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The Complexity of Szilard Languages of Matrix Grammars Revisited

Cojocaru L., Mäkinen E.

Fundamenta Informaticae

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2013

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Vol. 123, nr 4

381--399

EN

The regulated rewriting mechanism is one of the most efficient methods to augment the Chomsky hierarchy with a large variety of language classes. In this paper we investigate the derivation mechanism in regulated rewriting grammars such as matrix grammars, by studying their Szilard languages. We focus on the complexity of Szilard languages associated with unrestricted and leftmost-like derivations in matrix grammars, with or without appearance checking. The reason is twofold. First, to relate these classes of languages to parallel complexity classes such as NC1 and AC1, and, second, to improve some previous results. We prove that unrestricted Szilard languages and certain leftmost Szilard languages of context-free matrix grammars, without appearance checking, can be accepted by indexing alternating Turing machines in logarithmic time and space. Consequently, these classes are included in UE-uniform NC1. Unrestricted Szilard languages of matrix grammars with appearance checking can be accepted by deterministic Turing machines in O(n log n) time and O(log n) space. Leftmost-like Szilard languages of context-free matrix grammars, with appearance checking, can be recognized by nondeterministic Turing machines by using the same time and space resources. Hence, all these classes are included in AC1.

2

(Tissue) P Systems with Unit Rules and Energy Assigned to Membranes

Alhazov A., Freund R., Leporati A., Oswald M., Zandron C.

Fundamenta Informaticae

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2006

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Vol. 74, nr 4

391-408

EN

We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for systems working in the sequential mode with a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets of languages generated by context-free matrix grammars. On the other hand, when using the maximally parallel mode, we do not need a priority relation to obtain computational completeness. Finally, we introduce the corresponding model of tissue P systems with energy assigned to the membrane of each cell and objects moving from one cell to another one in the environment as well as being able to change the energy of a cell when entering or leaving the cell. In each derivation step, only one object may pass through the membrane of each cell. When using priorities on the rules in the sequential mode (where in each derivation step only one cell is affected) as well as without priorities in the maximally parallel mode (where in each derivation step all cells possible are affected) we again obtain computational completeness, whereas without priorities on the rules in the sequential mode we only get a characterization of the family of Parikh sets of languages generated by context-free matrix grammars.

3

Membrane Systems with Coupled Transport: Universality and Normal Forms

Martin-Vide C., Paun A., Paun G., Rozenberg G.

Fundamenta Informaticae

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2002

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Vol. 49, nr 1-3

1-15

EN

This paper continues research on membrane systems which function by communication only, meaning that there are no evolving rules for molecules. The whole computation process relies on passage of molecules through membranes - this provides communication between regions of the membrane system. Next to transport of single molecules through membranes (uniport) we also study a coupled transport of molecules, with two molecules passing either in the same direction (symport) or in opposite directions (antiport). We study the computational power of such membrane systems and prove that using only symport one gets Turing universality. Moreover, we prove that five membranes suffice to get Turing universality, and the number of membranes can be decreased to three if forbidding context conditions for transport are used.

4

On synchronization in P systems

Paun G., Yu S

Fundamenta Informaticae

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1999

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Vol. 38, Nr 4

397-410

EN

The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can evolve, from all membranes, must evolve. We consider here the case when this restriction is removed. As expected, unsynchronized systems (even using catalysts) are weaker than the synchronized ones, providing that no priority relation among rules is considered. The power of P systems is not diminished when a priority is used and, moreover, the catalysts can change their states, among two possible states for each catalyst.