Solvable models for the gamma deformation having X(5) as limiting symmetry. Removing some drawbacks of the existent descriptions

Two solvable Hamiltonians for describing the dynamic gamma deformation, are proposed. The limiting case of each of them is the X(5) Hamiltonian. Analytical solutions for both energies and wave functions, which are periodic in $\gamma$, are presented in terms of spheroidal and Mathieu functions, respectively. Moreover, the gamma depending factors of the transition operator can be treated.Comment: four two column pages, 1 figur

Towards Bridging Two Cell-Inspired Models: P Systems and R Systems

We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the "threshold" and "no permanence" ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics.Junta de Andalucía P08 – TIC 0420

An infinite hierarchy of languages defined by dP systems

Here, we continue the study of the recently introduced dP automata. They are symport/antiport P systems consisting of a number of components, each one accepting a string, and working together in recognizing the concatenation of these separate strings; the overall string is distributed to the dP automaton components in a balanced way, i.e., in equal parts up to one symbol, like in the communication complexity area. The question whether or not the number of components induces an infinite hierarchy of the recognized languages was formulated as an open problem in the literature.Wesolve here affirmatively this question (by connecting P automata with right linear simple matrix grammars), then we also briefly discuss the relation between the balanced and the non-balanced way of splitting the input string among components; settling this latter problem remains as a research topic. Some other open problems are also formulated.Junta de Andalucía P08-TIC-0420

P and dP Automata: A Survey

This is a quick survey of basic notions and results related to P automata (P systems with symport/antiport rules working in the accepting mode), with some emphasis on the recently introduced dP automata (a distributed version of the standard P automata), ending with some open problems and research topics which we find of interest in this area.Junta de Andalucía P08 – TIC 0420

Languages and P Systems: Recent Developments

Languages appeared from the very beginning in membrane computing, by their length sets or directly as sets of strings. We briefly recall here this relationship, with some details about certain recent developments. In particular, we discuss the possibility to associate a control word with a computation in a P system. An improvement of a result concerning the control words of spiking neural P systems is given: regular languages can be obtained as control words of such systems with only four neurons (and with usual extended rules: no more spikes are produces than consumed). Several research topics are pointed out.Junta de Andalucía P08 – TIC 0420

P automata revisited

We continue here the investigation of P automata, in their non-extended case, a class of devices which characterize non-universal family of languages. First, a recent conjecture is confirmed: any recursively enumerable language is obtained from a language recognized by a P automaton, to which an initial (arbitrarily large) string is added. Then, we discuss possibilities of extending P automata, following suggestions from string finite automata. For instance, automata with a memory (corresponding to push-down automata) are considered and their power is briefly investigated, as well as some closure properties of the family of languages recognized by P automata. In the context, a brief survey of results about P and dP automata (a distributed version of P automata) is provided, and several further research topics are formulated.Junta de Andalucía P08-TIC-0420

dP Automata versus Right-Linear Simple Matrix Grammars

We consider dP automata with the input string distributed in an arbitrary (hence not necessary balanced) way, and we investigate their language accepting power, both in the case when a bound there is on the number of objects present inside the system and in the general case. The relation with right-linear simple matrix grammars is useful in this respect. Some research topics and open problems are also formulated.Junta de Andalucía P08 – TIC 0420

Polarizationless P Systems with Active Membranes Working in the Minimally Parallel Mode

We investigate the computing power and the efficiency of P systems with active membranes without polarizations, working in the minimally parallel mode. We prove that such systems are computationally complete and able to solve NP-complete problems even when the rules are of a restricted form, e.g., for establishing computational completeness we only need rules handling single objects and no division of non-elementary membranes is usedMinisterio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58

Spiking Neural P Systems with Neuron Division and Budding

In order to enhance the e±ciency of spiking neural P systems, we introduce the features of neuron division and neuron budding, which are processes inspired by neural stem cell division. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time. We illustrate this possibility with SAT problem.Junta de Andalucía P08 – TIC 0420

Bridging Membrane and Reaction Systems - Further Results and Research Topics

This paper continues an investigation into bridging two research areas con- cerned with natural computing: membrane computing and reaction systems. More specif- ically, the paper considers a transfer of two assumptions/axioms of reaction systems, non- permanency and the threshold assumption, into the framework of membrane computing. It is proved that: SN P systems with non-permanency of spikes assumption charac- terize the semilinear sets of numbers, and symport/antiport P systems with threshold assumption (translated as ! multiplicity of objects) can solve SAT in polynomial time. Also, several open research problems are stated.Junta de Andalucía P08 – TIC 0420