Particular Results for Variants of P Systems with One Catalyst in One Membrane

Purely catalytic P systems can generate all recursively enumerable sets of natural numbers with only three catalysts in one membrane, whereas we know that one catalyst in one membrane is not enough. On the other hand, P systems also allowing (non-catalytic) non-cooperative evolution rules with only two catalysts in one membrane are already computationally complete, too. We here investigate special variants of P systems with only one catalyst in one membrane that are not computationally complete, i.e., variants of P systems with only one catalyst in one membrane that cannot generate all recursively enumerable sets of natural numbers

One-Membrane P Systems with Activation and Blocking of Rules

We introduce new possibilities to control the application of rules based on the preceding applications, which can be de ned in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even for one-membrane P systems with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation. When we allow the application of rules to in uence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a derivation step, we can even \go beyond Turing"

On the Properties of Language Classes Defined by Bounded Reaction Automata

Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in [4]. In this paper we continue the investigation of reaction automata with a focus on the formal language theoretic properties of subclasses of reaction automata, called linearbounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and lambda-LRAs. Further, we establish new relationships of language classes accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results include the following : (i) the class of languages accepted by lambda-LRAs forms an AFL with additional closure properties, (ii) any recursively enumerable language can be expressed as a homomorphic image of a language accepted by an LRA, (iii) the class of languages accepted by ERAs coincides with the class of context-sensitive languages.Comment: 23 pages with 3 figure

Introducing the Concept of Activation and Blocking of Rules in the General Framework for Regulated Rewriting in Sequential Grammars

We introduce new possibilities to control the application of rules based on the preceding application of rules which can be de ned for a general model of sequential grammars and we show some similarities to other control mechanisms as graph-controlled grammars and matrix grammars with and without applicability checking as well as gram- mars with random context conditions and ordered grammars. Using both activation and blocking of rules, in the string and in the multiset case we can show computational com- pleteness of context-free grammars equipped with the control mechanism of activation and blocking of rules even when using only two nonterminal symbols

Small Universal Antiport P Systems and Universal Multiset Grammars

Based on the construction of a universal register machine we construct a universal antiport P system working with 31 rules in the maximally parallel mode in one membrane, and a universal antiport P system with forbidden context working with 16 rules in the sequential derivation mode in one membrane for computing any partial recursive function on the set of natural numbers. For accepting/generating any arbitrary recursively enumerable set of natural numbers we need 31/33 and 16/18 rules, respectively. As a consequence of the result for antiport P systems with forbidden context we immediately infer similar results for forbidden random context multiset grammars with arbitrary rules

Boundaries of membrane in P systems relying on multiset approximation spaces in language R

Membrane computing is an area within computer science which aims to develop a new computational model through the study of the characteristics of biological cells. It is a distributed and parallel computing model. Communication between regions through membranes, as well as membrane system and its environment, plays an important role in the process. Combination of P system with multiset approximation space leads to the abstract concept of ‘to be close enough to a membrane’. The designated goal is to perform calculations in this two-fold system by the help of language R. Some packages can perform calculations with multisets in R (such as ‘sets’ package), but they are more closely linked to fuzzy systems. In this paper a new program library in language R is initiated which had been created to encourage some fundamental calculations in membrane systems combined with multiset approximation spaces. Data structures and functions are illustrated by examples. Keywords: multiset approximation spaces, membrane computing, R languag

Reaction Automata

Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy.Comment: 19 pages, 6 figure

Multiset random context grammars, checkers, and transducers

We introduce a general model of random context multiset grammars as well as the concept of multiset random context checkers and transducers. Our main results show how recursively enumerable sets of finite multisets can be generated using these models of computing; corresponding results for antiport P systems are established, too