Spiking Neural P Systems with Cooperating Rules
20 Aug 2014-pp 314-329
TL;DR: This paper considers the terminating mode, in which the switching occurs when no rule is enabled in the active component of any neuron in the system, and investigates the computational power of asynchronous and sequential SN P systems with standard rules.
Abstract: The concept of cooperation and distribution as known from grammar systems is introduced to spiking neural P systems (in short, SN P systems) in which each neuron has a finite number of sets (called components) of rules. During computations, at each step only one of the components can be active for the whole system and one of the enabled rules from this active component of each neuron fires. The switching between the components occurs under different cooperation strategies. This paper considers the terminating mode, in which the switching occurs when no rule is enabled in the active component of any neuron in the system. By introducing this new mechanism, the computational power of asynchronous and sequential SN P systems with standard rules is investigated. The results are that asynchronous standard SN P systems with two components and strongly sequential unbounded SN P systems with two components are Turing complete.
Citations
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Journal Article•
TL;DR: Characterizations of sets definable by partially blind multicounter machines in terms of k-output SNPs operating in a sequential mode are given and slight variations of the models make them universal.
Abstract: A κ-output spiking neural P system (SNP) with output neurons, O 1 ,..., O k , generates a tuple (n 1 ,..., n k ) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each O i generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is n i . After the output neurons generate their pairs of spikes, the system eventually halts. We give characterizations of sets definable by partially blind multicounter machines in terms of κ-output SNPs operating in a sequential mode. Slight variations of the models make them universal.
26 citations
01 Mar 2021
TL;DR: In this article, a universal SNPSP system with structural plasticity was proposed, where all the neurons in the system use the same set of rules and the behavior of a neuron can be "programmed" by giving it a set of different rules.
Abstract: Spiking neural P system (SNP system) is a model of computation inspired by the mechanism of spiking neurons. An SNP system is a directed graph of neurons that can communicate with each other using an object known as a spike (the object spike represents action potential or nerve impulse). Spiking neural P systems with structural plasticity (SNPSP system) is a variant of the SNP system model. It incorporates the concept of structural plasticity to the SNP system model. SNPSP systems have the ability to add and delete connections between neurons. In SNPSP systems, the behavior of a neuron can be “programmed” by giving it a set of rules. Different set of rules will result in different behaviors. In this work, we show that it is possible to construct a universal SNPSP system where all the neurons in the system use the same set of rules. Such systems are called homogeneous SNPSP systems.
24 citations
TL;DR: It is proved that asynchronous PSN P systems with extended rules (the application of a rule can produce more than one spikes) or standard rules (all rules can only produce a spike) can both characterize partially blind counter machines, hence, such systems are not Turing universal.
18 citations
20 Aug 2014
TL;DR: By using 59 neurons, a small universal SN P system with two components, working in the terminating mode, is constructed for computing functions.
Abstract: The paper considers spiking neural P systems (SN P systems) with cooperating rules where each neuron has the same number of sets of rules, labelled identically. Each set is called a component (maybe empty). At each step only one of the components can be active for the whole system, and only the rules from the active component are enabled. Each neuron with enabled rules from this active component can fire. By using 59 neurons, a small universal SN P system with two components, working in the terminating mode, is constructed for computing functions.
7 citations
Cites background or methods from "Spiking Neural P Systems with Coope..."
...The concept of cooperation and distribution as known from the CD grammar systems is introduced to spiking neural P systems [4]....
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...In this paper, we take on one of the problems mentioned in [4]....
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...Cooperating SN P systems are indeed more powerful by offering seamless synchronization without the use of any delays as seen in [4], where computational completeness has been proved for asynchronous as well as sequential cooperating SN P systems with two components using unbounded as well as general neurons...
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2 citations
References
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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
01 Apr 1997
TL;DR: This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field.
Abstract: The theory of formal languages is the oldest and most fundamental area of theoretical computer science. It has served as a basis of formal modeling from the early stages of programming languages to the recent beginnings of DNA computing. This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field. Best specialists of various subareas, altogether 50 in number, are among the authors. The maturity of the field makes it possible to include a historical perspective in many presentations. The individual chapters can be studied independently, both as a text and as a source of reference. The Handbook is an invaluable aid for advanced students and specialists in theoretical computer science and related areas in mathematics, linguistics, and biology.
1,915 citations
Journal Article•
TL;DR: In this article, the authors introduce a class of neural-like P systems which they call spiking neural P systems (in short, SN P systems), in which the result of a computation is the time between the moments when a specified neuron spikes.
Abstract: This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural P systems (in short, SN P systems). In these devices, the time (when the neurons fire and/or spike) plays an essential role. For instance, the result of a computation is the time between the moments when a specified neuron spikes. Seen as number computing devices, SN P systems are shown to be computationally complete (both in the generating and accepting modes, in the latter case also when restricting to deterministic systems). If the number of spikes present in the system is bounded, then the power of SN P systems falls drastically, and we get a characterization of semilinear sets. A series of research topics and open problems are formulated.
589 citations
TL;DR: This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants, and proposes a methodology based on the information given by the transition diagram associated with an SN P system which establishes the soundness and completeness of the system with respect to the problem it tries to resolve.
Abstract: This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants. A methodology based on the information given by the transition diagram associated with an SN P system is presented. The analysis of the diagram cycles codifies invariants formulae which enable us to establish the soundness and completeness of the system with respect to the problem it tries to resolve. We also study the universality of asynchronous and sequential SN P systems and the capability these models have to generate certain classes of languages. Further, by making a slight modification to the standard SN P systems, we introduce a new variant of SN P systems with a special I/O mode, called SN P modules, and study their computing power. It is demonstrated that, as string language acceptors and transducers, SN P modules can simulate several types of computing devices such as finite automata, a-finite transducers, and systolic trellis automata.
408 citations
10 Jul 1995
TL;DR: This book investigates two major systems, cooperating distributed grammar systems and parallel communicating grammar systems, which concerns hierarchies with respect to different variants of cooperation, relations with classical formal language theory, syntactic parameters such as the number of components and their size, power of synchronization, and general notions generated from artificial intelligence.
Abstract: From the Publisher:
This book investigates two major systems: firstly, cooperating distributed grammar systems, where the grammars work on one common sequential form and the cooperation is realized by the control of the sequence of active grammars; secondly, parallel communicating grammar systems, where each grammar works on its own sequential form and cooperation is done by means of communicating between grammars. The investigation concerns hierarchies with respect to different variants of cooperation, relations with classical formal language theory, syntactic parameters such as the number of components and their size, power of synchronization, and general notions generated from artificial intelligence.
395 citations