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This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices. [ABSTRACT FROM AUTHOR]

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron's firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively. [ABSTRACT FROM AUTHOR]

The standard definition of tissue P systems includes a special alphabet whose elements are assumed to appear in the initial configuration of the system in an arbitrarily large number of copies. These objects reside in a distinguished place of the system, called the environment. Such potentially infinite supply of objects seems an unfair tool when designing efficient solutions to computationally hard problems in the framework of membrane computing, by performing a space–time trade-off. This paper deals with computational aspects of tissue P systems with cell division where there is no environment having the property mentioned above. Specifically, we prove that the polynomial complexity classes associated with tissue P systems with cell division and with or without environment are actually identical. As a consequence, we conclude that it is not necessary to have infinitely many copies of some objects in the initial configuration in order to solveNP–complete problems in an efficient way. [ABSTRACT FROM PUBLISHER]

This article introduces a general formalism/framework flexible enough to cover descriptions of different variants of P systems having a dynamic membrane structure. Our framework can be useful for the precise definition of new variants of P systems with a dynamic structure and for the comparison of existing definitions as well as for their extension. We give a detailed definition of the formalism and we present some examples of how to translate several existing variants of P systems with a dynamic structure. [ABSTRACT FROM PUBLISHER]

At the beginning of 2005, Gheorghe Păun formulated a conjecture stating that in the framework of recognizer P systems with active membranes (evolution rules, communication rules, dissolution rules and division rules for elementary membranes), polarizations cannot be avoided in order to solve computationally hard problems efficiently (assuming that P ≠ NP). At the middle of 2005, a partial positive answer was given, proving that the conjecture holds if dissolution rules are forbidden. In this paper we give a detailed and complete proof of this result modifying slightly the notion of dependency graph associated with recognizer P systems. [ABSTRACT FROM AUTHOR]