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1

Tissue P Systems with Small Cell Volume

Leporati A., Manzoni L., Mauri G., Porreca A. E., Zandron C.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

261--275

EN

Traditionally, P systems allow their membranes or cells to grow exponentially (or even more) in volume with respect to the size of the multiset of objects they contain in the initial configuration. This behaviour is, in general, biologically unrealistic, since large cells tend to divide in order to maintain a suitably large surface-area-to-volume ratio. On the other hand, it is usually the number of cells that needs to grow exponentially with time by binary division in order to solve NP-complete problems in polynomial time. In this paper we investigate families of tissue P systems with cell division where each cell has a small volume (i.e., sub-polynomial with respect to the input size), assuming that each bit of information contained in the cell, including both those needed to represent the multiset of objects and the cell label, occupies a unit of volume. We show that even a constant volume bound allows us to reach computational universality for families of tissue P systems with cell division, if we employ an exponential-time uniformity condition on the families. Furthermore, we also show that a sub-polynomial volume does not suffice to solve NP-complete problems in polynomial time, unless the satisfiability problem for Boolean formulae can be solved in sub-exponential time, and that solving an NP-complete problem in polynomial time with logarithmic cell volume implies P = NP.

2

Membrane Division, Oracles, and the Counting Hierarchy

Leporati A., Manzoni L., Mauri G., Porreca A. E., Zandron C.

Fundamenta Informaticae

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2015

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Vol. 138, nr 1/2

97--111

EN

Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary (leaf) membrane division rules are allowed, the computing power decreases to PPP = P#P, the class of problems solvable in polynomial time by deterministic Turingmachines equipped with oracles for counting (or majority) problems. In this paper we investigate a variant of intermediate power, limiting membrane nesting (hence membrane division) to constant depth, and we prove that the resulting P systems can solve all problems in the counting hierarchy CH, which is located between PPP and PSPACE. In particular, for each integer k ≥ 0 we provide a lower bound to the computing power of P systems of depth k.

3

Constant-Space P Systems with Active Membranes

Leporati A., Manzoni L., Mauri G., Porreca A. E., Zandron C.

Fundamenta Informaticae

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2014

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Vol. 134, nr 1/2

111--128

EN

We show that a constant amount of space is sufficient to simulate a polynomial-space bounded Turing machine by P systems with active membranes. We thus obtain a new characterisation of PSPACE, which raises interesting questions about the definition of space complexity for P systems. We then propose an alternative definition, where the size of the alphabet and the number of membrane labels of each P system are also taken into account. Finally we prove that, when less than a logarithmic number of membrane labels is available, moving the input objects around the membrane structure without rewriting them is not enough to even distinguish inputs of the same length.

4

Solving SUBSET SUM by Spiking Neural P Systems with Pre-computed Resources

Leporati A., Gutiérrez-Naranjo M.

Fundamenta Informaticae

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2008

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Vol. 87, nr 1

61-77

EN

Recently the possibility of using spiking neural P systems for solving computationally hard problems has been considered. Such solutions assume that some (possibly exponentially large) pre–computed resources are given in advance, provided that their structure is “regular” and they do not contain neither “hidden information” that simplify the solution of specific instances, nor an encoding of all possible solutions (that is, an exponential amount of information that allows to cheat while solving the instances of the problem). In this paper we continue this research line, and we investigate the possibility of solving numerical NP-complete problems such as SUBSET SUM. In particular, we first propose a semi–uniform family of spiking neural P systems in which every system solves a specific instance of SUBSET SUM. Then, we exploit a technique used to calculate ITERATED ADDITION with Boolean circuits to obtain a uniform family of spiking neural P systems in which every system is able to solve any instance of SUBSET SUM of a fixed size. All the systems here considered are deterministic, and their size generally grows exponentially with respect to the instance size.

5

On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution

Zandron C., Leporati A., Ferretti C., Mauri G., Pérez-Jiménez M.J.

Fundamenta Informaticae

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2008

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Vol. 87, nr 1

79-91

EN

Recognizer P systems with active membranes have proven to be very efficient computing devices, being able to solve NP-complete decision problems in a polynomial time. However such solutions usually exploit many powerful features, such as electrical charges (polarizations) associated to membranes, evolution rules, communication rules, and strong or weak forms of division rules. In this paper we contribute to the study of the computational power of polarizationless recognizer P systems with active membranes. Precisely, we show that such systems are able to solve in polynomial time the NP-complete decision problem 3-SAT by using only dissolution rules and a form of strong division for non–elementary membranes, working in the maximallly parallel way.

6

(Tissue) P Systems with Unit Rules and Energy Assigned to Membranes

Alhazov A., Freund R., Leporati A., Oswald M., Zandron C.

Fundamenta Informaticae

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2006

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Vol. 74, nr 4

391-408

EN

We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for systems working in the sequential mode with a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets of languages generated by context-free matrix grammars. On the other hand, when using the maximally parallel mode, we do not need a priority relation to obtain computational completeness. Finally, we introduce the corresponding model of tissue P systems with energy assigned to the membrane of each cell and objects moving from one cell to another one in the environment as well as being able to change the energy of a cell when entering or leaving the cell. In each derivation step, only one object may pass through the membrane of each cell. When using priorities on the rules in the sequential mode (where in each derivation step only one cell is affected) as well as without priorities in the maximally parallel mode (where in each derivation step all cells possible are affected) we again obtain computational completeness, whereas without priorities on the rules in the sequential mode we only get a characterization of the family of Parikh sets of languages generated by context-free matrix grammars.

7

Reversible P Systems to Simulate Fredkin Circuits

Leporati A., Zandron C., Mauri G.

Fundamenta Informaticae

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2006

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Vol. 74, nr 4

529-548

EN

We introduce energy-based P systems as a parallel and distributed model of computation in which the amount of energy manipulated and/or consumed during computations is taken into account. Basing upon the seminal paper of Fredkin and Toffoli on conservative logic, we first show how energy-based P systems can be used to simulate the Fredkin gate, a reversible and conservative three-input/three-output boolean gate which is functionally complete for boolean logic. Then, we show how any reversible Fredkin circuit can be simulated by energy-based P systems whose number of membranes is independent of the number of gates occurring in the simulated circuit. The simulating P systems turn out to be themselves reversible and conservative.