Grammar systems form an important part of investigation of formal aspects of multi-agent systems. Cooperation, distribution and complexity are basic research topics of grammar systems. Recently the theory covers different types of systems motivated by technology as well as by biology. We present some representative variants of grammar systems, e.g. CD grammar systems, PC grammar colonies and eco-grammar systems. We illustrate different behavior of these systems like sequential, parallel behavior, and their more complex combinations, based on the motivation to introduce systems. We recapitulate some representative research topics, typical and interesting results, including provocative open problems and present rich references.

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Variants of Grammar Systems: Motivations and Problems.

The concept and the reality of self–organizing networks have come to pervade modern society. But what exactly is a self–organizing network? Scientists from a range of disciplines have been pursuing questions on the particularities of self–organizing networks. Our work addresses self–organizing systems that compile to the scale–free small world model. We model self–organizing networks at syntactical level as well as reveal some semantical and experimental aspects related to them. At syntactical level, we use devices from grammar systems theory: in grammar systems theory the agents are represented by grammars and the generated strings describe the behaviour of the system. At experimental level, we utilize the methods of selective learning and value estimation under evolutionary pressure. The selection is influenced by the ever changing external world and by the competing individuals. First, we model peer–to–peer networks with the aid of networks of parallel multiset string processors. We establish the connection between the growth of the number of strings being present during the computation at the components of these networks of parallel multiset string processors and the growth function of a developmental system. We formalize security rules that conform to self–organizing dynamic systems and allow intra– and intercommunity collaborations. Our approach guarantees quick and efficient local analysis of the security requirements, thus reducing the need for global verification. Secondly, we illustrate the great diversity of employing regulated rewriting devices in eco– grammar systems to describe the search strategy of Internet crawlers. We prove that if we ignore the aging of the web pages in the model, then systems with rather simple component grammars suffice to identify any recursively enumerable language. Whereas if the web pages may become obsolete, then the efficiency of the cooperation of the agents decreases considerably. We also examine the extent to which communication makes a goal– oriented community efficient in different graph topologies through simulations. Finally, we extend the conditions of dynamic team constitution in eco–grammar systems to capture the behaviour of agents participating in network cluster formation. From the language classes that these systems are capable of generating, we deduce the difficulty of the problem they can solve. Depending on the team constitution mode, different classes of languages can be obtained. For all self–organizing networks to be presented in this dissertation, we also propose some further research directions.

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A Formal Language Theoretic Approach to Self–Organizing Networks

In this paper we discuss a size property of Probabilistic Cooperating Distributed Grammar Systems, grammatical constructs designed for modelling distributed random processing. We show that, with respect to the number of productions of a component grammar as a complexity measure, these systems exhibit a language specification of low complexity.

On rule-number complexity of components of probabilistic cooperating distributed grammar systems

Probabilistic cooperating distributed grammar systems introduced in [1] are systems of probabilistic grammars in the sense of [9], i.e., a probability is associated with any transition from one rule to another rule and with any transition from one probabilistic grammar to another probabilistic grammar; a probabilistic grammar stops, if the chosen rule cannot be applied; and the generated language contains only words where the product of the transitions is larger than a certain cut-point). We study the families obtained with cut-point 0 by restricting the number of rules in a probabilistic component. We show that at most two productions in any component are sufficient to generate any recursively enumerable language. If one restricts to probabilistic components with one production in any component, then one obtains the family of deterministic ET0L systems.

On the Size of Components of Probabilistic Cooperating Distributed Grammar Systems

We introduce an alternative definition of random graphs as a language generated by a stochastic cooperating distributed grammar system. We show a relationship between our definition and four known definitions of random graphs, an example of using our model to prove graph-theoretic properties, and we define k-probabilistic model of random graphs as an extension. The first important acquisition of our definition is that only a small modification of a stochastic cooperating distributed grammar system may effect the substantial change of the generated random graph model. Other important result resides in the fact that our approach enables the use of a new proving technique in the random graph theory which is based on the generative paradigm inherent in the formal languages theory.

Stochastic cooperative distributed grammar systems and random graphs

On the Number of Rules in Components of Cooperating Distributed Grammar Systems with Probabilities.

Grammar systems are theoretical models of distributed computing which play a major role in modern Computer Science. In this paper, we define and study a variant of Parallel Communicating(PC) grammar systems namely, Probabilistic PC grammar systems which serves as a grammatical model for random distributed processing. We study the construct with two different models of communication protocols namely, communication by request and communication by command. We explore the generative capacity of the variant with regular, context-free and context-sensitive rules in both models of communication.

K. Arthi

Papers

On rule-number complexity of components of probabilistic cooperating distributed grammar systems

On the Number of Rules in Components of Cooperating Distributed Grammar Systems with Probabilities.

Probabilistic Parallel Communicating Grammar Systems