462 research outputs found
An Inefficient Representation of the Empty Word
We show that Post's system of tag with alphabet , deletion number 3, productions and , and initial string (330 times) converges to the empty word after a very large number of rewriting steps
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
A Characterization of ET0L and EDT0L Languages
There exists a PT0L language such that the following holds. A language is an ET0L language if and only if there exists a mapping induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that . There exists an infinite collection of EPDT0L languages () such that the family EDT0L is characterized in the following way. A language is an EDT0L language if and only if there exists , a homomorphism and a regular language such that .\u
Fibonacci-like Differential Equations with a Polynomial Non-Homogeneous Part
We investigate non-homogeneous linear differential equations of the form where is either a polynomial or a factorial polynomial in . We express the solution of these differential equations in terms of the coefficients of , in the initial conditions, and in the solution of the corresponding homogeneous differential equation with
Generating All Permutations by Context-Free Grammars in Greibach Normal Form
We consider context-free grammars in Greibach normal form and, particularly, in Greibach -form () which generates the finite language of all strings that are permutations of different symbols (). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of as functions of . As in the case of Chomsky normal form these descriptional complexity measures grow faster than any polynomial function
Complete Symmetry in D2L Systems and Cellular Automata
We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes
A Simple Discrete System with Chaotic Behavior
We discuss the behavior of a particular discrete system, viz. Post's system of tag with alphabet , deletion number , and rules: , . As initial strings we consider all strings of length less than or equal to 15 as well as all 'worst case' inputs of the form with
A Bibliography on Fuzzy Automata, Grammars and Lanuages
This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing
Permuting operations on strings and their relation to prime numbers
Some length-preserving operations on strings only permute the symbol positions in strings; such an operation gives rise to a family of similar permutations. We investigate the structure and the order of the cyclic group generated by . We call an integer -{\em prime} if consists of a single cycle of length (). Then we show some properties of these -primes, particularly, how -primes are related to -primes as well as to ordinary prime numbers. Here and range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on Archimedes spiral and on the Josephus problem
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