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 ... more >>>

Kummer's cardinality theorem states that a language is recursive if a Turing machine can exclude for any n words one of the n + 1 possibilities for the number of words in the language. It is known that this theorem does not hold for polynomial-time computations, but there is evidence ... more >>>

Let $\F\{x_1,x_2,\cdots,x_n\}$ be the noncommutative polynomial ring over a field $\F$, where the $x_i$'s are free noncommuting formal variables. Given a finite automaton $\A$ with the $x_i$'s as alphabet, we can define polynomials $\f( mod A)$ and $\f(div A)$ obtained by natural operations that we call \emph{intersecting} and \emph{quotienting} the ... more >>>