We describe a technique that maps unranked trees to their hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to techniques implemented with minimal tree automata, our procedure builds a pseudo-minimal DTA. Pseudo-minimal automata are larger than the minimal ones but in turn the mapping can be arbitrary, so it can be determined prior to the automaton construction. We al...

A generalized automaton (GA) is a nite automaton where the single transitions are deened on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable. We deene the model of deterministic generalized automaton (DGA) and study the problem of its minimization. A DGA has the restriction...

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have...

The factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of factors of w. It is a data structure allowing the search of a pattern in a text in time and space proportional to the length of the pattern. In this paper we link classical combinatorial parameters on words to the size and the structure of the factor automaton. As a main result, we give a chara...

We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language L is accepted by a Las Vegas automaton having r states such that the probability for a definite answer to occur is at least p, then r ≥ np, where n is the number of the states of the m...

The Magicicada spp. life cycles with its prime periods and highly synchronized emergence have defied reasonable scientific explanation since its discovery. During the last decade several models and explanations for this phenomenon appeared in the literature along with a great deal of discussion. Despite this considerable effort, there is no final conclusion about this long standing biological p...

Regular trees can he detined by two types of rational exprwions. For these two types w;isolve the star-height problem, i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal deterministic automaton for regular languages). In one case, the minimal starheight is the rank (in the Sense of Eggan) of the...

We present a transparent condition on a minimal automaton which is equivalent to piecewise testability of the corresponding regular language. The condition simplifies the original Simon’s condition on the minimal automaton in a different way than conditions of Stern and Trahtman. Secondly, we prove that every piecewise testable language L is k-piecewise testable for k equal to the depth of the ...

A cover-automaton A of a "nite language L⊆ ∗ is a "nite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic "nite cover automaton (DFCA) of a "nite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of "nite la...

A set is called recurrent if its minimal automaton is strongly connected and birecurrent if additionally the same holds for the minimal automaton of its reversal. We study recurrent and birecurrent sets. Our main results are a new proof of an old result (the well-known theorem of Schützenberger concerning codes with bounded synchronization delay) and a series of new results concerning birecurre...