Decision Trees for Applicability of Evolution Rules in Transition P Systems

Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of active evolution rules subset inside each membrane of the P system. But, to establish the active evolution rules subset, it is required the previous calculation of useful and applicable rules. Hence, computation of applicable evolution rules subset is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. The work presented here shows advantages of incorporating decision trees in the evolution rules applicability algorithm. In order to it, necessary formalizations will be presented to consider this as a classification problem, the method to obtain the necessary decision tree automatically generated and the new algorithm for applicability based on it.

Delimited Massively Parallel Algorithm Based on Rules Elimination for Application of Active Rules in Transition P Systems

In the field of Transition P systems implementation, it has been determined that it is very important to determine in advance how long takes evolution rules application in membranes. Moreover, to have time estimations of rules application in membranes makes possible to take important decisions related to hardware / software architectures design. The work presented here introduces an algorithm for applying active evolution rules in Transition P systems, which is based on active rules elimination. The algorithm complies the requisites of being nondeterministic, massively parallel, and what is more important, it is time delimited because it is only dependant on the number of membrane evolution rules.

HW Implementation of a Optimized Algorithm for the Application of Active Rules in a Transition P-system

P systems or Membrane Computing are a type of a distributed, massively parallel and non deterministic system based on biological membranes. They are inspired in the way cells process chemical compounds, energy and information. These systems perform a computation through transition between two consecutive configurations. As it is well known in membrane computing, a configuration consists in a m-tuple of multisets present at any moment in the existing m regions of the system at that moment time. Transitions between two configurations are performed by using evolution rules which are in each region of the system in a non-deterministic maximally parallel manner. This work is part of an exhaustive investigation line. The final objective is to implement a HW system that evolves as it makes a transition P-system. To achieve this objective, it has been carried out a division of this generic system in several stages, each of them with concrete matters. In this paper the stage is developed by obtaining the part of the system that is in charge of the application of the active rules. To count the number of times that the active rules is applied exist different algorithms. Here, it is presents an algorithm with improved aspects: the number of necessary iterations to reach the final values is smaller than the case of applying step to step each rule. Hence, the whole process requires a minor number of steps and, therefore, the end of the process will be reached in a shorter length of time.

Fast Linear Algorithm for Active Rules Application in Transition P Systems

Transition P systems are computational models based on basic features of biological membranes and the observation of biochemical processes. In these models, membrane contains objects multisets, which evolve according to given evolution rules. In the field of Transition P systems implementation, it has been detected the necessity to determine whichever time are going to take active evolution rules application in membranes. In addition, to have time estimations of rules application makes possible to take important decisions related to the hardware / software architectures design. In this paper we propose a new evolution rules application algorithm oriented towards the implementation of Transition P systems. The developed algorithm is sequential and, it has a linear order complexity in the number of evolution rules. Moreover, it obtains the smaller execution times, compared with the preceding algorithms. Therefore the algorithm is very appropriate for the implementation of Transition P systems in sequential devices.

Static Analysis of Usefulness States in Transition P Systems

Transition P Systems are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations that are determined by the membrane structure and multisets present inside membranes. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules. But, to establish the rules to be applied, it is required the previous calculation of useful, applicable and active rules. Hence, computation of useful evolution rules is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in every evolution step. This work defines usefulness states through an exhaustive analysis of the P system for every membrane and for every possible configuration of the membrane structure during the computation. Moreover, this analysis can be done in a static way; therefore membranes only have to check their usefulness states to obtain their set of useful rules during execution.

A Circuit Implementing Massive Parallelism in Transition P Systems

ransition P-systems are based on biological membranes and try to emulate cell behavior and its evolution due to the presence of chemical elements. These systems perform computation through transition between two consecutive configurations, which consist in a m-tuple of multisets present at any moment in the existing m regions of the system. Transition between two configurations is performed by using evolution rules also present in each region. Among main Transition P-systems characteristics are massive parallelism and non determinism. This work is part of a very large project and tries to determine the design of a hardware circuit that can improve remarkably the process involved in the evolution of a membrane. Process in biological cells has two different levels of parallelism: the first one, obviously, is the evolution of each cell inside the whole set, and the second one is the application of the rules inside one membrane. This paper presents an evolution of the work done previously and includes an improvement that uses massive parallelism to do transition between two states. To achieve this, the initial set of rules is transformed into a new set that consists in all their possible combinations, and each of them is treated like a new rule (participant antecedents are added to generate a new multiset), converting an unique rule application in a way of parallelism in the means that several rules are applied at the same time. In this paper, we present a circuit that is able to process this kind of rules and to decode the result, taking advantage of all the potential that hardware has to implement P Systems versus previously proposed sequential solutions.

A Hierarchical Architecture with Parallel Comunication for Implementing P Systems

Membrane systems are computational equivalent to Turing machines. However, its distributed and massively parallel nature obtain polynomial solutions opposite to traditional non-polynomial ones. Nowadays, developed investigation for implementing membrane systems has not yet reached the massively parallel character of this computational model. Better published approaches have achieved a distributed architecture denominated “partially parallel evolution with partially parallel communication” where several membranes are allocated at each processor, proxys are used to communicate with membranes allocated at different processors and a policy of access control to the communications is mandatory. With these approaches, it is obtained processors parallelism in the application of evolution rules and in the internal communication among membranes allocated inside each processor. Even though, external communications share a common communication line, needed for the communication among membranes arranged in different processors, are sequential. In this work, we present a new hierarchical architecture that reaches external communication parallelism among processors and substantially increases parallelization in the application of evolution rules and internal communications. Consequently, necessary time for each evolution step is reduced. With all of that, this new distributed hierarchical architecture is near to the massively parallel character required by the model.

Simulating Membrane Systems in Digital Computers

* Work partially supported by contribution of EU commission Under The Fifth Framework Programme, project “MolCoNet” IST-2001-32008.

P Systems Goedelization

This paper presents a method for assigning natural numbers to Transition P systems based on a Gödelization process. The paper states step by step the way for obtaining Gödel numbers for each one of the fundamental elements of Transition P systems –multisets of objects, evolution rules, priorities relation, membrane structure- until defining the Gödel number of a given Transition P system.

Extended Networks of Evolutionary Processors

This paper presents an extended behavior of networks of evolutionary processors. Usually, such nets are able to solve NP-complete problems working with symbolic information. Information can evolve applying rules and can be communicated though the net provided some constraints are verified. These nets are based on biological behavior of membrane systems, but transformed into a suitable computational model. Only symbolic information is communicated. This paper proposes to communicate evolution rules as well as symbolic information. This idea arises from the DNA structure in living cells, such DNA codes information and operations and it can be sent to other cells. Extended nets could be considered as a superset of networks of evolutionary processors since permitting and forbidden constraints can be written in order to deny rules communication.