G. Fici proved that a finite word has a minimal suffix automaton if and only if all its left special factors occur as prefixes. He called LSP all finite and infinite words having this latter property. We characterize here infinite LSP words in terms of S-adicity. More precisely we provide a finite set of morphisms S and an automaton A such that an infinite word is LSP if and only if it is S-adi...

We present a supervised, interactive learning technique that infers control structures of computer programs from user-demonstrated traces. A two-stage process is applied: rst, a minimal deterministic nite automaton (DFA) M labeled by the instructions of the program is learned from a set of example traces and membership queries to the user. It accepts all pre xes of traces of the target program....

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In ...

In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, itera...

We present a reinterpretation of the Kameda-Weiner method of finding a minimal nondeterministic finite automaton (NFA) of a language, in terms of atoms of the language. We introduce a method to generate NFAs from a set of languages, and show that the Kameda-Weiner method is a special case of it. Our method provides a unified view of the construction of several known NFAs, including the canonica...

The problem of inducing automata of minimal size consistent with finite sets of examples and counter-examples is the combinatorial optimization task of grammatical inference and is known to be computationally hard. Both an exact and a heuristic method of finding a non-deterministic finite automaton (NFA) with a given number of states such that all examples are accepted and all counter-examples ...

Introduction In formal language theory, several models characterize regular languages: finite au-tomata, congruences of finite index, monadic second-order logic (MSO), see e.g. [Büc60, Elg61, Tra61]. Further connections exist between monoid varieties and logical fragments of MSO, for instance aperiodic monoids have been shown to recognize exactly the word languages defined by first-order (FO) f...

We present a reflection on the evolution of the different methods for constructing minimal deterministic acyclic finite-state automata from a finite set of words. We outline the most important methods, including the traditional ones (which consist of the combination of two phases: insertion of words and minimization of the partial automaton) and the incremental algorithms (which add new words o...

Game automata are known to recognise languages arbitrarily high in both the non-deterministic and alternating Rabin–Mostowski index hierarchies. Recently it was shown that for this class both hierarchies are decidable. Here we complete the picture by showing that the weak index hierarchy is decidable as well. We also provide a procedure computing for a game automaton an equivalent weak alternat...

Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not necessarily unique, moreover, there are languages having arbitrarily large reversible recognizers possessing no nontrivial reversible congruence. However, the...