This paper gives a tableau-based technique for converting formulas in finite propositional linear-time temporal logic (Finite LTL) into finite-state automata whose languages are the models of given formula. Finite LTL differs from traditional that interpreted with respect to finite, rather than infinite, sequences states; this fact means automata, ω -automata such as those developed by Büchi an...

A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Černý conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n−1). We consider automata with aperiodi...

A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Černý conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n−1). We consider automata with aperiodi...

Hyper-minimization aims to compute a minimal deterministic finite automaton (dfa) that recognizes the same language as a given dfa up to a finite number of errors. Algorithms for hyper-minimization that run in time O(n logn), where n is the number of states of the given dfa, have been reported recently in [Gawrychowski and Jeż: Hyperminimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and ...

Finite automata used to represent large vocabularies of natural languages are quite sparse in the following sense: for the vast majority of states, almost all transitions lead to the rejecting state. This suggests a representation of the automaton in which each state is a small list of transitions entering non rejecting states. By reordering those lists and merging common sublists, it is possib...

It is shown that certain ascending HNN extensions of free abelian groups of finite rank, as well as various lamplighter groups, can be realized as automaton groups, i.e., can be given a self-similar structure. This includes the solvable Baumslag-Solitar groups BS(1, m), for m 6= ±1. In addition, it is shown that, for any relatively prime integers m, n ≥ 2, the pair of Baumslag-Solitar groups BS...

Let S be a string of length n with characters from an alphabet of size σ. The subsequence automaton of S (often called the directed acyclic subsequence graph) is the minimal deterministic finite automaton accepting all subsequences of S. A straightforward construction shows that the size (number of states and transitions) of the subsequence automaton is O(nσ) and that this bound is asymptotical...

Abstract We show the decidability of finite sequentiality problem for unambiguous max-plus tree automata. A automaton is called if there at most one accepting run on every tree. The asks whether a given automaton, exist finitely many deterministic automata whose pointwise maximum equivalent to automaton.