We first give a historical overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters. We consider the number of membranes (cells in tissue P systems), the weight of the rules, and the number of objects. Then we establish our newest results: P systems with only one membrane, symport rules of weight three, and with only seven additional objects remaining in the skin membrane at the end of a halting computation are computationally complete; P systems with minimal cooperation, i.e., P systems with symport/antiport rules of size one and P systems with symport rules of weight two, are computationally complete with only two membranes with only three and six, respectively, superfluous objects remaining in the output membrane at the end of a halting computation.

Computational power of symport/antiport : History, advances, and open problems

5′ → 3′ WK-automata are Watson-Crick automata whose two heads start on opposite ends of the input word and always run in opposite directions. One full reading in both directions is called a run. We prove that the expressive power of these automata increases with every additional run that they can make, both for deterministic and non-deterministic machines. This defines two incomparable infinite hierarchies of language classes between the regular and the context-sensitive languages. These hierarchies are complemented with classes defined by several restricted variants of 5′ → 3′ WK-automata like stateless automata. Finally we show that several standard problems are undecidable for languages accepted by 5′ → 3′ WK-automata in only one run, for example the emptiness and the finiteness problems.

5' → 3' Watson-Crick Automata with Several Runs.

Test-driven development is a software development methodology that has recently gained a great deal of traction in the software development community. It focuses on creating software-based test cases that define the business requirements of an application before beginning the coding of the application itself. This paper proposes that test-driven development could be a useful methodology for data warehouse projects, in that it could help team members avoid some of the major pitfalls of data warehousing, and result in a higher-quality end product.

Test-Driven Development of Data Warehouses

Computational completeness is known for P systems with two catalysts and purely catalytic P systems with three catalysts as well as for P systems with one bi-stable catalyst We complete this picture by showing computational completeness for purely catalytic P systems with one bi-stable catalyst and one catalyst Moreover, we present some concrete universal P systems, eg, for P systems with one multi-stable catalyst and for P systems with multiple catalysts Furthermore, we optimize the descriptional complexity of Minsky's reduction from register machines with an arbitrary number of registers to register machines with only two registers In that way, we are able to transform the universal machines U22 and U20 of Korec into weakly universal register machines with only two decrementable registers, one even with unencoded output Based on these universal register machines, we then construct small universal P systems with one bi-stable catalyst and one catalyst as well as small universal purely catalytic P systems with three catalysts With respect to the number of rules, the smallest universal P systems can be obtained with multi-stable catalysts and with multiple catalysts The number of rules in all these systems can be further reduced by adding the concept of toxic objects a specified subset of objects, where all computation branches not evolving all toxic objects in every computation step do not yield a result

Variants of Small Universal P Systems with Catalysts

Computational power of symport/antiport: history, advances, and open problems

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a â€œbridgeâ€ between these domains is important, for instance, by designing P systems reproducing the modus ponens-based forward and backward chaining that can be used as tools for reasoning in propositional logic. In this paper, the authors show how powerful and intuitive the formalism of membrane computing is and how it can be used to represent concepts and notions from unrelated areas.

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Forward and Backward Chaining with P Systems

In this paper obligatory hybrid networks of evolutionary processors (a variant of hybrid networks of evolutionary processors model) are proposed. In the obligatory hybrid network of evolutionary processors a node discards the strings to which no operations are applicable. We show that such networks have the same computability power as Turing machines only using one operation per node (deletion on the left end and insertion on the right end of the string) no rewriting and no filters.

Obligatory hybrid networks of evolutionary processors

In this paper we consider symport/antiport P systems with one membrane and rules having at most two objects. Although it has been proved that only finite number sets can be generated by both OP1(sym2) (one-membrane systems with symport rules of weight at most 2) and OP1(sym1, anti1) (one-membrane systems with symport/antiport rules of weight 1), the exact characterization is still an open question. We give some lower bounds, consider a few extensions, and state some open questions.

Minimal Cooperation in Symport/Antiport P Systems with One Membrane

In this paper we consider universal systems based on splicing. As in previous works, we take the number of rules as the parameter for the descriptional complexity. We present three results: universal double splicing extended H system with 5 rules, universal splicing test tube system with 8 rules and a universal splicing P system with 5 rules.

On small universal splicing systems

P systems are a model of compartmentalized multiset rewriting inspired by the structure of living cells and the way they function. In this paper, we focus of a variant in P systems in which membranes have limited capacity, i.e., the number of objects they may hold is limited by a fixed bound. This feature corresponds to an important physical property of cellular compartments. We propose several possible semantics of limited capacity and show that one of them allows real-time simulations of partially blind register machines, while the other one allows for obtaining computational completeness.

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Artiom Alhazov

Papers

Forward and Backward Chaining with P Systems

Obligatory hybrid networks of evolutionary processors

Minimal Cooperation in Symport/Antiport P Systems with One Membrane

On small universal splicing systems

P systems with limited number of objects