Rudolf Freund

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Steven J. Miller

Williams College

Andreas Umland

National University of "Kyiv-Mohyla Academy"

Armando Marques-Guedes

UNL - New University of Lisbon

John Sutton

Macquarie University

Eros Carvalho

Universidade Federal do Rio Grande do Sul

Stephanie Seul

University of Bremen

Ibrahim Cahit

Near East University

Stefano Villani

University of Maryland

Kobi Kabalek

Pennsylvania State University

Jakob Tanner

University of Zurich, Switzerland

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Papers by Rudolf Freund

Contextual Array Grammars

Series in Machine Perception and Artificial Intelligence

Watson-Crick finite automata

DNA Based Computers III

ABSTRACT

Variants of Small Universal P Systems with Catalysts

Fundamenta Informaticae

ABSTRACT Computational completeness is known for P systems with two catalysts and purely catalyti... more ABSTRACT 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, e.g., for P systems with one multi-stable catalyst and for P systems with multiple catalysts. Furthermore, we optimize the descriptional complexity of Minsky&#39;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.

Length P Systems

Fundamenta Informaticae

ABSTRACT In this paper, we examine P systems with a linear membrane structure, i.e., P systems in... more ABSTRACT In this paper, we examine P systems with a linear membrane structure, i.e., P systems in which only one membrane is elementary and the output of which is read out as the sequence of membrane labels in the halting configuration or vectors/numbers represented by this sequence. We investigate the computational power of such systems, depending on the number of membrane labels, kinds of rules used, and some other possible restrictions. We prove that two labels, elementary membrane creation and dissolution, together with the usual send-in and send-out rules, suffice to achieve computational completeness, even with the restriction that only one object is allowed to be present in any configuration of the system. On the other hand, limiting the number of labels to one reduces the computational power to the regular sets of non-negative integers. We also consider other possible variants of such P systems, e.g., P systems in which all membranes but one have the same label, P systems with membrane duplication rules, or systems in which multiple objects are allowed to be present in a configuration, and we describe the computational power of all these models.

Catalytic and Purely Catalytic P Systems and P Automata: Control Mechanisms for Obtaining Computational Completeness

Fundamenta Informaticae

ABSTRACT The questions whether catalytic P systems with only one catalyst and purely catalytic P ... more ABSTRACT The questions whether catalytic P systems with only one catalyst and purely catalytic P systems with only two catalysts can already be computationally complete in the generative case, still are open problems. For accepting P systems or P automata, the situation is even more complicated when we consider sets of vectors of natural numbers and not only sets of natural numbers - the number of catalysts increases with the dimension of the vectors. We here establish computational completeness for catalytic P systems and P automata with only one catalyst as well as for purely catalytic P systems and P automata with only two catalysts in the skin membrane by using specific variants of additional control mechanisms: in P systems and P automata with label selection, we only use rules from one set of a finite number of sets of rules in each computation step; in time-varying P systems and P automata the available sets of rules change periodically with time. The same control mechanisms also allow for computing partial recursive relations or functions of (vectors of) natural numbers when being used in catalytic P systems with one catalyst and purely catalytic P systems with two catalysts. Finally, these variants of P systems can also be used to generate or accept strings and to compute partial relations or functions on strings, and again we obtain computational completeness with only one catalyst in the case of catalytic P systems and two catalysts in the case of purely catalytic P systems.

Partial Halting and Minimal Parallelism Based on Arbitrary Rule Partitions

Fundamenta Informaticae

We consider a new variant of the halting condition in P systems, i.e., a computation in a P syste... more We consider a new variant of the halting condition in P systems, i.e., a computation in a P system is already called halting if not for all membranes a rule is applicable anymore at the same time, whereas usually a computation is called halting if no rule is applicable anymore in the whole system. This new variant of partial halting is especially investigated for several variants of P systems using membrane rules with permitting contexts and working in different transition modes, especially for minimal parallelism. Both partial halting and minimal parallelism are based on an arbitrary set of subsets from the set of rules assigned to the membranes.

Rudolf Freund

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