On string languages generated by spiking neural p systems with anti-spikes
20 Nov 2011-International Journal of Foundations of Computer Science (World Scientific Publishing Company)-Vol. 22, Iss: 01, pp 15-27
TL;DR: These computing devices allow non-determinism between the rules ac → a and ac → ā, c ϵ ℕ, thus help to generate languages which cannot be generated using simple SN P systems.
Abstract: An Spiking Neural P system with anti-spikes uses two types of objects called spikes and anti-spikes which can encode binary digits in a natural way. The step when system emits a spike or an anti-spike is associated with symbol 1 and 0, respectively. Here we consider these computing devices as language generators. They allow non-determinism between the rules ac → a and ac → ā, c ϵ ℕ, thus help to generate languages which cannot be generated using simple SN P systems.
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TL;DR: A novel method of constructing logic circuits that work in a neural-like manner is demonstrated, as well as shed some lights on potential directions of designing neural circuits theoretically.
121 citations
TL;DR: It is obtained that SN P systems with request rules are Turing universal, even with a small number of neurons, and with 47 neurons such systems can compute any Turing computable function.
108 citations
TL;DR: A Turing universal spiking neural P system with rules on synapses having 6 neurons is constructed, which can generate any set of Turing computable natural numbers.
Abstract: Spiking neural P systems with rules on synapses are a new variant of spiking neural P systems. In the systems, the neuron contains only spikes, while the spiking/forgetting rules are moved on the synapses. It was obtained that such system with 30 neurons (using extended spiking rules) or with 39 neurons (using standard spiking rules) is Turing universal. In this work, this number is improved to 6. Specifically, we construct a Turing universal spiking neural P system with rules on synapses having 6 neurons, which can generate any set of Turing computable natural numbers. As well, it is obtained that spiking neural P system with rules on synapses having less than two neurons are not Turing universal: i) such systems having one neuron can characterize the family of finite sets of natural numbers; ii) the family of sets of numbers generated by the systems having two neurons is included in the family of semi-linear sets of natural numbers.
66 citations
Cites background from "On string languages generated by sp..."
...Inspired by different biological facts, many variants of SN P systems have also been proposed, such as asynchronous SN P systems [12], asynchronous SN P systems with local synchronization [13], SN P systems with astrocyte-like control [14], [15], SN P systems with anti-spikes [16], [17], sequential SN P systems [18]–[20]....
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TL;DR: The Turing universality as number generating and accepting devices is proved at first, and then a universal SN P systems with multiple channels and anti-spikes for computing functions is investigated.
Abstract: Spiking neural P systems (SN P systems) with multiple channels are a variant of SN P systems presented recently. By introducing anti-spikes in neurons, SN P systems with multiple channels and anti-spikes are constructed in this work, where both spikes and anti-spikes are used in rules with channel labels. The Turing universality as number generating and accepting devices is proved at first, and then a universal SN P systems with multiple channels and anti-spikes for computing functions is investigated. At last, a small universal system using 65 neurons for computing any Turing computable function is given.
38 citations
01 Dec 2019
TL;DR: This work investigates the computational completeness of SNGR P systems and makes an improvement regarding to these related parameters, which provides an answer to the open problem mentioned in original work.
Abstract: Taken inspiration from biological phenomenon that neurons communicate via spikes, spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing devices. So far firing rules in most of the SN P systems usually work in a sequential way or in an exhaustive way. Recently, a combination of the two ways mentioned above is considered in SN P systems. This new strategy of using rules, which is called a generalized way of using rules, is applicable for both firing rules and forgetting rules. In SN P systems with generalized use of rules (SNGR P systems, for short), if a rule is used at some step, it can be applied any possible number of times, nondeterministically chosen. In this work, the computational completeness of SNGR P systems is investigated. Specifically, a universal SNGR P system is constructed, where each neuron contains at most 5 rules, and for each time each firing rule consumes at most 6 spikes and each forgetting rule removes at most 4 spikes. This result makes an improvement regarding to these related parameters, thus provides an answer to the open problem mentioned in original work. Moreover, with this improvement we can use less resources (neurons and spikes involved in the evolution of system) to construct universal SNGR P systems.
37 citations
References
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01 Jan 1979
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
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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.
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01 Mar 1974
TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.
Abstract: The 80 revised papers presented together with two keynote contributions and four invited papers were carefully reviewed and sele... The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest i...
2,029 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 simple extension of spiking neural P systems is shown to considerably simplify the universality proofs in this area, where all rules become of the form bc → b′ or bc → lambda , where b,b′ are spikes or anti-spikes.
Abstract: Besides usual spikes employed in spiking neural P systems, we consider “anti-spikes", which participate in spiking and forgetting rules, but also annihilate spikes when meeting in the same neuron. This simple extension of spiking neural P systems is shown to considerably simplify the universality proofs in this area: all rules become of the form bc → b′ or bc → lambda , where b,b′ are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possi- ble, identifying only a singleton. A possible variation is not to produce anti-spikes in neurons, but to consider some “inhibitory synapses", which transform the spikes which pass along them into anti-spikes. Also in this case, universality is rather easy to obtain, with rules of the above simple forms.
197 citations
"On string languages generated by sp..." refers background in this paper
...SN P system with anti spikes (or SN PA system) introduced in [7], is a variant of an SN P system consisting of two types of objects, spikes (denoted as a) and anti-spikes (denoted as a)....
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