Introducing the Concept of Activation and Blocking of Rules in the General Framework for Regulated Rewriting in Sequential Grammars

We introduce new possibilities to control the application of rules based on the preceding application of rules which can be de ned for a general model of sequential grammars and we show some similarities to other control mechanisms as graph-controlled grammars and matrix grammars with and without applicability checking as well as gram- mars with random context conditions and ordered grammars. Using both activation and blocking of rules, in the string and in the multiset case we can show computational com- pleteness of context-free grammars equipped with the control mechanism of activation and blocking of rules even when using only two nonterminal symbols

Shuffle on array languages generated by array grammars

Motivated by the studies done by G. Siromoney et al. (1973) and Alexan- dru Mateescu et al. (1998) we examine the language theoretic results related to shuf- fle on trajectories by making use of Siromoney array grammars such as (R : R)AG, (R : C F )AG, (C F : R)AG, (C F : C F )AG, (C S : R)AG, (C S : C S)AG and (C F : C S)AG which are more powerful than the Siromoney matrix grammars (1972) and are used to make digital pictures

KMS states on Quantum Grammars

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results. We prove existence of the dynamics in both Schroedinger and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We show (for high temperatures) that for each system where the lattice undergoes quantum evolution, there is a natural scaling leading to a quantum spin system on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page

Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Pure 2D picture grammars and languages

A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids

Genomics and proteomics: a signal processor's tour

The theory and methods of signal processing are becoming increasingly important in molecular biology. Digital filtering techniques, transform domain methods, and Markov models have played important roles in gene identification, biological sequence analysis, and alignment. This paper contains a brief review of molecular biology, followed by a review of the applications of signal processing theory. This includes the problem of gene finding using digital filtering, and the use of transform domain methods in the study of protein binding spots. The relatively new topic of noncoding genes, and the associated problem of identifying ncRNA buried in DNA sequences are also described. This includes a discussion of hidden Markov models and context free grammars. Several new directions in genomic signal processing are briefly outlined in the end

Array P Systems and t−Communication

The two areas of grammar systems and P systems, which have provided interesting computational models in the study of formal string language theory have been in the recent past effectively linked in [4] by incorporating into P systems, a communication mode called t−mode of cooperating distributed grammar systems. On the other hand cooperating array grammar systems [5]and array P systems [1] have been developed in the context of two-dimensional picture description. In this paper, motivated by the study of [4], these two systems are studied by linking them through the t−communication mode, thus bringing out the picture description power of these systems