Jozef Jirásek

STATE COMPLEXITY OF CONCATENATION AND COMPLEMENTATION

We investigate the state complexity of concatenation and the nondeterministic state complexity of complementation of regular languages. We show that the upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state. In the case of nondeterministic state complexity of complementation, we show that the entire range of complexities, up to the known upper bound can be produced.

State complexity of concatenation and complementation of regular languages

We investigate the state complexity of concatenation and the nondeterministic state complexity of complementation of regular languages. We show that the upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state. In the case of nondeterministic state complexity of complementation, we show that the entire range of complexities, up to the known upper bound can be produced.

Cyclic Shift on Prefix-Free Languages

We prove that the cyclic shift of a prefix-free language represented by a minimal complete n-state deterministic finite automaton is recognized by a deterministic automaton of at most (2n − 3) n − 2 states. We also show that this bound is tight in the quaternary case, and that it cannot be met by using any smaller alphabet. In the ternary and binary cases, we still get exponential lower bounds.

Operations on Unambiguous Finite Automata

A nondeterministic finite automaton is unambiguous if it has at most one accepting computation on every input string. We investigate the complexity of basic regular operations on languages represented by unambiguous finite automata. We get tight upper bounds for intersection mn, left and right quotients

On the boundary of regular languages

2^n-1

Prefix-free languages

, positive closure

Prefix-Free Subsets of Regular Languages and Descriptional Complexity

{3\over 4}\cdot 2^n-1