PROBABILISTIC REWRITING P SYSTEMS

2003 ◽  
Vol 14 (01) ◽  
pp. 157-166 ◽  
Author(s):  
MUTYAM MADHU
Keyword(s):  
P Systems ◽  
Cut Point ◽  
Recursively Enumerable ◽  
The Family ◽  
Rewriting Rules ◽  
Recursively Enumerable Languages ◽  
Selection Of

In this paper we define a variant of P systems, namely, probabilistic rewriting P systems, where the selection of rewriting rules is probabilistic. We show that, with non-zero cut-point, probabilistic rewriting P systems with/without priorities generate only finite languages, but with zero cut/point and without priorities, probabilistic rewriting P systems of degree 1 characterize the family of languages generated by matrix grammars. We also prove that probabilistic rewriting P systems of degree 1 with zero cut-point and priorities characterize recursively enumerable languages.

COMPUTING WITH MEMBRANES (P SYSTEMS): A VARIANT

2000 ◽  
Vol 11 (01) ◽  
pp. 167-181 ◽  
Author(s):  
GHEORGHE PĂUN
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Pass Through ◽  
The One ◽  
Priority Relation ◽  
Recursively Enumerable Languages ◽  
Biochemical Features ◽  
Computing Models

Membrane Computing is a recently introduced area of Molecular Computing, where a computation takes place in a membrane structure where multisets of objects evolve according to given rules (they can also pass through membranes). The obtained computing models were called P systems. In basic variants of P systems, the use of objects evolution rules is regulated by a given priority relation; moreover, each membrane has a label and one can send objects to precise membranes, identified by their labels. We propose here a variant where we get rid of both there rather artificial (non-biochemical) features. Instead, we add to membranes and to objects an "electrical charge" and the objects are passed through membranes according to their charge. We prove that such systems are able to characterize the one-letter recursively enumerable languages (equivalently, the recursively enumerable sets of natural numbers), providing that an extra feature is considered: the membranes can be made thicker or thinner (also dissolved) and the communication through a membrane is possible only when its thickness is equal to 1. Several open problems are formulated.

scholarly journals Adding Matrix Control: Insertion-Deletion Systems with Substitutions III

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 131
Author(s):  
Martin Vu ◽  
Henning Fernau
Keyword(s):  
Turing Machines ◽  
Biological Mechanisms ◽  
Computational Completeness ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Short Program ◽  
Matrix Control ◽  
Recursively Enumerable Languages

Insertion-deletion systems have been introduced as a formalism to model operations that find their counterparts in ideas of bio-computing, more specifically, when using DNA or RNA strings and biological mechanisms that work on these strings. So-called matrix control has been introduced to insertion-deletion systems in order to enable writing short program fragments. We discuss substitutions as a further type of operation, added to matrix insertion-deletion systems. For such systems, we additionally discuss the effect of appearance checking. This way, we obtain new characterizations of the family of context-sensitive and the family of recursively enumerable languages. Not much context is needed for systems with appearance checking to reach computational completeness. This also suggests that bio-computers may run rather traditionally written programs, as our simulations also show how Turing machines, like any other computational device, can be simulated by certain matrix insertion-deletion-substitution systems.

scholarly journals On Promoters/Inhibitors and Symport/Antiport with Traces in P Systems

Triangle ◽  
2018 ◽  
pp. 67
Author(s):  
Mihai Ionescu
Keyword(s):  
Direct Relationship ◽  
The Other ◽  
P Systems ◽  
P System ◽  
Infinite Hierarchy ◽  
Recursively Enumerable ◽  
Computational Universality ◽  
The One ◽  
Recursively Enumerable Languages

This article brings together some rather powerful results on P systems in which the computation is performed by the communication of objects through symport and antiport rules considering the trace of an object through membranes, on the one hand, and by P systems with object-rewriting non-cooperative rules, promoters/inhibitors at the level of rules and only one catalyst, on the other. It is recalled here that computational universality can be reached whit these formalisms and that some of the proofs can be sketched. Three ideas are also put forward to brake the direct relationship (infinite hierarchy) induced by the size of the considered alphabet and the number of the membranes needed in a P system (with traces) to generate recursively enumerable languages on the chosen alphabet.

Jumping Grammars

2015 ◽  
Vol 26 (06) ◽  
pp. 709-731 ◽  
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Finite Index ◽  
Open Problems ◽  
Generative Power ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x → y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x. The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars. A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

scholarly journals On the Power of Small Size Insertion P Systems

2011 ◽  
Vol 6 (2) ◽  
pp. 266 ◽  
Author(s):  
Alexander Krassovitskiy
Keyword(s):  
P Systems ◽  
Computational Power ◽  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
The Family ◽  
Context Free

In this article we investigate insertion systems of small size in the framework of P systems. We consider P systems with insertion rules having one symbol context and we show that they have the computational power of context-free matrix grammars. If contexts of length two are permitted, then any recursively enumerable language can be generated. In both cases a squeezing mechanism, an inverse morphism, and a weak coding are applied to the output of the corresponding P systems. We also show that if no membranes are used then corresponding family is equal to the family of context-free languages.

CD GRAMMAR SYSTEMS WITH REGULAR START CONDITIONS

2008 ◽  
Vol 19 (04) ◽  
pp. 767-779
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD
Keyword(s):  
Finite Index ◽  
Hybrid Mode ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
The Family ◽  
Grammar Systems ◽  
Regular Sets ◽  
Classical Derivation ◽  
Recursively Enumerable Languages

We consider cooperating distributed grammar systems with the components working in different derivation modes as well as with regular sets as additional start conditions for the components. With the classical derivation modes ≤ k and = k as well as with the internally hybrid mode (≥ ℓ∧ ≤ k) we obtain a characterization of the family of recursively enumerable languages even with only one component, with the derivation modes *, t, and ≥ k as well as with the internally hybrid mode (t∧ ≥ k) two components working in the same mode and only one common regular set for both components yield computational completeness. For the internally hybrid modes (t∧ ≤ k) and (t∧ = k) we only obtain languages of finite index, but combining one component working in one of these modes (t∧ ≤ k) and (t∧ = k) with a component working in one of the modes * and ≥ k we again obtain a characterization of the family of recursively enumerable languages.

scholarly journals When catalytic P systems with one catalyst can be computationally complete

2021 ◽  
Author(s):  
Artiom Alhazov ◽  
Rudolf Freund ◽  
Sergiu Ivanov
Keyword(s):  
Computational Complexity ◽  
P Systems ◽  
Membrane Systems ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets

AbstractCatalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.

Counseling Parents of Children With Behavior Problems: The Use of Extinction and Time-Out Techniques

PEDIATRICS ◽  
1977 ◽  
Vol 59 (1) ◽  
pp. 78-85
Author(s):  
Ronald S. Drabman ◽  
Greg Jarvie
Keyword(s):  
Problem Behaviors ◽  
Inappropriate Behavior ◽  
Time Intervals ◽  
Alternative Behavior ◽  
Home Setting ◽  
Time Out ◽  
Behavior Response ◽  
Disciplinary Problems ◽  
The Family ◽  
Selection Of

The pediatrician is the professional most frequently sought out for advice concerning disciplinary problems with children in the home. Behavioral psychologists have advocated the use of contingent ignoring and time-out procedures to help reduce problem behaviors; however, practicing pediatricians have found that these two procedures are often not successful. In fact, sometimes the two procedures seem to exacerbate inappropriate behavior. This paper documents the difficulties found in using the ignoring and/or time-out procedures in the home setting. Potential pitfalls in the use of ignoring, including not specifying the target behavior, not taking a baseline, inadvertently, intermittently reinforcing the inappropriate behavior, response bursts, spontaneous recovery, and not reinforcing an appropriate alternative behavior, are described. In addition, several pitfalls in the use of the time-out procedure, including selection of isolation area, inappropriate selection of time intervals, interference from others in the family, and escape attempts on the part of the child are discussed. For each potential problem a remedy is suggested.

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