An effective implementation of a Directed Acyclic Word Graph (DAWG) automaton is shown. A DAWG for a text T is a minimal automaton that accepts all substrings of a text T, so it represents a complete index of the text. While all usual implementations of DAWG needed about 30 times larger storage space than was the size of the text, here we show an implementation that decreases this requirement d...

This work considers weak deterministic Büchi automata reading encodings of non-negative reals in a fixed base. A Real Number Automaton is an automaton which recognizes all encoding of elements of a set of reals. It is explained how to decide in linear time whether a set of reals recognized by a given minimal weak deterministic RNA is FO [R; +, <, 1]definable. Furthermore, it is explained how to...

We introduce a two generated weakly branch contracting automaton group $G$ which is generated by a two state automaton on a three letter alphabet. Using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. Furthermore some algebraic properties of $G$ are detected .

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

Two examples of automata-theoretic models for the validation of xml documents against user-de ned schema are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree aut...

We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimaltime solution. Both solutions use fewer states than the previous bestknown minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We sh...

Non-deterministic and deterministic automata both have the expressive power to recognize regular languages; thus, for any non-deterministic automaton there exists an equivalent deterministic automaton that recognizes the same regular language (and vice versa). Depending on the regular language recognized, however , the number of states in minimal NFAs and DFAs recognizing the language may diffe...

For each regular language L we describe a family of canonical nondeterministic acceptors (nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally finite variety V , and apply an equivalence between the finite V-algebras and a category of finite structured sets and relations. By instantiating this to different varieties we recover three well-studied canonical...

Given an integer base b > 1, a set of integers is represented in base b by a language over {0, 1, ..., b − 1}. The set is said to be b-recognisable if its representation is a regular language. It is known that ultimately periodic sets are b-recognisable in every base b, and Cobham’s theorem implies the converse: no other set is b-recognisable in every base b. We are interested in deciding wheth...

We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the computations of an alternating Turing machine whose space is polynomially bounded. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints AR;t to a rewrite system R and a term t. This automaton is d...