We proposes an algorithm to learn automata infinite alphabets, or at least too large to enumerate. We apply it to define a generic model intended for regression, with transitions constrained by intervals over the alphabet. The algorithm is based on the Red & Blue framework for learning from an input sample. We show two small case studies where the alphabets are respectively the natural and real...

The problem of converting deterministic finite automata into (short) regular expressions is considered. It is known that the required expression size is 2 in the worst case for infinite languages, and for finite languages it is n log n) and n, if the alphabet size grows with the number of states n of the given automaton. A new lower bound method based on communication complexity for regular exp...

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automat...

Tree-walking automata are a natural sequential model for recognizing languages of finite trees. Such automata walk around the tree and may decide in the end to accept it. It is shown that deterministic tree-walking automata are weaker than nondeterministic tree-walking automata.

We introduce linear expressions for unrestricted dags (directed acyclic graphs) and finite deterministic and nondeterministic automata operating on them. Those dag automata are a conservative extension of the Tu,u-automata of Courcelle on unranked, unordered trees and forests. Several examples of dag languages acceptable and not acceptable by dag automata and some closure properties are given.

In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidabl...

For a givenweighted finite automaton over a strong bimonoid we construct its reducedNerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics.We show that the reducedNerode automaton is even smaller than theNerode automaton, which was previously used in determinization related to this semantics. We determine ne...

This paper presents and analyzes an incremental algorithm for the construction of Acyclic Nondeterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons. The proposed algorithm produces compact NFAs, i.e. NFAs that do not contain equivalent states. Unlike Deterministic Finite-state Automata (DFA), this property ...

Nearly all algorithms for learning an unknown regular language, in particular the popular L∗ algorithm, yield deterministic finite automata. It was recently shown that the ideas of L∗ can be extended to yield non-deterministic automata, and that the respective learning algorithm, NL∗, outperforms L∗ on randomly generated regular expressions. We conjectured that this is due to the existential na...