59 research outputs found
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
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
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
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
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
Towards Robustness in Parsing - Fuzzifying Context-Free Language Recognition
We discuss the concept of robustness with respect to parsing a context-free language. Our approach is based on the notions of fuzzy language, (generalized) fuzzy context-free grammar and parser / recognizer for fuzzy languages. As concrete examples we consider a robust version of Cocke-Younger-Kasami's algorithm and a robust kind of recursive descent recognizer
Permuting operations on strings: Their permutations and their primes
We study some length-preserving operations on strings that permute the symbol positions in strings. These operations include some well-known examples (reversal, circular or cyclic shift, shuffle, twist, operations induced by the Josephus problem) and some new ones based on Archimedes spiral. Such a permuting operation gives rise to a family of similar permutations. We investigate the structure and the order of the cyclic group generated by such a permutation . We call an integer -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
Controlled Fuzzy Parallel Rewriting
We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages
Generating all permutations by context-free grammars in Chomsky normal form
Let Ln be the finite language of all n! strings that are permutations of n different symbols (n1). We consider context-free grammars Gn in Chomsky normal form that generate Ln. In particular we study a few families {Gn}n1, satisfying L(Gn)=Ln for n1, with respect to their descriptional complexity, i.e. we determine the number of nonterminal symbols and the number of production rules of Gn as functions of n
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