Networks of Uniform Splicing Processors: Computational Power and Simulation

Sandra Gómez-Canaval,Victor Mitrana,Mihaela Păun,José Sanchez Martín,José Sánchez Couso

doi:10.3390/math8081217

Abstract

We investigated the computational power of a new variant of network of splicing processors, which simplifies the general model such that filters remain associated with nodes but the input and output filters of every node coincide. This variant, called network of uniform splicing processors, might be implemented more easily. Although the communication in the new variant seems less powerful, the new variant is sufficiently powerful to be computationally complete. Thus, nondeterministic Turing machines were simulated by networks of uniform splicing processors whose size depends linearly on the alphabet of the Turing machine. Furthermore, the simulation was time efficient. We argue that the network size can be decreased to a constant, namely six nodes. We further show that networks with only two nodes are able to simulate 2-tag systems. After these theoretical results, we discuss a possible software implementation of this model by proposing a conceptual architecture and describe all its components.

Highlights

In the last two decades, computational models inspired by different phenomena that appear in nature have been vividly researched from a formal perspective
There is a huge degree of similarity between these networks and other models of computation with related or different origins: tissue-like P systems ([2]) in the membrane computing area ([3]), evolutionary systems abstracted from the evolution of various cell populations ([4]), networks of parallel language processors, which has been introduced as a parallel language-theoretic model ([5]), flow-based programming, which is a programming paradigm widely known ([6]), connection machine, which may be viewed as a network, Mathematics 2020, 8, 1217; doi:10.3390/math8081217
The methods and techniques used in these simulations were the standard ones in such types of investigations: we explain how each computational step of a Turing machine or a 2-tag system can be simulated by a number of steps in a network of uniform splicing processors

Summary

Introduction

In the last two decades, computational models inspired by different phenomena that appear in nature have been vividly researched from a formal perspective. We investigated the possibility to simulate another computationally complete model, namely the 2-tag system with these networks We performed such a simulation having two important properties: each application of a tag operation is simulated in 8 computational steps (4 splicing steps and 4 communication steps) by the network and the size of the simulating network is optimal, that has 2 nodes only. The methods and techniques used in these simulations were the standard ones in such types of investigations: we explain how each computational step of a Turing machine or a 2-tag system can be simulated by a number of steps in a network of uniform splicing processors. The fourth section presents an efficient simulation of another computationally complete model, that of a 2-tag system In this case, the simulation can be accomplished by a network with only two uniform splicing processors, the simulation is an optimal one

Basic Definitions

Efficient Simulations of Turing Machines

Efficient Simulations of 2-Tag Systems

Towards a Computational Simulation of NUSP

Conclusions and Further Work