


 Department of Computer Hardware 
 Computer Logical Design Laboratory 

 
 V. B. Marakhovsky Professor 


In 2003, the laboratory research has been conducting in two directions: CMOS betaDriven Threshold Elements and Artificial Neurons, and CMOS NeuroFuzzy Circuits and Devices. Digitalanalog CMOS threshold elements and artificial neurons have been very popular for some application during the last decade. One of the important characteristics of these devices is the degree of their implementability, i.e. the restriction on the class of the threshold functions that can be reliably implemented by a single element under the drift of technological and environmental parameters. For most available implementations, this restriction is defined by the biggest permissible sum of the input weights and threshold. Previously we have suggested new CMOS betadriven threshold element, for which the limiting parameter is only the threshold value. The idea of such threshold element is based on the representation of the threshold function in the ratio form. It allows implementing threshold functions as a ratio of conductivities of n and p chains of CMOS device. We studied the problems of increasing functional power of an artificial neuron on the base of the betadriven CMOS threshold element. The following results were obtained:
 The betadriven artificial neuron learnable to nonisotonous threshold functions was studied. We suggested the neuron synapse capable to form the weight and type (excitatory or inhibitory) of the input during the learning using only increment and decrement signals. The neuron with such synapses can be learned to an arbitrary threshold function of a certain number of variables.
 Synapse circuits were suggested with two memory elements for storing positive and negative input weights along with the procedure of onchip learning.
The results of Spice simulation proved that the problem of neuron teaching to nonisotonous threshold functions has been successfully solved.
The second direction is connected with the problem of designing CMOS NeuroFuzzy Circuits and Devices. During several last decades for solutions of sophisticated control problems and data processing effectively developed neuromorphic methods, i.e. methods inspired with knowledge of processes in a nervous system. The special place among these methods takes ANN (Artificial Neural Networks). ANN can be realized as software implementation on universal or specialized processors. Alternative to this is analogdigital hardware implementation of the ANN. The main advantage analogdigital implementation as contrasted to software implementation is the principled increase of relation throughput/complexity. The main lack of this implementation is the limitation on implementability, i.e. on complexity of functions implemented by one element. Increasing of above relation is the main result of the betadriven circuitry application. The niche for analog digital ANN actuates: image preprocessing (artificial retina etc.), intellectual fuzzy controllers, robotic control (locomotion, scrub moving etc.), pattern recognition, fault detection, and many others. The research in this direction implies the creation of methods and tools of designing full and semicustom neurofuzzy VLSI and embedded devices and systems. These methods and tools include creating threshold elements and devices, learnable betadriven artificial neurons, fuzzy threshold elements and devices; embedded neuroprocessors, neuroarrays and fuzzy controllers and correspondent IP (intellectual properties); design methods and design knowhow for analog/digital devices and systems. 


 [marak01:2003]  V. Varshavsky, V. Marakhovsky, I. Levin, and N. Kravchenko. Summing Amplifier as a MultiValued Logical Element for Fuzzy Control. WSEAS Transactions on Circuit and Systems, 2(3):625631, 2003.
It is offered to implement fuzzy devices as multivalued logic functions, using directly analog input variables and forming the output variables as analog ones as well. It is offered to use CMOS summing amplifiers as basic elements for designing appropriate circuits. It has been proved that a CMOS summing amplifier is a functionally complete element in arbitraryvalued logic. In a plenty of cases this approach enables principally simplification of fuzzy logic controllers for a broad class of applications. All mentioned above is illustrated by examples. 
 [marak02:2003]  V. Varshavsky and V. Marakhovsky. Artificial Neuron Learnable to Threshold Functions. WSEAS Transactions on Circuits and Systems, 3(1):141148, 2003.
In the paper, we discuss a possibility of digitalanalog CMOS implementation of the artificial neuron learnable to logical threshold functions. The implementation is based on earlier suggested (driven neuron circuit consisting of synapses with excitatory inputs, (comparator and three output amplifiers. Such a circuit can be taught only to threshold functions with positive weights of variables, which belong to the class of isotonous Boolean functions. However, most problems solved by artificial neural networks either require inhibitory inputs. It means that a neuron should have synapses capable of forming weights and types of inputs (excitatory or inhibitory) during the learning using only increment and decrement signals. The neuron with such synapses can be learned to an arbitrary threshold function of a certain number of variables. The synapse circuit with two memory elements for storing positive and negative input weights and onchip learning algorithm are suggested. The results of SPICE simulation prove that this algorithm provides the learning process convergence independently from initial conditions. 

 Refereed Proceeding Papers 

 [marak03:2003]  V. Varshavsky, V. Marakhovsky, I. Levin, and N. Kravchenko. Summing Amplifier as a MultiValued Logical Element for Fuzzy Control. In 3rd WSEAS Int. Conf. on Systems Theory and Scientific Computation (ISTASC'03), CD edition, page 6, Rhodes Island, Greece, Nov. 2003. WSEAS.
It is offered to implement fuzzy devices as multivalued logic functions, using directly analog input variables and forming the output variables as analog ones as well. It is offered to use CMOS summing amplifiers as basic elements for designing appropriate circuits. It has been proved that a CMOS summing amplifier is a functionally complete element in arbitraryvalued logic. In a plenty of cases this approach enables principally simplification of fuzzy logic controllers for a broad class of applications. All mentioned above is illustrated by examples. 
 [marak04:2003]  V. Varshavsky and V. Marakhovsky. Artificial Neuron Learnable to Threshold Functions. In 4th WSEAS Int. Conf. on Automation and Information (ICAI'03), CDedition, page 7, Tenerife, Spain, Dec. 2003. WSEAS.
In the paper, we discuss a possibility of digitalanalog CMOS implementation of the artificial neuron learnable to logical threshold functions. The implementation is based on earlier suggested (driven neuron circuit consisting of synapses with excitatory inputs, (comparator and three output amplifiers. Such a circuit can be taught only to threshold functions with positive weights of variables, which belong to the class of isotonous Boolean functions. However, most problems solved by artificial neural networks either require inhibitory inputs. It means that a neuron should have synapses capable of forming weights and types of inputs (excitatory or inhibitory) during the learning using only increment and decrement signals. The neuron with such synapses can be learned to an arbitrary threshold function of a certain number of variables. The synapse circuit with two memory elements for storing positive and negative input weights and onchip learning algorithm are suggested. The results of SPICE simulation prove that this algorithm provides the learning process convergence independently from initial conditions. 
 [marak05:2003]  V. Varshavsky, V. Marakhovsky, and I. Levin. Artificial Neurons Based on CMOS BetaDriven Threshold Elements with Functional Inputs. In 5rd WSEAS Int. Conf. on Neural Networks and Applications (NNA'04), CD edition, page 6, Udine, Italy, March 2004. WSEAS.
This paper deals with a CMOS based artificial neuronimplemented by threshold elements.We consider the artificial neuron as a threshold element with controlled inputs having weights formed during a learning process. A socold betadriven threshold element is used for in the scheme of the neuron.Functioning of this element is described in a specific ratio form. The betadriven implementation is based on using summarized conductivities of n and pchains of a CMOS gate as the ratio of weighted sums. The thresh old element has a wider functional capability in comparison with the traditional functional basis. Moreover, its functional capability can be enriched. We propose a method for increasing the functional capability of the threshold element by introducing socalled functional inputs.Each functional input corresponds to a boolean sum (or product) of a particular subset of input variables. This sum (or product) serves as a single input of the threshold element. It is shown that introducing functional inputs enables expansion of the functional capability of betadriven elements up to the capability to implement an arbitrary monotonic function. The CMOS based implementation of the betadriven threshold element with newly proposed functional inputs is presented. Methods of the current stabilization of functional inputs are proposed. In the proposed implementation of the artificial neuron, each input weight is determined by the current value via a suitable current stabilizer. This value can be effectively controlled by the value of the voltage at the gate of one of the current stabilizer's transistors. The paper presents examples of the SPICE simulation of behavior of the proposed artificial neuron in the modes of learning and maintaining the input weight values. 
 [marak06:2003]  V. Varshavsky, I. Levin, V. Marakhovsky, A. Ruderman, and N. Kravchenko. CMOS Fuzzy Decision Diagram Implementation. In 5rd WSEAS Int. Conf. on Fuzzy Sets and Fuzzy Systems (FSFS'04), CD edition, page 6, Udine, Italy, March 2004. WSEAS.
The subject of the study is design of multivalued (analog) CMOS fuzzy controllers. A functional completeness of summing amplifier with saturation in a multivalued logic of an arbitrary value proven in previous works gives a theoretical background for analog implementation of fuzzy devices. Compared with the traditional approach based on explicit fuzzification / defuzzification procedures analog fuzzy implementation has the advantages of higher speed, lower consumption, smaller die area and more. In the present paper, we expand functional capabilities of summing amplifier by using "masking of the input". The paper provides design example for an industrial fuzzy controller implementation by the proposed mask circuit and SPICE simulations of the controller. 


 [marak07:2003]  V. Marakhovsky, 2003.
Member of IEEE

 [marak08:2003]  V. Marakhovsky, 2003.
Member of ACM



 [marak09:2003]  V. Varshavsky, V. Marakhovsky, I. Levin, and N. Kravchenko.
Fuzzy Device, July 2003. 
 [marak10:2003]  V. Varshavsky, V. Marakhovsky, I. Levin, and N. Kravchenko.
MultiValued Logic Device, March 2004. 


 [marak11:2003]  Sadao Niitsuma. Graduation Thesis: Summing Amplifier as a MultiValued Logical Element for Fuzzy Control, University of Aizu, 2004.
Thesis Advisor: Marakhovsky, V. 
