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...

Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have i...

Quasi-reversible automata is a suitable representation for reversible languages. In this work a method is proposed to obtain such an automaton for any given reversible language represented by its minimal DFA. Our method runs in polynomial time respect to the size of the minimal DFA and improves a previous exponential method. Previous bound for the size of quasi-reversible automata is also reduc...

Motivated by recent applications of finite automata to theoretical physics, we study the minimization problem for nondeterministic automata (with outputs, but no initial states). We use Ehrenfeucht–Fräısse-like games to model automata responses and simulations. The minimal automaton is constructed and, in contrast with the classical case, proved to be unique up to an isomorphism. Finally, we in...

We show that weighted automata over the field of two elements can be exponentially more compact than non-deterministic finite state automata. To this, we combine ideas from theory and communication complexity. However, are also efficiently learnable in Angluin's minimal adequate teacher model a number queries is polynomial size automaton. include an algorithm for learning WAs any based on linea...

Quotient is a basic operation of formal languages, which plays key role in the construction minimal deterministic finite automata (DFA) and universal automata. In this paper, we extend to power series systemically investigate its implications study weighted particular, define two quotient operations for are called (left or right) quotients residuals respectively. Algebraic properties closure (w...

We study the state complexity of the reverse of acyclic minimal deterministic finite automata, and the computational complexity of the following problem: Given an acyclic minimal DFA, is the minimal DFA for the reverse also acyclic? Note that we allow self-loops in acyclic automata. We show that there exists a language accepted by an acyclic minimal DFA such that the minimal DFA for its reverse...

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple nondeterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs c...

Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are n...