s), nondeterministic finite automata (NFA’s) and probabilistic finite automata (PFA’s) with respect to their size. Given a unary PFA with n states and an -isolated cutpoint, we show that the minimal equivalent DFA has at most n 1 2 states in its cycle. This result is almost optimal, since for any α < 1 a famil...

Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent One-Way and Two-Way Deterministic Automata

We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent oneway and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e √ n·lnn) and p(n) states,...

Regularly Extended Two-Way Nondeterministic Tree Automata

We establish that regularly extended two-way nondeterministic tree automata with unranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is th...