Search results for "Formal Language"

Coding Partitions: Regularity, Maximality and Global Ambiguity

2007

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an ap…

Words and forbidden factors

2002

AbstractGiven a finite or infinite word v, we consider the set M(v) of minimal forbidden factors of v. We show that the set M(v) is of fundamental importance in determining the structure of the word v. In the case of a finite word w we consider two parameters that are related to the size of M(w): the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w. We derive sharp upper and lower bounds for both parameters. We prove also that the second parameter is related to the minimal period of the word w. We are further interested to the algorithmic point of view. Indeed, we design linear time algorithm for the following two p…

Symbolic Dynamics of Geodesic Flows on Trees

2019

In this chapter, we give a coding of the discrete-time geodesic ow on the nonwandering sets of quotients of locally finite simplicial trees X without terminal vertices by nonelementary discrete subgroups of Aut(X) by a subshift of finite type on a countable alphabet.

On bijections vs. unary functions

1996

A set of finite structures is in Binary NP if it can be characterized by existential second order formulas in which second order quantification is over relations of arity 2. In [DLS95] subclasses of Binary NP were considered, in which the second order quantifiers range only over certain classes of relations. It was shown that many of these subclasses coincide and that all of them can be ordered in a three-level linear hierarchy, the levels of which are represented by bijections, successor relations and unary functions respectively.

Tally languages accepted by alternating multitape finite automata

1997

We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)(Σ*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than $$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$ leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respe…

K4-free Graphs as a Free Algebra

2017

International audience; Graphs of treewidth at most two are the ones excluding the clique with four vertices (K4) as a minor, or equivalently, the graphs whose biconnected components are series-parallel. We turn those graphs into a finitely presented free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting these graphs: in addition to parallel composition and series composition, it suffices to consider the neutral elements of those operations and a unary transpose operation. Then we give a finite equational presentation and we prove it complete: two terms from the syntax are congruent if and only if they …

Software Architectures for Human-Machine Interaction Using Natural Language

Il linguaggio naturale rappresenta un sistema di comunicazione a carattere inferenziale in opposizione ai sistemi di comunicazione a codice che non prevedono una forma di ragionamento intelligente da parte del ricevente, ma si basano sul riconoscimento di patterns dell'informazione. In un sistema di comunicazione di tipo inferenziale, infatti, si parte dal presupposto che il ricevente abbia una certa "intelligenza" e sia, quindi, capace di comprendere, elaborare ed inferire il contenuto informativo di una comunicazione attraverso ragionamenti su un background di conoscenze (come modelli di mondo e di linguaggio) condivisi sia dalla sorgente che dal destinatario. L'attività di ricerca, svolt…

Equivalence closure in the two-variable guarded fragment

2015

We consider the satisfiability and finite satisfiability problems for the extension of the two-variable guarded fragment in which an equivalence closure operator can be applied to two distinguished binary predicates. We show that the satisfiability and finite satisfiability problems for this logic are 2-ExpTime-complete. This contrasts with an earlier result that the corresponding problems for the full two-variable logic with equivalence closures of two binary predicates are 2-NExpTime-complete.

Learning by the Process of Elimination

2002

AbstractElimination of potential hypotheses is a fundamental component of many learning processes. In order to understand the nature of elimination, herein we study the following model of learning recursive functions from examples. On any target function, the learning machine has to eliminate all, save one, possible hypotheses such that the missing one correctly describes the target function. It turns out that this type of learning by the process of elimination (elm-learning, for short) can be stronger, weaker or of the same power as usual Gold style learning.While for usual learning any r.e. class of recursive functions can be learned in all of its numberings, this is no longer true for el…

A Fast Algorithm Finding the Shortest Reset Words

2013

In this paper we present a new fast algorithm for finding minimal reset words for finite synchronizing automata, which is a problem appearing in many practical applications. The problem is known to be computationally hard, so our algorithm is exponential in the worst case, but it is faster than the algorithms used so far and it performs well on average. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare subsets. Also a number of heuristics are applied. We give both theoretical and practical arguments showing that the effective branching factor is considerably reduced. As a practical test we perform an experimental study of the length of the shortest …