On string languages generated by spiking neural p systems with anti-spikes

Design of logic gates using spiking neural P systems with homogeneous neurons and astrocytes-like control

Abstract: In biological nervous systems, the operation of interacting neurons depends largely on the regulation from astrocytes. Inspired by this biological phenomenon, spiking neural P systems, i.e. SN P systems, with astrocyte-like control were proposed and were proven to have "Turing completeness" as computing models. In this work, the application of such systems for creating logical operators is investigated. Specifically, it is obtained in a constructive way that SN P systems with astrocyte-like control can synthesize the operations of Boolean logic gates, i.e. AND, OR, NOT, NOR, XOR and NAND gates. The resulting systems are simple and homogeneous, which means only one type of neuron with a unique spiking rule is used. With these neural-like logic gates, more complex Boolean circuits with cascade connections can be constructed. As such, they can be used to implement finite computing devices, such as the finite transducers. These results demonstrate a novel method of constructing logic circuits that work in a neural-like manner, as well as shed some lights on potential directions of designing neural circuits theoretically.

Spiking neural P systems with request rules

Abstract: Spiking neural P systems, shortly called SN P systems, are a class of distributed and parallel neural-like computing models, inspired from the way of neurons spiking and communicating with each other by means of spikes. In this work, we propose a new variant of SN P systems, called SN P systems with request rules. In such a system, besides spiking and forgetting rules, a neuron can have request rules, with which the neuron can sense "stimulus" from the environment by receiving a certain number of spikes. We investigate the computation power of SN P systems with request rules. It is obtained that such systems are Turing universal, even with a small number of neurons. Specifically, (i) SN P systems with request rules having 4 neurons can compute any set of Turing computable natural numbers and (ii) with 47 neurons such systems can compute any Turing computable function.

On the Universality and Non-Universality of Spiking Neural P Systems With Rules on Synapses

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.

Spiking neural P systems with multiple channels and anti-spikes.

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.

On Languages Generated by Cell-Like Spiking Neural P Systems

Abstract: Cell-like spiking neural P systems are a variant of standard spiking neural P systems, which have a cell-like instead of neural-like architecture. It has been proved that cell-like spiking neural P systems can generate Turing computable sets of numbers. In this work, the computational power of cell-like spiking neural P systems as language generators is investigated. Characterization of finite languages is obtained with cell-like spiking neural P systems when the number of spikes produced is less than the number of spikes consumed, and characterization of recursively enumerable languages is obtained by cell-like spiking neural P systems when there is no restriction on the number of produced spikes. The relationships of the languages generated by cell-like spiking neural P systems with regular, non-context-free and non-semilinear languages are also investigated.

Introduction to Automata Theory, Languages, and Computation

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.

Computation: Finite and Infinite Machines

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.

Automata, Languages, and Machines

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...

Spiking Neural P Systems

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.

On String Languages Generated by Spiking Neural P Systems

Abstract: We continue the study of spiking neural P systems by considering these computing devices as binary string generators: the set of spike trains of halting computations of a given system constitutes the language generated by that system. Although the "direct" generative capacity of spiking neural P systems is rather restricted (some very simple languages cannot be generated in this framework), regular languages are inverse-morphic images of languages of finite spiking neural P systems, and recursively enumerable languages are projections of inverse-morphic images of languages generated by spiking neural P systems.