Petri net controlled grammars

Different types of regulated grammars have been introduced in order to supplement shortcomings of context-free grammars in applications preserving their elegant mathematical properties. However, the rapid developments in present day industry, biology, and other areas challenge to deal with various tasks which need suitable tools for their modelling and investigation. We propose Petri net controlled grammars as models for representing and analyzing of metabolic pathways in living cells where Petri nets are responsible for the structure and communication of the pathways, and grammars represent biochemical processes. On the other hand, the control by Petri nets has also theoretical interest: it extends possibilities to introduce and investigate concurrent control mechanisms in formal language theory. The thesis introduces various variants of Petri net controlled grammars using different types of Petri nets and investigates their mathematical properties such as computational power and closure properties.Los diferentes tipos de gramáticas con reescritura regulada han sido introducidas para complementar las deficiencias de las gramáticas libres del contexto en las aplicaciones, preservando sus propiedades matemáticas. Por otro lado, la rápida evolución la biología, y otras áreas actuales supone un reto para tratar de las tareas varias que necesitan las herramientas adecuadas para la elaboración de modelos e investigación. Proponemos gramáticas controladas por redes de Petri como modelos para representar y analizar los procesos bioquímicos en las células vivas donde redes de Petri son responsables de la estructura, y gramáticas representan los procesos generativos. Además, el control de redes de Petri también tiene interés teórico: amplía las posibilidades de investigar los mecanismos de control concurrente en la teoría de lenguajes formales. La tesis presenta distintas variantes de gramáticas controladas por redes de Petri e investiga sus propiedades matemáticas

Petri net controlled grammars with a bounded number of additional places

A context-free grammar and its derivations can be described by a Petri net, called a context-free Petri net, whose places and transitions correspond to the nonterminals and the production rules of the grammar, respectively, and tokens are separate instances of the nonterminals in a sentential form. Therefore , the control of the derivations in a context-free grammar can be implemented by adding some features to the associated cf Petri net. The addition of new places and new arcs from/to these new places to/from transitions of the net leads grammars controlled by k-Petri nets, i.e., Petri nets with additional k places. In the paper we investigate the generative power and give closure properties of the families of languages generated by such Petri net controlled grammars, in particular, we show that these families form an infinite hierarchy with respect to the numbers of additional places

Grammars controlled by petri nets with inhibitor arcs.

A Petri net controlled grammar is a grammar equipped with a Petri net whose transitions are labeled with production rules of the grammar, and the associated language consists of all terminal strings which can be derived in the grammar and the sequence of rules in every terminal derivation corresponds to some occurrence sequence of transitions of the Petri net which is enabled at the initial marking and finished at a final marking of the net. In this paper we define grammars controlled by Petri nets with inhibitor arcs and investigate their computational capacities

Nonterminal complexity of tree controlled grammars

This paper studies the nonterminal complexity of tree controlled grammars. It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals

Static watson-crick linear grammars and its computational power

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional siliconchips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate doublestranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. There is a difference in generating double-stranded strings between a dynamic Watson-Crick linear grammar and a static Watson-Crick linear grammar. A dynamic Watson-Crick linear grammar produces each stranded string independently and only check for the Watson-Crick complementarity of a generated complete double-stranded string at the end; while the static Watson-Crick linear grammar generates both stranded strings dependently, i.e., checking for the WatsonCrick complementarity for each complete substring. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented

Some properties of probabilistic semi-simple splicing systems

The concept of splicing system was first introduced by Head in 1987. This model has been introduced to investigate the recombinant behavior of DNA molecules. Over the years, various types of splicing languages have been defined and studied by different mathematicians. Splicing systems with finite sets of axioms only generate regular languages. Therefore, different restrictions have been considered to increase the computational power up to the recursively enumerable languages. In this research, a variant of splicing systems called probabilistic splicing systems has been used to define different types of splicing systems such as probabilistic simple splicing systems, probabilistic semi-simple splicing systems and probabilistic one-sided splicing systems. In probabilistic splicing systems, probabilities (real numbers in the range of 0 and 1) are associated with the axioms, and the probability p(z)of the string z generated from two strings x and y is calculated from the probability p(x)and p(y) according to the operation *(multiplication) defined on the probabilities, i.e., p(z) = p(x) * p(y)

The properties of probabilistic simple regular sticker system

A mathematical model for DNA computing using the recombination behavior of DNA molecules, known as a sticker system, has been introduced in 1998. In sticker system, the sticker operation is based on the Watson-Crick complementary feature of DNA molecules. The computation of sticker system starts from an incomplete double-stranded sequence. Then by iterative sticking operations, a complete double-stranded sequence is obtained. It is known that sticker systems with finite sets of axioms and sticker rule (including the simple regular sticker system) generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of the languages generated by the sticker systems. In this paper, we study the properties of probabilistic simple regular sticker systems. In this variant of sticker system, probabilities are associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings. The language are selected according to some probabilistic requirements. We prove that the probabilistic enhancement increases the computational power of simple regular sticker systems

Probabilistic simple sticker systems

A model for DNA computing using the recombination behavior of DNA molecules, known as a sticker system, was introduced by by L. Kari, G. Paun, G. Rozenberg, A. Salomaa, and S. Yu in the paper entitled DNA computing, sticker systems and universality from the journal of Acta Informatica vol. 35, pp. 401-420 in the year 1998. A sticker system uses the Watson-Crick complementary feature of DNA molecules: starting from the incomplete double stranded sequences, and iteratively using sticking operations until a complete double stranded sequence is obtained. It is known that sticker systems with finite sets of axioms and sticker rules generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of sticker systems. Recently, a variant of restricted sticker systems, called probabilistic sticker systems, has been introduced [4]. In this variant, the probabilities are initially associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings in the computation of the string. Strings for the language are selected according to some probabilistic requirements. In this paper, we study fundamental properties of probabilistic simple sticker systems. We prove that the probabilistic enhancement increases the computational power of simple sticker systems

Consensus of fractional nonlinear dynamics stochastic operators for multiagent systems

In this paper, we consider nonlinear models of DeGroot, quadratic stochastic operators (QSO) and doubly stochastic quadratic operators (DSQO) with fractional degree for consensus problem in multi-agent systems (MAS).By the limit behaviour of nonlinear approach, we discuss the convergence of the solutions of the models considered. The findings from the results of the carried out investigation demonstrates an efficient approach to convergence for consensus problem in MAS. The main advantages of the proposed work are i) fast convergence to consensus ii) flexible and low complexity in computation iii) ability to achieve optimal consensus. The study is built on fractional representation of 1/n where n→∞. Further, the simulation results on the related protocols are also presented

Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite- dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex