121,552 research outputs found
An approach to computing downward closures
The downward closure of a word language is the set of all (not necessarily
contiguous) subwords of its members. It is well-known that the downward closure
of any language is regular. While the downward closure appears to be a powerful
abstraction, algorithms for computing a finite automaton for the downward
closure of a given language have been established only for few language
classes.
This work presents a simple general method for computing downward closures.
For language classes that are closed under rational transductions, it is shown
that the computation of downward closures can be reduced to checking a certain
unboundedness property.
This result is used to prove that downward closures are computable for (i)
every language class with effectively semilinear Parikh images that are closed
under rational transductions, (ii) matrix languages, and (iii) indexed
languages (equivalently, languages accepted by higher-order pushdown automata
of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom
Relational Graph Models at Work
We study the relational graph models that constitute a natural subclass of
relational models of lambda-calculus. We prove that among the lambda-theories
induced by such models there exists a minimal one, and that the corresponding
relational graph model is very natural and easy to construct. We then study
relational graph models that are fully abstract, in the sense that they capture
some observational equivalence between lambda-terms. We focus on the two main
observational equivalences in the lambda-calculus, the theory H+ generated by
taking as observables the beta-normal forms, and H* generated by considering as
observables the head normal forms. On the one hand we introduce a notion of
lambda-K\"onig model and prove that a relational graph model is fully abstract
for H+ if and only if it is extensional and lambda-K\"onig. On the other hand
we show that the dual notion of hyperimmune model, together with
extensionality, captures the full abstraction for H*
Higher-dimensional categories with finite derivation type
We study convergent (terminating and confluent) presentations of
n-categories. Using the notion of polygraph (or computad), we introduce the
homotopical property of finite derivation type for n-categories, generalizing
the one introduced by Squier for word rewriting systems. We characterize this
property by using the notion of critical branching. In particular, we define
sufficient conditions for an n-category to have finite derivation type. Through
examples, we present several techniques based on derivations of 2-categories to
study convergent presentations by 3-polygraphs
A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition
Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free -grammars, to model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism.
Our first result characterizes the generating capacity of these fuzzy context-free -grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free -grammars shares closure properties very similar to those of the family of ordinary context-free languages.
The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger- Kasami's algorithm and some recursive descent algorithms. These algorithms turn out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms
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