In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that Černý’s conjecture generalizes to CNFAs and that the general upper bound for the length of a shortest D3-directing word is equal to the Pin-Frankl bound for DFAs. As a second consequence, for several classes of CNFAs sharper bounds are established. Final...

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa’s) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the concept of communication complexity is app...

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and orthomodular lattice-valued finite automata with empty string-moves. Based on these equivalences, we study the algebraic operations on orthomodular lattice-valued re...

Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-determi-

Okhotin [9] showed an exponential trade-off in the conversion from nondeterministic unary finite automata to unambiguous nondeterministic unary finite automata. In this paper, we consider the trade-off in the case of unary symmetric difference finite automata to finitely ambiguous unary symmetric difference finite automata. Surprisingly, the trade-off is linear in the number of states of the fi...

3 Finite Automata 11 3.1 Deterministic finite automata . . . . . . . . . . . . . . . . . . . . 11 3.1.1 What is a DFA? . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.2 The language of a DFA . . . . . . . . . . . . . . . . . . . 13 3.2 Nondeterministic finite automata . . . . . . . . . . . . . . . . . . 14 3.2.1 What is an NFA? . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.2 The lan...

Using a result of B.H. Neumann we extend Eilenberg’s Equality Theorem to a general result which implies that the multiplicity equivalence problem of two (nondeterministic) multitape finite automata is decidable. As a corollary we solve a long standing open problem in automata theory, namely, the equivalence problem for multitape deterministic finite automata. The main theorem states that there ...