Author name cluster

Petr Sosík

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

12 papers

1 author row

TCS Journal 2018 Journal Article

Generalized P colonies with passive environment

Lucie Ciencialová
Luděk Cienciala
Petr Sosík

We study two variants of P colonies with initial content of P colony and so-called passive environment: P colonies with two objects inside each agent that can only consume or generate objects, and P colonies with one object inside each agent using rewriting and communication rules. We show that the first kind of P colonies with one consumer agent and one sender agent can generate all sets of natural numbers computed by register machines, and hence they are computationally complete in the Turing sense. Similarly, also the second kind of systems with three agents with rewriting/communication rules is computationally complete. The paper improves previously published universality results concerning generalized P colonies, and it also extends the knowledge about very simple multi-agent systems capable of universal computation.

Details DOI

TCS Journal 2016 Journal Article

Small (purely) catalytic P systems simulating register machines

Petr Sosík
Miroslav Langer

The paper contributes to the topic of (purely) catalytic P systems. Catalytic P systems represent the original and likely the simplest class of membrane computing models. It is known that (purely) catalytic P systems with two (respectively three) catalysts and one membrane can simulate any Minsky register machine and, hence, they are computationally complete. However, the problem of minimal size of such a universal catalytic P system remains open for about ten years. We improve known results about small catalytic P systems simulating register machines in three different modes (generating, accepting, computing functions). Together with some specific universal register machine [7], one could eventually construct a small universal catalytic P system. As a consequence, we also improve the previous construction of a minimal catalytic P system generating a non-semilinear set, diminishing the number of necessary rules from 29 to 24.

Details DOI

TCS Journal 2013 Journal Article

P systems with proteins on membranes characterize PSPACE

Petr Sosík
Andrei Păun
Alfonso Rodríguez-Patón

The paper studies algorithmic properties of operations with membrane proteins modeled within the framework of membrane systems (also called P systems). Membrane systems are biologically inspired models of parallel and distributed computing based on the information processing in cells and cellular membranes. We show that the computational potential of P systems with proteins on membranes is equivalent to that of parallel computing models as the alternating Turing machine or the PRAM. These abstract machines characterize by their polynomial time-bounded computations the class PSPACE, and simultaneously they serve as idealized models of real parallel machines. Therefore, this and other related results suggest the existence of a homology between the potential of silicon and biological parallel information processing.

Details DOI

TCS Journal 2011 Journal Article

On the scalability of biocomputing algorithms: The case of the maximum clique problem

Daniel Manrique
Alfonso Rodríguez-Patón
Petr Sosík

The paper aims at demonstrating and confirming that breadth first search or pruning techniques can substantially improve the effectiveness of biomolecular algorithms. A breadth first search-based DNA algorithm solving the maximum clique problem for a graph is presented, and its complexity and scalability parameters are studied. The analysis shows that parameters like the number of steps, the length and volume of DNA strands, the number of enzymes and the concentration of the molecules encoding solutions are dramatically improved in comparison with previous approaches to the same problem and, theoretically, they would allow to process graphs with thousands of vertices. These parameters are also compared with several related results focusing on the scalability of DNA computing methods. Finally, an analysis of error-resistance of the algorithm is given.

Details DOI

TCS Journal 2008 Journal Article

On the weight of universal insertion grammars

Lila Kari
Petr Sosík

We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. We also study an application in DNA computing and improve some known results concerning the power of insertion–deletion DNA systems.

Details DOI

TCS Journal 2007 Journal Article

Normal forms for spiking neural P systems

Oscar H. Ibarra
Andrei Păun
Gheorghe Păun
Alfonso Rodríguez-Patón
Petr Sosík
Sara Woodworth

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.

Details DOI

TCS Journal 2006 Journal Article

Algebraic properties of substitution on trajectories

Michael Domaratzki
Petr Sosík
Alfonso Rodríguez-Patón

Language operations on trajectories provide a generalization of many common operations such as concatenation, quotient, shuffle and others. A trajectory is a syntactical condition determining positions where an operation is applied. Besides their elegant language-theoretical properties, the operations on trajectories have been used to solve problems in coding theory, bio-informatics and concurrency theory. We focus on algebraic properties of substitution on trajectories. Their characterization in terms of language-theoretical properties of the associated sets of trajectories is given. The transitivity property is of particular interest. Unlike, e. g. , shuffle on trajectories, in the case of substitution the transitive closure of a regular set of trajectories is again regular. This result has consequences in the above-mentioned application areas.

Details DOI

TCS Journal 2005 Journal Article

Aspects of shuffle and deletion on trajectories

Lila Kari
Petr Sosík

Word and language operations on trajectories provide a general framework for the study of properties of sequential insertion and deletion operations. A trajectory gives a syntactical constraint on the scattered insertion (deletion) of a word into(from) another one, with an intuitive geometrical interpretation. Moreover, deletion on trajectories is an inverse of the shuffle on trajectories. These operations are a natural generalization of many binary word operations like catenation, quotient, insertion, deletion, shuffle, etc. Besides they were shown to be useful, e. g. in concurrent processes modelling and recently in biocomputing area. We begin with the study of algebraic properties of the deletion on trajectories. Then we focus on three standard decision problems concerning linear language equations with one variable, involving the above mentioned operations. We generalize previous results and obtain a sequence of new ones. Particularly, we characterize the class of binary word operations for which the validity of such a language equation is (un)decidable, for regular and context-free operands.

Details DOI

TCS Journal 2005 Journal Article

Computationally universal P systems without priorities: two catalysts are sufficient

Rudolf Freund
Lila Kari
Marion Oswald
Petr Sosík

The original model of P systems with symbol objects introduced by Păun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosík and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosík 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.

Details DOI

TCS Journal 2005 Journal Article

On properties of bond-free DNA languages

Lila Kari
Stavros Konstantinidis
Petr Sosík

The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a double-stranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.

Details DOI

TCS Journal 2003 Journal Article

Watson–Crick D0L systems: generative power and undecidable problems

Petr Sosík

The properties of Watson–Crick D0L system, a language–theoretical formalism inspired by natural DNA processing, are studied. The model incorporates the iterated D0L-like morphism and the DNA complementarity principle represented by a letter-to-letter morphism. These two morphisms are connected by a natural condition called the trigger. We show first that this very simple model has rather unexpected power; it can closely and simply simulate any Minsky register machine. As a consequence, any recursively enumerable language can be obtained as a projection of the language of some standard Watson–Crick D0L system. Finally, we show that the graph reachability problem, equivalence problems and some other problems of standard Watson–Crick D0L systems are undecidable.

Details DOI

TCS Journal 2003 Journal Article

Watson–Crick D0L systems: the power of one transition

Arto Salomaa
Petr Sosík

We investigate the class of functions computable by uni-transitional Watson–Crick D0L systems: only one complementarity transition is possible during each derivation. The class is characterized in terms of a certain min-operation applied to Z -rational functions. We also exhibit functions outside the class, and show that the basic decision problems are equivalent or harder than a celebrated open problem. For instance, the latter alternative applies to the growth-bound problem for functions in the class.

Details DOI