Finite automata and unary languages

Limited Automata and Unary Languages

Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. When d = 1 these models characterize regular languages. An exponential gap between the size of limited automata accepting unary languages and the size of equivalent finite automata is proved. Since a similar gap was already known from unary c...

Deterministic Pushdown Automata and Unary Languages

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, i...

Events and Languages on Unary Quantum Automata

Limitations of Unary Finite Automata

NFA (Non-deterministic Finite Automata) usually require significantly less states than DFA (Deterministic Finite Automata) to recognize the same language. The power of NFA lies in its ability to be in many states simultaneously (i.e., in a subset of its state set). The usage of one letter input alphabet puts some restrictions on this ability of NFAs and decreases the gap between NFAs and DFAs. ...

Unambiguous Finite Automata over a Unary Alphabet

Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a one-letter alphabet, and determines the exact number of states in DFAs needed to represent unary languages recognized by n-state UFAs in terms of a new number-theoretic function g̃. The growth rate of g̃(n), and theref...