Three Quantum Algorithms to Solve 3-SAT

We propose three quantum algorithms to solve the 3-SAT NP-complete decision problem. The first algorithm builds, for any instance Á of 3-SAT, a quantum Fredkin circuit that computes a superposition of all classical evaluations of Á in a given output line. Similarly, the second and third algorithms compute the same superposition on a given register of a quantum register machine, and as the energy of a given membrane in a quantum P system, respectively. Assuming that a specific non-unitary operator, built using the well known creation and annihilation operators, can be realized as a quantum gate, as an instruction of the quantum register machine, and as a rule of the quantum P system, respectively, we show how to decide whether Á is a positive instance of 3-SAT. The construction relies also upon the assumption that an external observer is able to distinguish, as the result of a measurement, between a null and a non-null vector

Modeling and Analysis of Firewalls by (Tissue-like) P Systems

We propose to use tissue-like P systems as a tool to model and analyse the security properties of ¯rewall systems. The idea comes from a clear analogy between firewall rules and P systems rules: they both modify and or move objects (data packets, or symbols of an alphabet) among the regions of the system. The use of P systems for modeling packet filters, routers and firewalls gives the possibility to check - and possibly mathematically prove - some security properties

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

Characterizing the Computational Power of Energy-Based P Systems

We investigate the computational power of energy-based P systems, a model of membrane systems where a fixed amount of energy is associated with each object and the rules transform single objects by adding or removing energy from them. We answer recently proposed open questions about the power of such systems without priorities associated to the rules, for both sequential and maximally parallel modes. We also conjecture that deterministic energy-based P systems are not computationally complete

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

First Steps Towards a CPU Made of Spiking Neural P Systems

We consider spiking neural P systems as devices which can be used to perform some basic arithmetic operations, namely addition, subtraction, comparison and multiplica- tion by a fixed factor. The input to these systems are natural numbers expressed in binary form, encoded as appropriate sequences of spikes. A single system accepts as inputs num- bers of any size. The present work may be considered as a first step towards the design of a CPU based on the working of spiking neural P systems