Petr Sosík

Bio: Petr Sosík is an academic researcher from Silesian University. The author has contributed to research in topics: Membrane computing & P system. The author has an hindex of 20, co-authored 88 publications receiving 1247 citations. Previous affiliations of Petr Sosík include Technical University of Madrid & University of Western Ontario.

Computationally universal P systems without priorities: two catalysts are sufficient

Abstract: The original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosik considered several variants of P systems with catalysts (but without priorities) and investigated the number of catalysts needed for these specific variants to be computationally universal. It was shown that for the classic model of P systems with the minimal number of two membranes the number of catalysts can be reduced from six to five; using the idea of final states the number of catalysts could even be reduced to four. In this paper we are able to reduce the number of catalysts again: two catalysts are already sufficient. For extended P systems we even need only one membrane and two catalysts. For the (purely) catalytic systems considered by Ibarra only three catalysts are already enough.

Normal Forms for Spiking Neural P Systems

Abstract: The spiking neural P systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing. In this paper we prove a series of normal forms for spiking neural P systems, concerning the regular expressions used in the firing rules, the delay between firing and spiking, the forgetting rules used, and the outdegree of the graph of synapses. In all cases, surprising simplifications are found, without losing the computational completeness - sometimes at the price of (slightly) increasing other parameters which describe the complexity of these systems.

The computational power of cell division in P systems: Beating down parallel computers?

Abstract: We study the computational power of cell division operations in the formal framework of P systems, a mathematical model of cell-like membrane structure with regulated transport of objects (molecules) through membranes. We show that a uniform family of P systems with active membranes and 2-division is able to solve the well-known PSPACE-complete problem QBF in linear time. This result implies that such a family of P systems modelling cell division is at least as powerful as so-called Second Machine Class computers. The Second Machine Class, containing most of the fundamental parallel computer models such as parallel RAM machines of types SIMD and MIMD, vector machines and others, is characterized by using an exponential amount of resources (processing units) with respect to the computing time.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Molecular self-assembly and nanochemistry: A chemical strategy for the synthesis of nanostructures

Abstract: Molecular self-assembly is the spontaneous association of molecules under equilibrium conditions into stable, structurally well-defined aggregates joined by noncovalent bonds. Molecular self-assembly is ubiquitous in biological systems and underlies the formation of a wide variety of complex biological structures. Understanding self-assembly and the associated noncovalent interactions that connect complementary interacting molecular surfaces in biological aggregates is a central concern in structural biochemistry. Self-assembly is also emerging as a new strategy in chemical synthesis, with the potential of generating nonbiological structures with dimensions of 1 to 10(2) nanometers (with molecular weights of 10(4) to 10(10) daltons). Structures in the upper part of this range of sizes are presently inaccessible through chemical synthesis, and the ability to prepare them would open a route to structures comparable in size (and perhaps complementary in function) to those that can be prepared by microlithography and other techniques of microfabrication.

On spiking neural P systems

Abstract: This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants. A methodology based on the information given by the transition diagram associated with an SN P system is presented. The analysis of the diagram cycles codifies invariants formulae which enable us to establish the soundness and completeness of the system with respect to the problem it tries to resolve. We also study the universality of asynchronous and sequential SN P systems and the capability these models have to generate certain classes of languages. Further, by making a slight modification to the standard SN P systems, we introduce a new variant of SN P systems with a special I/O mode, called SN P modules, and study their computing power. It is demonstrated that, as string language acceptors and transducers, SN P modules can simulate several types of computing devices such as finite automata, a-finite transducers, and systolic trellis automata.

Small universal spiking neural P systems.

Abstract: In search for small universal computing devices of various types, we consider here the case of spiking neural P systems (SN P systems), in two variants: as devices that compute functions and as devices that generate sets of numbers. We start with the first case and we produce a universal spiking neural P system with 84 neurons. If a slight generalization of the used rules is adopted, namely, we allow rules for producing simultaneously several spikes, then a considerable reduction, to 49 neurons, is obtained. For SN P systems used as generators of sets of numbers, we find a universal system with restricted rules having 76 neurons and one with extended rules having 50 neurons.

A programming language for composable DNA circuits.

Abstract: Recently, a range of information-processing circuits have been implemented in DNA by using strand displacement as their main computational mechanism. Examples include digital logic circuits and catalytic signal amplification circuits that function as efficient molecular detectors. As new paradigms for DNA computation emerge, the development of corresponding languages and tools for these paradigms will help to facilitate the design of DNA circuits and their automatic compilation to nucleotide sequences. We present a programming language for designing and simulating DNA circuits in which strand displacement is the main computational mechanism. The language includes basic elements of sequence domains, toeholds and branch migration, and assumes that strands do not possess any secondary structure. The language is used to model and simulate a variety of circuits, including an entropy-driven catalytic gate, a simple gate motif for synthesizing large-scale circuits and a scheme for implementing an arbitrary system of chemical reactions. The language is a first step towards the design of modelling and simulation tools for DNA strand displacement, which complements the emergence of novel implementation strategies for DNA computing.