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Efficient solutions to hard computational problems by P systems with symport/antiport rules and membrane division
Bosheng Song1, Mario J Pérez-Jiménez2, Linqiang Pan3
1Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China; Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain.
Bio Systems
|March 25, 2015
Summary
This study introduces membrane division into P systems, enabling exponential workspace growth for efficient computation. This model provides linear-time solutions for NP-complete problems like Subset Sum and PSPACE-complete problems such as QSAT.
Area of Science:
- Theoretical Computer Science
- Biologically Inspired Computing
- Formal Languages and Automata Theory
Background:
- P systems are a class of computing models inspired by biological cell membranes.
- Existing P systems often lack mechanisms for efficient workspace expansion.
- Communication rules (symport/antiport) govern object movement without modification.
Purpose of the Study:
- To introduce membrane division into cell-like P systems with communication rules.
- To analyze the computational efficiency of these enhanced P systems.
- To demonstrate their capability in solving complex computational problems.
Main Methods:
- Incorporation of membrane division rules into P systems.
- Utilizing symport/antiport communication rules for object transport.
- Designing uniform solutions for NP-complete and PSPACE-complete problems.
Main Results:
- A linear-time uniform solution for the Subset Sum problem using elementary membrane division.
- Demonstration of efficient uniform solving of the QSAT problem with non-elementary membrane division.
- Achieving exponential workspace in linear time through membrane division.
Conclusions:
- Membrane division significantly enhances the computational power and efficiency of P systems.
- These P systems offer effective solutions for computationally hard problems.
- The model provides a powerful framework for exploring biological computation.
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