Spiking Neural dP Systems

Ionescu, Mihai; Păun, Gheorghe; Pérez–Jiménez, Mario J.; Yokomori, Takashi

doi:10.3233/fi-2011-571

Cited by 179 publications

(304 citation statements)

References 9 publications

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“…Spiking neural P systems (SN P systems) [5] are quite a new computational model that are a synergy inspired by P systems and spiking neural networks. It has been shown that these systems are computationally universal [5].…”

Section: Introductionmentioning

confidence: 99%

A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems

Neary

2010

Language and Automata Theory and Applications

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In this work we offer a significant improvement on the previous smallest spiking neural P systems and solve the problem of finding the smallest possible extended spiking neural P system. Pȃun and Pȃun [15] gave a universal spiking neural P system with 84 neurons and another that has extended rules with 49 neurons. Subsequently, Zhang et al. [18] reduced the number of neurons used to give universality to 67 for spiking neural P systems and to 41 for the extended model. Here we give a small universal spiking neural P system that has only 17 neurons and another that has extended rules with 5 neurons. All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machines. Using a more relaxed encoding technique we get a universal spiking neural P system that has extended rules with only 4 neurons. This latter spiking neural P system simulates 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines. We show that extended spiking neural P systems with 3 neurons are simulated by log-space bounded Turing machines, and so there exists no such universal system with 3 neurons. It immediately follows that our 4-neuron system is the smallest possible extended spiking neural P system that is universal. Finally, we show that if we generalise the output technique we can give a universal spiking neural P system with extended rules that has only 3 neurons. This system is also the smallest of its kind as a universal spiking neural P system with extended rules and generalised output is not possible with 2 neurons.Key words: spiking neural P systems, small universal spiking neural P systems, computational complexity, strong universality, weak universality Email address: tneary@cs.nuim.ie (Turlough Neary).

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Section: Introductionmentioning

confidence: 99%

A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems

Neary

2010

Language and Automata Theory and Applications

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“…Among them, one can find some papers published in the area of membrane computing (or spiking neural P-systems) where a string is encoded in some manner as a natural number and a language is specified as a set of natural numbers (e.g., [3]). Further, recent developments concerning P-automata and its variant called dP-automata are noteworthy in the sense that they may give rise to a new type of computing devices that could be a bridge between P-system theory and the theory of reaction systems and automata ( [5,14,20]).…”

Section: Discussionmentioning

confidence: 99%

Reaction automata

Okubo

Kobayashi

Yokomori

2012

Theoretical Computer Science

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Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy. * Corresponding author level the way of emergence and evolution of biochemical functioning such as events and modules. In the same framework, they also introduced the notion of time into reaction systems and investigated notions such as reaction times, creation times of compounds and so forth. Rather recent two papers [10,11] continue the investigation of reaction systems, with the focuses on combinatorial properties of functions defined by random reaction systems and on the dependency relation between the power of defining functions and the amount of available resource.In the theory of reaction systems, a (biochemical) reaction is formulated as a triple a = (R a , I a , P a ), where R a is the set of molecules called reactants, I a is the set of molecules called inhibitors, and P a is the set of molecules called products. Let T be a set of molecules, and the result of applying a reaction a to T , denoted by res a (T ), is given by P a if a is enabled by T (i.e., if T completely includes R a and excludes I a ). Otherwise, the result is empty. Thus, res a (T ) = P a if a is enabled on T , and res a (T ) = ∅ otherwise. The result of applying a reaction a is extended to the set of reactions A, denoted by res A (T ), and an interactive process consisting of a sequence of res A (T )'s is properly introduced and investigated.In the last few decades, the notion of a multiset has frequently appeared and been investigated in many different areas such as mathematics, computer science, linguistics, and so forth. (See, e.g., [2] for the reference papers written from the viewpoint of mathematics and computer science.) The notion of a multiset has received more and more attention, particularly in the areas of biochemical computing and molecular computing (e.g., [19,23]).Motivated by these two notions of a reaction system and a multiset, in this paper we will introduce computing devices called reaction automata and show that they are computationally universal by proving that any recursively enumerable language is accepted by a reaction automaton. There are two points to be remarked: On one hand, the notion of reaction automata may be taken as a kind of an extension of reaction systems in the sense that our reaction automata deal with multisets rather than (usual) sets as reaction systems do, in the sequence of computational process. On the other hand, however, reaction automata are introduced as computing devices that accept the sets of string objects (i.e., languages over an...

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“…These characteristics, among others, are meant to capture the workings of a special type of cell known as the neuron. Neurons, such as those in the human brain, communicate or 'compute' by sending indistinct signals more commonly known as action potential or spikes [3]. Inf ormation is then communicated and encoded not by the spikes themselves, since the spikes are unrecognizable from one another, but by (a) the time elapsed between spikes, as well as (b) the number of spikes sent/received from one neuron to another, oftentimes under a certain time interval [3].…”

Section: Parallel Computing: Via Membranesmentioning

confidence: 99%

“…those that spike or transmit signals the moment they are able to do so [4,5]. Variants which allow for delays before a neuron produces a spike, are also available [3]. An SNP system without delay is of the form:…”

Section: Computing With Sn P Systemsmentioning

confidence: 99%

Simulating Spiking Neural P Systems Without Delays Using GPUs

Cabarle¹,

Adorna²,

Amor³

2014

Natural Computing for Simulation and Knowledge Discovery

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Summary. We present in this paper our work regarding simulating a type of P system known as a spiking neural P system (SNP system) using graphics processing units (GPUs). GPUs, because of their architectural optimization for parallel computations, are well-suited for highly parallelizable problems. Due to the advent of general purpose GPU computing in recent years, GPUs are not limited to graphics and video processing alone, but include computationally intensive scientific and mathematical applications as well. Moreover P systems, including SNP systems, are inherently and maximally parallel computing models whose inspirations are taken from the functioning and dynamics of a living cell. In particular, SNP systems try to give a modest but formal representation of a special type of cell known as the neuron and their interactions with one another. The nature of SNP systems allowed their representation as matrices, which is a crucial step in simulating them on highly parallel devices such as GPUs. The highly parallel nature of SNP systems necessitate the use of hardware intended for parallel computations. The simulation algorithms, design considerations, and implementation are presented. Finally, simulation results, observations, and analyses using an SNP system that generates all numbers in N -{1} are discussed, as well as recommendations for future work.

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Spiking Neural dP Systems

Cited by 179 publications

References 9 publications

A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems

A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems

Reaction automata

Simulating Spiking Neural P Systems Without Delays Using GPUs

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