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

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

Frequency Membrane Systems

We define a model of membrane system where each membrane is clocked independently from the others, in the sense that every derivation step is applied without a global synchronization. The computation is obtained by the execution of a limited amount of rules in each membrane, and only when they are allowed to execute a derivation step. Indeed, each membrane operates with a certain work frequency that can change across the system. Simple results show that this model is at least as powerful as the usual one, and the goal is to present a few examples that show it giving rise to interesting dynamic behaviors

On the Simulations of Evolution-Communication P Systems with Energy without Antiport Rules for GPUs

In this report, we present our initial proposal on simulating computations on a restricted variant of Evolution-Communication P system with energy (ECPe system) which will then be implemented in Graphics Processing Units (GPUs). This ECPe sys- tems variant prohibits the use of antiport rules for communication. Several possible levels of parallelizations for simulating ECPe systems computations on GPUs are emphasized. Our work is based on a localized matrix representation for the mentioned variant given in a previous literature. Our proposal employs a methodology for forward computing also discussed in the said literature.Junta de Andalucía P08-TIC04200Ministerio de Ciencia e Innovación TIN2009–1319

Reaction Cycles in Membrane Systems and Molecular Dynamics

We are considering molecular dynamics and (sequential) membrane systems from the viewpoint of Markov chain theory. The first step is to understand the structure of the configuration space, with respect to communicating classes. Instead of a reachability analysis by traditional methods, we use the explicit monoidal structure of this space with respect to rule applications. This leads to the notion of precycle, which is an element of the integer kernel of the stoichiometric matrix. The generators of the set of precycles can be effectively computed by an incremental algorithm due to Contejean and Devie. To arrive at a characterization of cycles, we introduce the notion of defect, which is a set of geometric constraints on a configuration to allow a precycle to be enabled, that is, be a cycle. An important open problem is the effcient calculation of the defects. We also discuss aspects of asymptotic behavior and connectivity, as well as give a biological example, showing the usefulness of the method for model checking

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.Comment: 19 pages, 7 figures, accepted author manuscript, to appear in J. Phys.: Cond. Mat

On Communication Complexity in Evolution-Communication P Systems

Looking for a theory of communication complexity for P systems, we consider here so-called evolution-communication (EC for short) P systems, where objects evolve by multiset rewriting rules without target commands and pass through membranes by means of symport/antiport rules. (Actually, in most cases below we use only symport rules.) We first propose a way to measure the communication costs by means of “quanta of energy” (produced by evolution rules and) consumed by communication rules. EC P systems with such costs are proved to be Turing complete in all three cases with respect to the relation between evolution and communication operations: priority of communication, mixing the rules without priority for any type, priority of evolution (with the cost of communication increasing in this ordering in the universality proofs). More appropriate measures of communication complexity are then defined, as dynamical parameters, counting the communication steps or the number (and the weight) of communication rules used during a computation. Such parameters can be used in three ways: as properties of P systems (considering the families of sets of numbers generated by systems with a given communication complexity), as conditions to be imposed on computations (accepting only those computations with a communication complexity bounded by a given threshold), and as standard complexity measures (defining the class of problems which can be solved by P systems with a bounded complexity). Because we ignore the evolution steps, in all three cases it makes sense to consider hierarchies starting with finite complexity thresholds. We only give some preliminary results about these hierarchies (for instance, proving that already their lower levels contain complex – e.g., non-semilinear – sets), and we leave open many problems and research issues.Junta de Andalucía P08 – TIC 0420