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"

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

P Systems: from Anti-Matter to Anti-Rules

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for rule labels as objects and anti-rule labels as the corresponding annihilation counterpart in P systems. In the presence of a corresponding anti-rule object, annihilation of a rule object happens before the rule that the rule object represents, can be applied. Applying a rule consumes the corresponding rule object, but may also produce new rule objects as well as anti-rule objects, too. Computational completeness in this setting then can be obtained in a one-membrane P system with non-cooperative rules and rule / anti-rule annihilation rules when using one of the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (i.e., non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects). When using the sequential derivation mode, at least the computational power of partially blind register machines is obtained

P Systems with Minimal Left and Right Insertion and Deletion

In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol

Controlled Rewriting Using Productions and Reductions

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages

Playing with Derivation Modes and Halting Conditions

In the area of P systems, besides the standard maximally parallel derivation mode, many other derivation modes have been investigated, too. In this paper, many variants of hierarchical P systems and tissue P systems using different derivation modes are considered and the effects of using di erent derivation modes, especially the maximally parallel derivation modes and the maximally parallel set derivation modes, on the generative and accepting power are illustrated. Moreover, an overview on some control mechanisms used for (tissue) P systems is given. Furthermore, besides the standard total halting mode, we also consider different halting conditions such as unconditional halting and partial halting and explain how the use of different halting modes may considerably change the computing power of P systems and tissue P systems

On Parallel Array P Systems

We further investigate the parallel array P systems recently introduced by K.G. Subramanian, P. Isawasan, I. Venkat, and L. Pan. We rst make explicit several classes of parallel array P systems (with one or more axioms, with total or maximal parallelism, with rules of various types). In this context, some results from the above mentioned paper by Subramanian et al. are improved. A series of open problems are formulated

P Systems with Minimal Left and Right Insertion and Deletion

Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.

M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of M-adhesive categories, where M-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules

First Steps Towards a Geometry of Computation

We introduce a geometrical setting which seems promising for the study of computation in multiset rewriting systems, but could also be applied to register machines and other models of computation. This approach will be applied here to membrane systems (also known as P systems) without dynamical membrane creation. We discuss the role of maximum parallelism and further simplify our model by considering only one membrane and sequential application of rules, thereby arriving at asynchronous multiset rewriting systems (AMR systems). Considering only one membrane is no restriction, as each static membrane system has an equivalent AMR system. It is further shown that AMR systems without a priority relation on the rules are equivalent to Petri Nets. For these systems we introduce the notion of asymptotically exact computation, which allows for stochastic appearance checking in a priori bounded (for some complexity measure) computations. The geometrical analogy in the lattice Nd0 ; d 2 N, is developed, in which a computation corresponds to a trajectory of a random walk on the directed graph induced by the possible rule applications. Eventually this leads to symbolic dynamics on the partition generated by shifted positive cones C+ p , p 2 Nd0 , which are associated with the rewriting rules, and their intersections. Complexity measures are introduced and we consider non-halting, loop-free computations and the conditions imposed on the rewriting rules. Eventually, two models of information processing, control by demand and control by availability are discussed and we end with a discussion of possible future developments