scholarly journals Spiking Neural P Systems with Weights

2010 ◽  
Vol 22 (10) ◽  
pp. 2615-2646 ◽  
Author(s):  
Jun Wang ◽  
Hendrik Jan Hoogeboom ◽  
Linqiang Pan ◽  
Gheorghe Păun ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Rational Numbers ◽  
P Systems ◽  
Natural Numbers ◽  
Open Problems ◽  
Spiking Neural P Systems ◽  
Semilinear Sets ◽  
The Family ◽  
Neuron Fire ◽  
Hard Problems

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values—weights, firing thresholds, potential consumed by each rule—can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, −1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

scholarly journals A Note on the Generative Power of Axon P Systems

2009 ◽  
Vol 4 (1) ◽  
pp. 92 ◽  
Author(s):  
Xingyi Zhang ◽  
Jun Wang ◽  
Linqiang Pan
Keyword(s):  
P Systems ◽  
Number Generator ◽  
Finite Sets ◽  
Open Problems ◽  
Spiking Neural P Systems ◽  
Generative Power ◽  
Semilinear Sets ◽  
The Family ◽  
Context Free

Axon P systems are a class of spiking neural P systems. In this paper, the axon P systems are used as number generators and language generators. As a language generator, the relationships of the families of languages generated by axon P systems with finite and context-free languages are considered. As a number generator, a characterization of the family of finite sets can be obtained by axon P systems with only one node. The relationships of sets of numbers generated by axon P systems with semilinear sets of numbers are also investigated. This paper partially answers some open problems formulated by H. Chen, T.-O. Ishdorj and Gh. Păun.

Spiking Neural P Systems with Astrocytes

2012 ◽  
Vol 24 (3) ◽  
pp. 805-825 ◽  
Author(s):  
Linqiang Pan ◽  
Jun Wang ◽  
Hendrik Jan Hoogeboom
Keyword(s):  
Nervous System ◽  
Simple Form ◽  
P Systems ◽  
Inhibitory Influence ◽  
Spiking Neural P Systems ◽  
Biological Inspiration ◽  
Semilinear Sets

In a biological nervous system, astrocytes play an important role in the functioning and interaction of neurons, and astrocytes have excitatory and inhibitory influence on synapses. In this work, with this biological inspiration, a class of computation devices that consist of neurons and astrocytes is introduced, called spiking neural P systems with astrocytes (SNPA systems). The computation power of SNPA systems is investigated. It is proved that SNPA systems with simple neurons (all neurons have the same rule, one per neuron, of a very simple form) are Turing universal in both generative and accepting modes. If a bound is given on the number of spikes present in any neuron along a computation, then the computation power of SNPA systems is diminished. In this case, a characterization of semilinear sets of numbers is obtained.

scholarly journals SPIKE TRAINS IN SPIKING NEURAL P SYSTEMS

2006 ◽  
Vol 17 (04) ◽  
pp. 975-1002 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
GRZEGORZ ROZENBERG
Keyword(s):  
Spike Train ◽  
Spike Trains ◽  
P Systems ◽  
P System ◽  
Spiking Neural P System ◽  
Spiking Neural P Systems ◽  
Semilinear Sets ◽  
Research Problems ◽  
Electrical Impulses

We continue here the study of the recently introduced spiking neural P systems, which mimic the way that neurons communicate with each other by means of short electrical impulses, identical in shape (voltage), but emitted at precise moments of time. The sequence of moments when a neuron emits a spike is called the spike train (of this neuron); by designating one neuron as the output neuron of a spiking neural P system II, one obtains a spike train of II. Given a specific way of assigning sets of numbers to spike trains of II, we obtain sets of numbers computed by II. In this way, spiking neural P systems become number computing devices. We consider a number of ways to assign (code) sets of numbers to (by) spike trains, and prove then computational completeness: the computed sets of numbers are exactly Turing computable sets. When the number of spikes present in the system is bounded, a characterization of semilinear sets of numbers is obtained. A number of research problems is also formulated.

Time-Free Spiking Neural P Systems

2011 ◽  
Vol 23 (5) ◽  
pp. 1320-1342 ◽  
Author(s):  
Linqiang Pan ◽  
Xiangxiang Zeng ◽  
Xingyi Zhang
Keyword(s):  
Environmental Factors ◽  
P Systems ◽  
P System ◽  
Spiking Neural P Systems ◽  
Computation Result ◽  
Semilinear Sets ◽  
Execution Times ◽  
Definition Of ◽  
Robust Systems

Different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, a realistic definition of nonsynchronized spiking neural P systems (SN P systems, for short) is considered: during the work of an SN P system, the execution times of spiking rules cannot be known exactly (i.e., they are arbitrary). In order to establish robust systems against the environmental factors, a special class of SN P systems, called time-free SN P systems, is introduced, which always produce the same computation result independent of the execution times of the rules. The universality of time-free SN P systems is investigated. It is proved that these P systems with extended rules (several spikes can be produced by a rule) are equivalent to register machines. However, if the number of spikes present in the system is bounded, then the power of time-free SN P systems falls, and in this case, a characterization of semilinear sets of natural numbers is obtained.

Spiking Neural P Systems with Thresholds

2014 ◽  
Vol 26 (7) ◽  
pp. 1340-1361 ◽  
Author(s):  
Xiangxiang Zeng ◽  
Xingyi Zhang ◽  
Tao Song ◽  
Linqiang Pan
Keyword(s):  
Parallel Computing ◽  
Open Problem ◽  
Spiking Neurons ◽  
P Systems ◽  
Spiking Neural P Systems ◽  
New Class ◽  
Semilinear Sets ◽  
The Family ◽  
Distributed And Parallel Computing ◽  
Computing Models

Spiking neural P systems with weights are a new class of distributed and parallel computing models inspired by spiking neurons. In such models, a neuron fires when its potential equals a given value (called a threshold). In this work, spiking neural P systems with thresholds (SNPT systems) are introduced, where a neuron fires not only when its potential equals the threshold but also when its potential is higher than the threshold. Two types of SNPT systems are investigated. In the first one, we consider that the firing of a neuron consumes part of the potential (the amount of potential consumed depends on the rule to be applied). In the second one, once a neuron fires, its potential vanishes (i.e., it is reset to zero). The computation power of the two types of SNPT systems is investigated. We prove that the systems of the former type can compute all Turing computable sets of numbers and the systems of the latter type characterize the family of semilinear sets of numbers. The results show that the firing mechanism of neurons has a crucial influence on the computation power of the SNPT systems, which also answers an open problem formulated in Wang, Hoogeboom, Pan, Păun, and Pérez-Jiménez ( 2010 ).

scholarly journals Secret Sharing Schemes on Sparse Homogeneous Access Structures with Rank Three

10.37236/1825 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaume Martí-Farré ◽  
Carles Padró
Keyword(s):  
Secret Sharing ◽  
Access Structure ◽  
Open Problems ◽  
Access Structures ◽  
The Family ◽  
Ideal Access Structures ◽  
Optimal Information ◽  
Made In ◽  
The Ideal

One of the main open problems in secret sharing is the characterization of the ideal access structures. This problem has been studied for several families of access structures with similar results. Namely, in all these families, the ideal access structures coincide with the vector space ones and, besides, the optimal information rate of a non-ideal access structure is at most $2/3$. An access structure is said to be $r$-homogeneous if there are exactly $r$ participants in every minimal qualified subset. A first approach to the characterization of the ideal $3$-homogeneous access structures is made in this paper. We show that the results in the previously studied families can not be directly generalized to this one. Nevertheless, we prove that the equivalences above apply to the family of the sparse $3$-homogeneous access structures, that is, those in which any subset of four participants contains at most two minimal qualified subsets. Besides, we give a complete description of the ideal sparse $3$-homogeneous access structures.

Evolution-Communication Spiking Neural P Systems

2020 ◽  
pp. 2050064
Author(s):  
Tingfang Wu ◽  
Qiang Lyu ◽  
Linqiang Pan
Keyword(s):  
Parallel Computation ◽  
Fire Behavior ◽  
Information Storage ◽  
P Systems ◽  
Computational Power ◽  
Spiking Neural P Systems ◽  
Integrate And Fire ◽  
Restricted Form ◽  
The Family ◽  
Novel Variant

Spiking neural P systems (SNP systems) are a class of distributed and parallel computation models, which are inspired by the way in which neurons process information through spikes, where the integrate-and-fire behavior of neurons and the distribution of produced spikes are achieved by spiking rules. In this work, a novel mechanism for separately describing the integrate-and-fire behavior of neurons and the distribution of produced spikes, and a novel variant of the SNP systems, named evolution-communication SNP (ECSNP) systems, is proposed. More precisely, the integrate-and-fire behavior of neurons is achieved by spike-evolution rules, and the distribution of produced spikes is achieved by spike-communication rules. Then, the computational power of ECSNP systems is examined. It is demonstrated that ECSNP systems are Turing universal as number-generating devices. Furthermore, the computational power of ECSNP systems with a restricted form, i.e. the quantity of spikes in each neuron throughout a computation does not exceed some constant, is also investigated, and it is shown that such restricted ECSNP systems can only characterize the family of semilinear number sets. These results manifest that the capacity of neurons for information storage (i.e. the quantity of spikes) has a critical impact on the ECSNP systems to achieve a desired computational power.

A CHARACTERIZATION OF RECOGNIZABLE PICTURE LANGUAGES

1994 ◽  
Vol 08 (02) ◽  
pp. 501-508 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI
Keyword(s):  
Finite Automata ◽  
Two Dimensional ◽  
Open Problems ◽  
Nondeterministic Finite Automata ◽  
Letter Alphabet ◽  
The Family ◽  
On Line ◽  
Picture Languages

This paper first shows that REC, the family of recognizable picture languages in Giammarresi and Restivo,3 is equal to the family of picture languages accepted by two-dimensional on-line tessellation acceptors in Inoue and Nakamura.5 By using this result, we then solve open problems in Giammarresi and Restivo,3 and show that (i) REC is not closed under complementation, and (ii) REC properly contains the family of picture languages accepted by two-dimensional nondeterministic finite automata even over a one letter alphabet.

EXTENDED SPIKING NEURAL P SYSTEMS WITH DECAYING SPIKES AND/OR TOTAL SPIKING

2008 ◽  
Vol 19 (05) ◽  
pp. 1223-1234 ◽  
Author(s):  
RUDOLF FREUND ◽  
MIHAI IONESCU ◽  
MARION OSWALD
Keyword(s):  
P Systems ◽  
Extended Model ◽  
Natural Numbers ◽  
Spiking Neural P Systems ◽  
Regular Sets

We consider extended variants of spiking neural P systems with decaying spikes (i.e., the spikes have a limited lifetime) and/or total spiking (i.e., the whole contents of a neuron is erased when it spikes). Although we use the extended model of spiking neural P systems, these restrictions of decaying spikes and/or total spiking do not allow for the generation or the acceptance of more than regular sets of natural numbers.

SPIKING NEURAL P SYSTEMS: AN EARLY SURVEY

2007 ◽  
Vol 18 (03) ◽  
pp. 435-455 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
ARTO SALOMAA
Keyword(s):  
Membrane Computing ◽  
Normal Forms ◽  
P Systems ◽  
Research Topics ◽  
Open Problems ◽  
Computing Power ◽  
Spiking Neural P Systems ◽  
A Cell ◽  
Early Survey ◽  
Basic Ideas

Spiking neural P systems were introduced in the end of the year 2005, in the aim of incorporating in membrane computing the idea of working with unique objects ("spikes"), encoding the information in the time elapsed between consecutive spikes sent from a cell/neuron to another cell/neuron. More than one dozen of papers where written in the meantime, clarifying many of the basic properties of these devices, especially related to their computing power. The present paper quickly surveys the basic ideas and the basic results, presenting a complete to-date bibliography, and also giving a completing result related to the normal forms possible for spiking neural P systems: we prove that the indegree of such systems (the maximal number of incoming synapses of neurons) can be bounded by 2 without losing the computational completeness. A series of research topics and open problems are formulated.

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