A universal context-free grammar

In this report we show that, for each alphabet Σ, there exists a context-free grammar G which satisfies the property that for each context-free language L ⊆ Σ* a regular control set C can be found such that LC(G) = L

On the Size Complexity of Non-Returning Context-Free PC Grammar Systems

Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six context-free components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the number of nonterminals are limited by certain constants, and these size parameters do not depend on the generated language

Role of Patterns in Automated Task-Driven Grammar Refactoring

Grammarware engineering, and grammar-dependent software development has received considerable attention in recent years. Despite of this fact, grammar refactoring as a significant cornerstone of grammarware engineering is still weakly understood and little practiced. In this paper, we address this issue by proposing universal algorithm for automated refactoring of context-free grammars called mARTINICA, and formal specification language for preserving knowledge of grammar engineers called pLERO. Significant advantage of mARTINICA with respect to other automated refactoring approaches is that it performs grammar refactoring on the bases of user-defined refactoring task, rather then operating under some fixed objective of refactoring process. In order to be able to understand unified refactoring process of mARTINICA this paper also provides brief insight in grammar refactoring operators, which in our approach provide universal refactoring transformations for specific context-free grammars. For preserving of knowledge considering refactoring process we propose formalism based on patterns which are well-proven method of knowledge preservation in variety of other domains, such as software architectures

Combined Parsing Based on Grammar Systems

Tato práce se zabývá kombinovanou syntaktickou analýzou založenou na gramatických systémech. Zavádí klasické modifikované metody gramatických systémů. Nejprve budou teoreticky popsané a v další části implementované v syntaktickém analyzátoru. Základem analyzátoru je CD gramatický systém. Implementace využívá rekursivní sestup a precedenční analýzu. Analyzátor je universální, použitelný pro jakékoli gramatické systémy založené na bezkontextových a některých ne bezkontextových.This thesis deals with a combined parsing based on grammar systems. Introduces modified method of classical grammar systems. At first they will be theoretically described and in the next part they will be implemented for parsing. The basis for the parser is a cooperating distributed grammar system. Implementation uses recursive method and case analysis. The parser is universal, applicable to any grammar systems based on context-free and some not context-free.

On vocabulary size of grammar-based codes

We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog of algorithmic mutual information. The aim is to strengthen inequalities which were discussed in a weaker form in linguistics but shed some light on redundancy of efficiently computable codes. The main contribution of the paper is a construction of universal grammar-based codes for which the excess lengths can be bounded easily.Comment: 5 pages, accepted to ISIT 2007 and correcte

Exploring the N-th Dimension of Language

This paper is aimed at exploring the hidden fundamental\ud computational property of natural language that has been so elusive that it has made all attempts to characterize its real computational property ultimately fail. Earlier natural language was thought to be context-free. However, it was gradually realized that this does not hold much water given that a range of natural language phenomena have been found as being of non-context-free character that they have almost scuttled plans to brand natural language contextfree. So it has been suggested that natural language is mildly context-sensitive and to some extent context-free. In all, it seems that the issue over the exact computational property has not yet been solved. Against this background it will be proposed that this exact computational property of natural language is perhaps the N-th dimension of language, if what we mean by dimension is\ud nothing but universal (computational) property of natural language

Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60\% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity calculator: http://complexitycalculator.com