Control Words of Transition P Systems
01 Jan 2013-pp 145-155
TL;DR: A new way of associating a language with the computation of a P system, where the labels are chosen from a finite alphabet or \(\lambda .\) is considered, that associates a string that is obtained by concatenating the labels of the rules in the transition sequence corresponding to a computation.
Abstract: A new way of associating a language with the computation of a P system is considered. A label is assigned to every rule in a P system, where the labels are chosen from a finite alphabet or \(\lambda .\) We associate a string, called control word, that is obtained by concatenating the labels of the rules in the transition sequence corresponding to a computation. We study the generative capacity of such control languages comparing them with family of languages such as regular, context-free, context-sensitive and recursively enumerable languages of Chomskian hierarchy.
Citations
More filters
TL;DR: It is proved that tissue P systems with antiport rules of weight one and without symport rules characterize regular languages and that the rule complexity is crucial for tissues P systems to achieve a desired computational power.
72 citations
Cites background or methods from "Control Words of Transition P Syste..."
...In this work, we give a new way to associate the computation result with the rules used during a computation, which is slightly different from that defined in [13,16,17]....
[...]
...Note that the way of label restricted transitions defined in this work is slightly different from that given in [13,16,17], where the authors considered transitions between configurations that use only rules with the same label b and rules labeled with k (that is, the labels of the used rules can be both b and k instead of only one of b or k)....
[...]
...The control language with such a label restriction was also investigated in transition P systems [16] and neural-like tissue P systems [17]....
[...]
...Recently, control languages have been considered for P systems [3,13,16,17]....
[...]
01 Jan 2013
TL;DR: The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length set of ET0L and of recursively enumerable languages.
Abstract: We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered in each step, all rules used have either the same label, or, possibly, the empty label, λ, then P systems with the computations controlled by languages as in context-free controlled grammars. The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework. A series of open problems and research topics are formulated.
15 citations
Cites background from "Control Words of Transition P Syste..."
...The first one, followed in [1], assumes the computations sequential, but here we follow the way suggested in [6] and further explored in [7]: in a step one may use only rules with the same label from a given set of labels, maybe also rules having no label (we say that such a rule has an empty label, denoted by λ)....
[...]
01 Jul 2013
TL;DR: This work considers a way to associate a language with the computations of a tissue P system, and assigns a label to every rule, where the labels are chosen from an alphabet or the label can be λ.
Abstract: We consider a way to associate a language with the computations of a tissue P system. We assign a label to every rule, where the labels are chosen from an alphabet or the label can be λ. The rules used in a transition should have either the empty label or the same label from the chosen alphabet. In this way, a string is associated with each halting computation, called the control word of the computation. The set of all control words associated with computations in a tP system form the control language of the system. We study the family of control languages of tP systems in comparison with the families of finite, regular, context-free, context-sensitive, and recursively enumerable languages.
10 citations
TL;DR: It is shown that context-free languages can be generated as Szilard and control languages and any non-empty context- free language is a morphic image of the SzILard language of this type of system with finite set of rules and axioms.
Abstract: Derivation languages are language theoretical tools that describe halting derivation processes of a generating device. We consider two types of derivation languages, namely Szilard and control languages for splicing systems where iterated splicing is done in non-uniform way defined by Mitrana, Petre and Rogojin in 2010. The families of Szilard (rules and labels are mapped in a one to one manner) and control (more than one rule can share the same label) languages generated by splicing systems of this type are then compared with the family of languages in the Chomsky hierarchy. We show that context-free languages can be generated as Szilard and control languages and any non-empty context-free language is a morphic image of the Szilard language of this type of system with finite set of rules and axioms. Moreover, we show that these systems with finite set of axioms and regular set of rules are capable of generating any recursively enumerable language as a control language.
9 citations
Cites background or methods from "Control Words of Transition P Syste..."
...The characterization of such control languages in terms of Chomsky hierarchy has been discussed for various P systems [15, 16, 21, 20]....
[...]
...The study of the derivation process has also been extended in the context of P systems ([15, 16, 21, 20])....
[...]
...Control languages have already been discussed for several variants of, for example, tissue P systems, spiking neural P systems, and P systems with isotonic array grammars ([15, 16, 21, 20]) to name a few....
[...]
...Note that we use the terms control word and control language in the sense of [15, 16, 21, 20] which differs from their original use [19]....
[...]
01 Dec 2017
TL;DR: Results on the language family generated by the labelled splicing system in comparison with the language families of the Chomsky hierarchy, including recursively enumerable languages, are obtained by involving only either one or two membranes in the P systems considered.
Abstract: Labelled splicing P systems are distributed parallel computing models, where sets of strings that evolve by splicing rules are labelled. In this work, we consider labelled splicing systems with the following modifications: (i) The strings in the membranes are present in arbitrary number of copies; (ii) the rules in the regions are finite in number. Results on the language family generated by the labelled splicing system in comparison with the language families of the Chomsky hierarchy, including recursively enumerable languages, are obtained, by involving only either one or two membranes in the P systems considered.
8 citations
References
More filters
TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.
2,327 citations
"Control Words of Transition P Syste..." refers background or methods in this paper
...We construct a P system Π = (O,{1}, [1]1,s,R1, / 0) , where Control Words of Transition P Systems 153...
[...]
...In Section 3, we give the definition of a system as defined in [1]....
[...]
...We construct a P system with one membrane Π2 = ({a1,b1,c1},{1}, [1]1,a1,λ ,R1, / 0) where,...
[...]
...P systems introduced in [1] by Gh....
[...]
...Using G′, we construct a P system with one membrane Π = (N′∪{$},{1}, [1]1,A1,R1, / 0) as follow:...
[...]
Book•
01 Jan 1967TL;DR: In this article, the authors present an abstract theory that categorically and systematically describes what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment, and the abstract theory tells us in no uncertain terms that the machines' potential range is enormous and that its theoretical limitations are of the subtlest and most elusive sort.
Abstract: From the Preface (See Front Matter for full Preface)
Man has within a single generation found himself sharing the world with a strange new species: the computers and computer-like machines. Neither history, nor philosophy, nor common sense will tell us how these machines will affect us, for they do not do "work" as did machines of the Industrial Revolution. Instead of dealing with materials or energy, we are told that they handle "control" and "information" and even "intellectual processes." There are very few individuals today who doubt that the computer and its relatives are developing rapidly in capability and complexity, and that these machines are destined to play important (though not as yet fully understood) roles in society's future. Though only some of us deal directly with computers, all of us are falling under the shadow of their ever-growing sphere of influence, and thus we all need to understand their capabilities and their limitations.
It would indeed be reassuring to have a book that categorically and systematically described what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment. However, although some books have purported to do this, it cannot be done for the following reasons: a) Computer-like devices are utterly unlike anything which science has ever considered---we still lack the tools necessary to fully analyze, synthesize, or even think about them; and b) The methods discovered so far are effective in certain areas, but are developing much too rapidly to allow a useful interpretation and interpolation of results. The abstract theory---as described in this book---tells us in no uncertain terms that the machines' potential range is enormous, and that its theoretical limitations are of the subtlest and most elusive sort. There is no reason to suppose machines have any limitations not shared by man.
2,219 citations
"Control Words of Transition P Syste..." refers background in this paper
..., [7]) that register machines (even with only three registers, but this detail is not relevant in what follows) accepts all sets of numbers which are Turing computable....
[...]
Book•
01 Jan 2002
TL;DR: This chapter discusses Membrane Computing, What It Is and What It is Not, and attempts to get back to reality with open problems and Universality results.
Abstract: Preface.- 1. Introduction: Membrane Computing, What It Is and What It Is Not.- 2. Prerequisites.- 3. Membrane Systems with Symbol-Objects.- 4. Trading Evolution for Communication.- 5. Structuring Objects.- 6. Networks of Membranes.- 7. Trading Space for Time.- 8. Further Technical Results.- 9. (Attempts to Get) Back to Reality.- Open Problems.- Universality Results. Bibliography.- Index.
1,760 citations
TL;DR: It is shown that for any recursively enumerable language, a Pautomaton and a certain type of projection can be constructed such that the given language is obtained as the image of the set of accepted input multiset sequences of the PAutomaton.
Abstract: In this paper we introduce the notion of a Pautomaton with one-way communication, a concept related both to Psystems and the traditional concept of automata. A Pautomaton with one-way communication is a purely communicating accepting P system. The result of the computation in these systems is the set of multiset sequences consumed by the skin membrane, supposing that the Pautomaton started functioning in an initial state and entered a so-called final state. As a result, we show that for any recursively enumerable language, a Pautomaton and a certain type of projection can be constructed such that the given language is obtained as the image of the set of accepted input multiset sequences of the Pautomaton.
87 citations
TL;DR: The fundamental properties of computations in such P systems with external output are investigated, including the computing power, normal forms, and basic decision problems.
Abstract: A membrane computing system (also called P system) consists of computing cells which are organized hierarchically by the inclusion relation: cells may include cells, which again may include cells, etc Each cell is enclosed by its membrane Each cell is an independent computing agent with its own computing program, which produces objects The interaction between cells consists of the exchange of objects through membranes The output of a computation is a partially ordered set of objects which leave the system through its external membrane The fundamental properties of computations in such P systems with external output are investigated These include the computing power, normal forms, and basic decision problems
67 citations