Spiking Rules Research Articles

Cell-like spiking neural P systems with evolution rules

Cell-like spiking neural P systems (abbreviated as cSN P systems) are a class of distributed and parallel computation devices which combine a hierarchical arrangement of membranes in rewriting P systems and evolution rules in spiking neural P systems. The existing results show that cSN P systems are Turing universal with replication target indication or general spiking rules that produce more spikes than the ones consumed. However, with neither the replication target indication nor general spiking rules, cSN P systems can only compute finite set of numbers. In this work, we introduce evolution rules into cSN P systems to compensate the loss of computation power, the application of which depends on the contents of a region. With an evolution rule, every copy of spike evolves to a designate multiset over one kind of objects. We prove that cSN P systems with evolution rules are computationally universal in the case of using traditional spiking rules while avoiding the replication target indication. We also investigate the influence of the target indications on the computation power of cSN P systems with evolution rules. The results show that removing some target indications has no influence on computation power but a corresponding increase in the number of membranes. Besides, the results give a solution to the open problem that seeks alternative methods for the replication of spikes in a cSN P system.

A new scalable parallel adder based on spiking neural P systems, dendritic behavior, rules on the synapses and astrocyte-like control to compute multiple signed numbers

Abstract This brief presents a scalable parallel neural adder circuit based on spiking neural P systems along with dendritic delays, dendritic feedback, rules on the synapses and astrocyte-like control to create a compact and highly scalable adder circuit. The proposed neural adder circuit adds multiple signed numbers either with few digits or with large number of digits in parallel employing a reduced number of neurons/synapses with simple and homogeneous spiking rules. The proposed neural adder was implemented in a DE0-Nano board (Altera Cyclone IV FPGA) to validate its performance. The results show that its implementation on a low-area low-cost FPGA requires small amount of circuitry. This potentially allows the development of highly parallel architectures that can be used in advanced applications, such as portable mobile robots, mobile devices, image and vision processing, among others.

Spiking neural P systems with rules on synapses and anti-spikes

Spiking neural P systems with anti-spikes (in short, ASN P systems) are a variant of spiking neural P systems (in short, SN P systems), inspired by the way in which neurons process information and communicate to each other through both excitatory and inhibitory impulses. In this work, we consider ASN P systems with rules on synapses, where all neurons contain only spikes or anti-spikes, and the rules are placed on the synapses. The computational power of ASN P systems with rules on synapses is investigated with the restrictions: (1) systems are simple in the sense that each synapse has only one rule; (2) all spiking rules on synapses are bounded; (3) the delay feature and forgetting rules are not used. Specifically, we prove that ASN P systems with pure spiking rules of categories (a,a) and (a,a¯) on synapses are universal as number generating and accepting devices. The universality of ASN P systems with spiking rules of categories (a,a¯) and (a¯,a) on synapses as generating and accepting devices is obtained, where synapses can change spikes to anti-spikes or change anti-spikes to spikes. We also prove that ASN P systems with inhibitory synapses using spiking rules of category (a,a) on synapses are universal as both generating and accepting devices. These results illustrate that simple form of spiking rules is enough for ASN P systems with rules on synapses to achieve Turing universality.

Spiking neural P systems with multiple channels

Spiking neural P systems (SNP systems, in short) are a class of distributed parallel computing systems inspired from the neurophysiological behavior of biological spiking neurons. In this paper, we investigate a new variant of SNP systems in which each neuron has one or more synaptic channels, called spiking neural P systems with multiple channels (SNP-MC systems, in short). The spiking rules with channel label are introduced to handle the firing mechanism of neurons, where the channel labels indicate synaptic channels of transmitting the generated spikes. The computation power of SNP-MC systems is investigated. Specifically, we prove that SNP-MC systems are Turing universal as both number generating and number accepting devices.

Spiking Neural P Systems With Polarizations.

Spiking neural P (SN P) systems are a class of parallel computation models inspired by neurons, where the firing condition of a neuron is described by a regular expression associated with spiking rules. However, it is NP-complete to decide whether the number of spikes is in the length set of the language associated with the regular expression. In this paper, in order to avoid using regular expressions, two major and rather natural modifications in their form and functioning are proposed: the spiking rules no longer check the number of spikes in a neuron, but, in exchange, a polarization is associated with neurons and rules, one of the three electrical charges -, 0,+. Surprisingly enough, the computing devices obtained are still computationally complete, which are able to compute all Turing computable sets of natural numbers. On this basis, the number of neurons in a universal SN P system with polarizations is estimated. Several research directions are mentioned at the end of this paper.

Cell-Like Spiking Neural P Systems With Request Rules.

Cell-like spiking neural (cSN) P systems are a class of distributed and parallel computation models inspired by both the way in which neurons process information and communicate to each other by means of spikes and the compartmentalized structures of living cells. cSN P systems have been proved to be Turing universal if more spikes can be produced by consuming some spikes or spikes can be replicated. In this paper, in order to answer the open problem whether this functioning of producing more spikes and replicating spikes can be avoided by using some strategy without the loss of computation power, we introduce cSN P systems with request rules, which have classical spiking rules and forgetting rules, and also request rules in the skin membrane. The skin membrane can receive spikes from the environment by the application of request rules. cSN P systems with request rules are proved to be Turing universal. The results show that the decrease of computation power caused by removing the internal functioning of producing more spikes and replicating spikes can be compensated by request rules, which suggests that the communication between a cell and the environment is an essential ingredient of systems in terms of computation power.

A compact divisor based on SN P systems along with dendritic behavior

The Spiking Neural P (SN P) system is defined as a type of parallel computing mechanism bio-inspired by the behavior of the soma. Several authors have been employing these systems in order to create efficient arithmetic divisor circuits exploiting at maximum their intrinsic parallel processing. However, the current neural divisors expend a large amount of neurons with complex spiking rules to synchronize the input information to be processed by the soma. This work proposes a compact neural divisor that uses eight neurons and two type spiking rules per neuron. In addition, the proposed circuit includes the dendrite’s behavior as feedback connections, dendritic delays, reduction in the dendrite length and dendritic pruning into the conventional SN P systems in order to simplify the synchronization of the neural processing carried out by the soma. The results show that the proposed neural divisor can be implemented in embedded neuromorphic circuits. This, potentially allows its use in portable applications such as vision processing systems for mobile robots and cryptographic systems for mobile communication devices.

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

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.

Cell-like spiking neural P systems

With mathematical motivation, we consider a combination of basic features of multiset-rewriting P systems and of spiking neural P systems, that is, we consider cell-like P systems with spiking rules in their membranes (hence dealing with only one kind of objects, the spikes). The universality of these systems as number generating devices is proved for the two usual ways to define the output (internally or externally) and for various restrictions on the spiking rules. Several research topics are also pointed out.

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

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.

Implementation of Arithmetic Operations With Time-Free Spiking Neural P Systems.

Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In most applications of SN P systems, synchronization plays a key role which means the execution of a rule is completed in exactly one time unit (one step). However, such synchronization does not coincide with the biological fact: in biological nervous systems, the execution times of spiking rules cannot be known exactly. Therefore, a "realistic" system called time-free SN P systems were proposed, where the precise execution time of rules is removed. In this paper, we consider building arithmetical operation systems based on time-free SN P systems. Specifically, adder, subtracter, multiplier, and divider are constructed by using time-free SN P systems. The obtained systems always produce the same computation result independently from the execution time of the rules.

Spiking neural P systems with homogeneous neurons and synapses

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons process information and communicate by means of spikes, where neurons are different in the sense that they can have different sets of spiking rules. In this work, we consider a variant of SN P systems with two restrictions: (1) all neurons contain only spikes (neurons are homogeneous in this case, since they can be considered as containers of spikes), while the spiking rules are moved on the synapses; (2) all synapses are homogeneous in the sense that each synapse has the same set of rules. These restrictions correspond to the fact that the SN P system consists of only one kind of neurons and one kind of synapses. The computational power of SN P systems with homogeneous neurons and synapses is investigated. Specifically, it is proved that such systems are Turing universal as both number generating and number accepting devices.

Spiking neural P systems with anti-spikes working in sequential mode induced by maximum spike number

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by spiking neurons. SN P systems with anti-spikes (ASN P systems) are a variant of SN P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider ASN P systems with the restrictions: (1) systems are simple in the sense that each neuron has only one rule; (2) at each step the neuron(s) with the maximum number of spikes among the neurons that are active (can spike) will fire; (3) the feature of delays and forgetting rules are not used. These restrictions make the systems working in a sequential way. We investigate the computational power of ASN P systems under these restrictions. Specifically, we prove that such systems with spiking rules of categories (a,a) and (a,a¯) are universal as both number generating and accepting devices. We also prove that ASN P systems with inhibitory synapses using spiking rules of category (a,a) are universal as both generating and accepting devices. These results show that ASN P systems are still powerful working with these restrictions.

Reversible Spiking Neural P Systems with Astrocytes

Spiking neural P systems with astrocytes (SNPA systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, we investigate the reversibility in SNPA systems as well as the computational power of reversible SNPA systems. It is proved that reversible SNPA systems are universal, where the forgetting rules and the feature of delay in spiking rules are not used, and each neuron contains only one spiking rule. The result suggests that the astrocytes play a key role in the functioning of reversible SNPA systems.

Spiking neural P systems with rules on synapses working in maximum spikes consumption strategy.

Spiking neural P systems (SN P systems, for short) are a class of parallel and distributed computation models inspired from the way the neurons process and communicate information by means of spikes. In this paper, we consider a new variant of SN P systems, where each synapse instead of neuron has a set of spiking rules, and the neurons contain only spikes; when the number of spikes in a given neuron is "recognized" by a rule on a synapse leaving from it, the rule is enabled; at a computation step, at most one enabled spiking rule is applied on a synapse, and k spikes are removed from a neuron if the maximum number of spikes that the applied spiking rules on the synapses starting from this neuron consume is k. The computation power of this variant of SN P systems is investigated. Specifically, we prove that such SN P systems can generate or accept any set of Turing computable natural numbers. This result gives an answer to an open problem formulated in Theor. Comput. Sci., vol. 529, pp. 82-95, 2014.

Spiking neural P systems with a generalized use of rules.

Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired by spiking neurons, where the spiking rules are usually used in a sequential way (an applicable rule is applied one time at a step) or an exhaustive way (an applicable rule is applied as many times as possible at a step). In this letter, we consider a generalized way of using spiking rules by "combining" the sequential way and the exhaustive way: if a rule is used at some step, then at that step, it can be applied any possible number of times, nondeterministically chosen. The computational power of SN P systems with a generalized use of rules is investigated. Specifically, we prove that SN P systems with a generalized use of rules consisting of one neuron can characterize finite sets of numbers. If the systems consist of two neurons, then the computational power of such systems can be greatly improved, but not beyond generating semilinear sets of numbers. SN P systems with a generalized use of rules consisting of three neurons are proved to generate at least a non-semilinear set of numbers. In the case of allowing enough neurons, SN P systems with a generalized use of rules are computationally complete. These results show that the number of neurons is crucial for SN P systems with a generalized use of rules to achieve a desired computational power.

Asynchronous Spiking Neural P Systems with Anti-Spikes

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes and inhibitory spikes. ASN P systems working in the synchronous manner with standard spiking rules have been proved to be Turing completeness, do what Turing machine can do. In this work, we consider the computing power of ASN P systems working in the asynchronous manner with standard rules. As expected, the non-synchronization will decrease the computability of the systems. Specifically, asynchronous ASN P systems with standard rules can only characterize the semilinear sets of natural numbers. But, by using weighted synapses, asynchronous ASN P systems can achieve the equivalence with Turing machine again. It implies that weighted synapses has some "programming capacity" in the sense of achieving computing power. The obtained results have a nice interpretation: the loss in power entailed by removing the synchronization from ASN P systems can be compensated by using weighted synapses among connected neurons.

Spiking neural P systems with anti-spikes and without annihilating priority as number acceptors

Spiking neural P systems with anti-spikes (ASN P systems) are variant forms of spiking neural P systems, which are inspired by inhibitory impulses/spikes or inhibitory synapses. The typical feature of ASN P systems is when a neuron contains both spikes and anti-spikes, spikes and anti-spikes will immediately annihilate each other in a maximal way. In this paper, a restricted variant of ASN P systems, called ASN P systems without annihilating priority, is considered, where the annihilating rule is used as the standard rule, i.e., it is not obligatory to use in the neuron associated with both spikes and anti-spikes. If the annihilating rule is used in a neuron, the annihilation will consume one time unit. As a result, such systems using two categories of spiking rules (identified by (a, a) and (a, ā)) can achieve Turing completeness as number accepting devices.

Spiking neural P systems with rules on synapses

Spiking neural P systems (SN P systems, for short) are a class of membrane systems inspired from the way the neurons process information and communicate by means of spikes. In this paper, we introduce and investigate a new class of SN P systems, with spiking rules placed on synapses. The computational completeness is first proved, then two small universal SN P systems with rules on synapses for computing functions are constructed. Specifically, when using standard spiking rules, we obtain a universal system with 39 neurons, while when using extended spiking rules on synapses, a universal SN P system with 30 neurons is constructed.

The Stochastic Loss of Spikes in Spiking Neural P Systems: Design and Implementation of Reliable Arithmetic Circuits

Spiking neural P systems (in short, SN P systems) have been introduced as computing devices inspired by the structure and functioning of neural cells. The presence of unreliable components in SN P systems can be considered in many different aspects. In this paper we focus on two types of unreliability: the stochastic delays of the spiking rules and the stochastic loss of spikes. We propose the implementation of elementary SN P systems with DRAM-based CMOS circuits that are able to cope with these two forms of unreliability in an efficient way. The constructed bio-inspired circuits can be used to encode basic arithmetic modules.