We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this construction to the case of C∞-words, i.e., words differentiable arbitrary many times. We thus obtain an infinite automaton for representing the set of C∞-words...

We present Stamina, a tool solving three algorithmic problems in automata theory. First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression. Second, decide limitedness for regular cost functions. Third, decide whether a probabilistic leaktight automaton has value 1, i.e. wheth...

For a Muller automaton only a subset of its states is needed to decide whether a run is accepting or not: The set I the innnitely often visited states can be replaced by the intersection I \ W with a xed set W of states, provided W is large enough to distinguish between accepting and non-accepting loops in the automaton. We call such a subset W a separating set. Whereas the idea was previously ...

Brüggemann-Klein and Wood define a one-unambiguous regular language as a language that can be recognized by a deterministic Glushkov automaton. They give a procedure performed on the minimal DFA, the BW-test, to decide whether a language is one-unambiguous. Block determinism is an extension of one-unambiguity while considering non-empty words as symbols and prefix-freeness as determinism. A blo...

The generic limit set of a dynamical system is the smallest that attracts most space in topological sense: it closed with comeager basin attraction. Introduced by Milnor, has been studied context one-dimensional cellular automata Djenaoui and Guillon, Delacourt, Törmä. In this article we present complexity bounds on realizations sets prescribed properties. We show have Π20 language if they are ...

This paper presents a new simplification method for weighted finite automata. The method suggests efficient approaches to some problems that are related to intersection of automata. Minimal automata can be made smaller through simplifications such as merging of states. Although such simplifications change the recognized language, some other essential properties of the automaton may be preserved...

This paper describes a method for constructing a minimal deterministic finite automaton (DFA) from a regular expression. It is based on a set of graph grammar rules for combining many graphs (DFA) to obtain another desired graph (DFA). The graph grammar rules are presented in the form of a parsing algorithm that converts a regular expression R into a minimal deterministic finite automaton M suc...

In this paper we investigate several questions related to syntactic congruences and to minimal automata associated with ω-languages. In particular we investigate relationships between the so-called simple (because it is a simple translation from the usual definition in the case of finitary languages) syntactic congruence and its infinitary refinement (the iteration congruence) investigated by A...

The synchronization problem for a deterministic n-state automaton consists in the search of an input-sequence, called a synchronizing word such that the state attained by the automaton, when this sequence is read, does not depend on the initial state of the automaton itself. If such a sequence exists, the automaton is called synchronizing. If the automaton is deterministic and complete, a well-...

Suffix automata and factor automata are efficient data structures for representing the full index of a set of strings. They are minimal deterministic automata representing the set of all suffixes or substrings of a set of strings. This paper presents a novel analysis of the size of the suffix automaton or factor automaton of a set of strings. It shows that the suffix automaton or factor automat...