Alexandros Palioudakis

Comparisons between Measures of Nondeterminism on Finite Automata

We study the interrelationships between various measures of nondeterminism for finite automata. The tree width of an NFA (nondeterministic finite automaton) A is a function that associates a positive integer n to the maximum number of leaves in any computation tree of A on an input of length n. The trace of an NFA is defined in terms of the maximum product of the degrees of nondeterministic choices in computation on inputs of given length. We establish upper and lower bounds for the trace function of an NFA in terms of its tree width. Additionally, the unbounded trace of an NFA has exponential growth.

State complexity and limited nondeterminism

We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight worst-case state size bound for determinizing an ftw-NFA A as a function of the tree width and the number of states of A. We introduce a lower bound technique for ftw-NFAs and consider the operational state complexity of this model.

State Complexity of Finite Tree Width NFAs

We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight worst-case state size bound for determinizing an ftw-NFA

Unary NFAs with Limited Nondeterminism

A

NONDETERMINISTIC STATE COMPLEXITY OF PROPORTIONAL REMOVALS

as a function of the tree width and the number of states of

Finite Nondeterminism vs. DFAs with Multiple Initial States

A

State complexity of permutation on finite languages over a binary alphabet

. We also introduce a lower bound technique for ftw-NFAs.

Operational state complexity of unary NFAs with finite nondeterminism

We consider unary finite automata employing limited nondeterminism. We show that for a unary regular language, a minimal finite tree width nondeterministic finite automaton (NFA) can always be found in Chrobak normal form. A similar property holds with respect to other measures of nondeterminism. The latter observation is used to establish relationships between classes of unary regular languages recognized by NFAs of given size where the nondeterminism is limited in various ways. Finally, we show that the branching measure of a unary NFA is always either bounded by a constant or has an exponential growth rate.

Nondeterministic State Complexity of Proportional Removals

The language

Worst Case Branching and Other Measures of Nondeterminism

\frac{1}{2}(L)