Solving Subset Sum in Linear Time by Using Tissue P Systems with Cell Division

Tissue P systems with cell division is a computing model in the framework of Membrane Computing based on intercellular communication and cooperation between neurons. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to NP-complete problems in polynomial time. In this paper we present a solution to the Subset Sum problem via a family of such devices. This is the first solution to a numerical NP-complete problem by using tissue P systems with cell division.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Cell-like Versus Tissue-like P Systems by Means of Sevilla Carpets

Sevilla Carpets are a handy tool for comparing computations performed by different systems solving the same problem. Such Sevilla Carpets provide on one hand quantitative information through parameters such as Weight, Surface and Average weight, and on the other hand they also provide a fast glimpse on the complexity of the computation thanks to their graphical representation. Up to now, Sevilla Carpets were only used on Cell-like P systems. In this paper we present a first comparison by means of Sevilla Carpets of the computations of three P systems (designed within different models), all of them solving the same instance of the Subset Sum problem. Two of these solutions use Cell-like P systems with active membranes, while the third one uses Tissue-like P systems with cell division.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08-TIC-0420

Computational Efficiency of Cellular Division in Tissue-like Membrane Systems

Tissue-like P systems with cell division are computing models in the framework of membrane computing. They are inspired by the intercellular communication and neuronal synaptics, their structures being formalized by underlying graphs. As usual in membrane computing, division rules allow the construction of an exponential workspace (described by the number of cells) in a linear time. In this paper this ability is used for presenting a uniform linear-time solution for the (NP{complete) Vertex Cover problem via a uniform family of such systems. This solution is compared to other ones obtained in the framework of cell-like membrane systems.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

A Uniform Solution to Common Algorithmic Problem by Tissue P Systems with Cell Division

Common algorithmic problem is an optimization problem, which has the nice property that several other NP-complete problems can be reduced to it in linear time. A tissue P system with cell division is a computing model which has two basic characters: intercellular communication and the ability of cell division. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to computationally hard problems in polynomial time. We here present an effective solution to the common algorithmic decision problem using a family of recognizer tissue P systems with cell division.Ministerio de Ciencia e Innovación TIN2009-13192Junta de Andalucía P08-TIC0420

Tissue-like P Systems Without Environment

In this paper we present a tissue-like P systems model with cell division the environment has been replaced by an extra cell. In such model, we present a uniform family of recognizer P systems which solves the Subset Sum problem. This solution establishes a new frontier for the tractability of computationally hard problems in Membrane Computing, since it proves that NP-complete problems can be solved without an arbitrarily large amount of objects in the environment.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420

Solving Common Algorithmic Problem by Recognizer Tissue P Systems

Common Algorithmic Problem is an optimization problem, which has the nice property that several other NP-complete problems can be reduced to it in linear time. In this work, we deal with its decision version in the framework of tissue P systems. A tissue P system with cell division is a computing model which has two types of rules: communication and division rules. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to computationally hard problems in polynomial time. We here present an effective solution to Common Algorithmic Decision Problem by using a family of recognizer tissue P systems with cell division. Furthermore, a formal verification of this solution is given.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

Solving the Independent Set problem by using tissue-like P systems with cell division

Tissue-like P systems with cell division is a computing model in the framework of Membrane Computing inspired by the intercellular communication and neuronal synaptics. It considers the cells as unit processors and the computation is performed by the parallel application of given rules. Division rules allow an increase of the number of cells during the computation. We present a polynomial-time solution for the Independent Set problem via a uniform family of such systems.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem

A Computational Complexity Theory in Membrane Computing

In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with di erent models of cell-like and tissue-like membrane systems are de ned and the most relevant results obtained so far are presented. Many attractive characterizations of P 6= NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420