In the traditional logic synthesis, different classifications of non-reversible Boolean functions... more In the traditional logic synthesis, different classifications of non-reversible Boolean functions have found many applications. Recently, some attempts to deal with classifications of reversible functions have been published. In this paper, an overview of our results towards constructing a new classification of reversible functions is presented. These results were obtained due to our discussions during two Short Term Scientific Missions (STSMs) as well as during our further research in the framework of COST Action IC1405 “Reversible Computation - Extending Horizons of Computing” and were published in five papers.
– This paper discusses methods for efficient implementation of algorithms for determination of Fi... more – This paper discusses methods for efficient implementation of algorithms for determination of Fixed-polarity Galois field (FPGF) expressions for q-valued logic functions (p- prime). Calculations of coefficients in FPGF expressions can be most efficiently performed in terms of space and time, if conversion of an expression for a given polarity into the expression for another polarity is done along the so-called extended dual polarity route. However, there are many possible extended dual polarity routes which differ in the associated processing rules. The complexity of whatever software or hardware resources required for calculations of FPGF expressions depends on the number of different processing rules required along a route. In this paper, we introduce the notion of homogeneous extended dual polarity routes and show that calculations along these routes can be performed with a reduced number of processing rules required. Due to that, both hardware and software implementation of the...
In the active learning framework, a modified query learning algorithm benefiting by a nontrivial ... more In the active learning framework, a modified query learning algorithm benefiting by a nontrivial helpful labeling is able to learn automata with a reduced number of queries. In extremis, there exists a helpful labeling allowing the algorithm to learn automata even without counterexamples. We also review the correction queries defining them as particular types of labeling. We introduce minimal corrections, maximal corrections, and random corrections. An experimental approach compares the performance and limitations of various types of queries and corrections. The results show that algorithms using corrections require fewer queries in most of the cases.
The problem of blind source separation consists in retrieving unknown source signals from their m... more The problem of blind source separation consists in retrieving unknown source signals from their mixtures. In the estimation of sources, most of the proposed algorithms use stochastic or natural gradient to optimize some contrast function obtained from the independence property of sources. In this paper, we deal with non-stationary source signals, and propose a new approach, based on the second order statistics, to blindly separate them. Our approach is based on the assumption that the cross correlations of the output signals should be equal to zero. The cross correlations are parameterized by the weights of a self organized neural network, which implements a demixing model. The dynamics of the neural network weights and observations of the cross correlations are represented using the state space model. Extended Kalman filter (EKF) is applied to estimate the unknown weights. As an on-line second order optimization algorithm, EKF showed superior convergence properties compared to the ...
This paper introduces the analysis of pattern properties by means of the two-sided Reed-Muller-Fo... more This paper introduces the analysis of pattern properties by means of the two-sided Reed-Muller-Fourier transform. Patterns are modelled as matrices of pixels and an integer coding for the colors is chosen. Work is done in the ring \((Z_{p},\oplus , \cdot )\), where \(p >2\) is not necessarily a prime. It is shown that the transform preserves the (diagonal) symmetry of patterns, is compatible with different operations on patterns, and allows detecting and localizing noise pixels in a pattern. Finally, it is shown that there are patterns which are fixed points of the transform.
The Reed-Muller-Fourier is reviewed and a new property is presented: The Reed-Muller-Fourier tran... more The Reed-Muller-Fourier is reviewed and a new property is presented: The Reed-Muller-Fourier transform of an n-place p-valued function preserves any permutation of the arguments. This leads to the additional result that the Reed-Muller-Fourier spectrum of an n-place p-valued symmetric function is also symmetric. Furthermore, the Reed-Muller and the Vilenkin-Chrestenson spectra of an n-place p-valued symmetric function are also symmetric.
In this paper we propose a method for optimization of fixed polarity arithmetic expressions (FPAE... more In this paper we propose a method for optimization of fixed polarity arithmetic expressions (FPAEs) based on dual polarity. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using dual polarity route. Conversion from one FPAE to another one is carried out using one-bit checking i.e. by using a very simple rule. Therefore, the proposed method is efficient. Experimental results show this.
Artificial neural networks (ANN) have received a great deal of attention in many fields of engine... more Artificial neural networks (ANN) have received a great deal of attention in many fields of engineering and science. Inspired by the study of brain architecture, ANN represent a class of non-linear models capable of learning from data. ANN have been applied in many areas where statistical methods are traditionally employed. They have been used in pattern recognition, classification, prediction and process control. The purpose of this paper is to discuss ANN and compare them to non-linear time series models. We begin exploring recent developments in time series forecasting with particular emphasis on the use of non-linear models. Thereafter we include a review of recent results on the topic of ANN. The relevance of ANN models for the statistical methods is considered using time series prediction problems. Finally we construct asymptotic prediction intervals for ANN and show how to use prediction intervals to choose the number of nodes in the ANN.
Proceedings 31st IEEE International Symposium on Multiple-Valued Logic, 2000
... Radomir S. Stankovic Claudio Moraga Milena Stankovic Dept. ... are word-level PKDDs with vari... more ... Radomir S. Stankovic Claudio Moraga Milena Stankovic Dept. ... are word-level PKDDs with variables ordered in descend-ing values of indices, the leftmost nodes determined as the Walsh nodes [13], and the other nodes as the integer counterparts of the Shannon nodes. ...
This paper discusses methods for efficient implementation of algorithms for determination of Fixe... more This paper discusses methods for efficient implementation of algorithms for determination of Fixed-polarity Galois field (FPGF) expressions for q-valued logic functions (p- prime). Calculations of coefficients in FPGF expressions can be most efficiently performed in terms of space and time, if conversion of an expression for a given polarity into the expression for another polarity is done along the so-called
In the paper a procedure for linearization of Ternary Decision Diagrams is proposed. Linearizatio... more In the paper a procedure for linearization of Ternary Decision Diagrams is proposed. Linearization is based on the properties of the Polynomial Chrestenson spectral coefficients of the considered function. In the cases of some functions, by using the proposed procedure, linearized TDDs are reduced when compared with the original TDDs.
It is shown in this paper that a model of multiplevalued logic over the field of complex numbers ... more It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids). Thus, it is possible to consider the genetic code as a partially defined multiple-valued function of a 20-valued logic. Consideration of the genetic code within the proposed mathematical model makes it possible to learn the code using a multilayer neural network based on multi-valued neurons (MLMVN). MLMVN is a neural network with traditional feedforward architecture, but with a highly efficient derivativefree learning algorithm and higher functionality than the one of the traditional feedforward neural networks and a variety of kernel-based networks. It is shown that the genetic code multiple-valued function can be easily trained by a significantly * Based on "The Genetic Code as a Multiple-Valued Function and its Implementation Using
Linguistic variables are reviewed and some aspects of the original definition revisited, showing ... more Linguistic variables are reviewed and some aspects of the original definition revisited, showing that they provide a first formal frame to do computing with words in a "narrow sense". A two-levels hierarchy of languages is discussed in order to move to simple cases of computing with words in natural language, supported by linguistic variables.
In the traditional logic synthesis, different classifications of non-reversible Boolean functions... more In the traditional logic synthesis, different classifications of non-reversible Boolean functions have found many applications. Recently, some attempts to deal with classifications of reversible functions have been published. In this paper, an overview of our results towards constructing a new classification of reversible functions is presented. These results were obtained due to our discussions during two Short Term Scientific Missions (STSMs) as well as during our further research in the framework of COST Action IC1405 “Reversible Computation - Extending Horizons of Computing” and were published in five papers.
– This paper discusses methods for efficient implementation of algorithms for determination of Fi... more – This paper discusses methods for efficient implementation of algorithms for determination of Fixed-polarity Galois field (FPGF) expressions for q-valued logic functions (p- prime). Calculations of coefficients in FPGF expressions can be most efficiently performed in terms of space and time, if conversion of an expression for a given polarity into the expression for another polarity is done along the so-called extended dual polarity route. However, there are many possible extended dual polarity routes which differ in the associated processing rules. The complexity of whatever software or hardware resources required for calculations of FPGF expressions depends on the number of different processing rules required along a route. In this paper, we introduce the notion of homogeneous extended dual polarity routes and show that calculations along these routes can be performed with a reduced number of processing rules required. Due to that, both hardware and software implementation of the...
In the active learning framework, a modified query learning algorithm benefiting by a nontrivial ... more In the active learning framework, a modified query learning algorithm benefiting by a nontrivial helpful labeling is able to learn automata with a reduced number of queries. In extremis, there exists a helpful labeling allowing the algorithm to learn automata even without counterexamples. We also review the correction queries defining them as particular types of labeling. We introduce minimal corrections, maximal corrections, and random corrections. An experimental approach compares the performance and limitations of various types of queries and corrections. The results show that algorithms using corrections require fewer queries in most of the cases.
The problem of blind source separation consists in retrieving unknown source signals from their m... more The problem of blind source separation consists in retrieving unknown source signals from their mixtures. In the estimation of sources, most of the proposed algorithms use stochastic or natural gradient to optimize some contrast function obtained from the independence property of sources. In this paper, we deal with non-stationary source signals, and propose a new approach, based on the second order statistics, to blindly separate them. Our approach is based on the assumption that the cross correlations of the output signals should be equal to zero. The cross correlations are parameterized by the weights of a self organized neural network, which implements a demixing model. The dynamics of the neural network weights and observations of the cross correlations are represented using the state space model. Extended Kalman filter (EKF) is applied to estimate the unknown weights. As an on-line second order optimization algorithm, EKF showed superior convergence properties compared to the ...
This paper introduces the analysis of pattern properties by means of the two-sided Reed-Muller-Fo... more This paper introduces the analysis of pattern properties by means of the two-sided Reed-Muller-Fourier transform. Patterns are modelled as matrices of pixels and an integer coding for the colors is chosen. Work is done in the ring \((Z_{p},\oplus , \cdot )\), where \(p >2\) is not necessarily a prime. It is shown that the transform preserves the (diagonal) symmetry of patterns, is compatible with different operations on patterns, and allows detecting and localizing noise pixels in a pattern. Finally, it is shown that there are patterns which are fixed points of the transform.
The Reed-Muller-Fourier is reviewed and a new property is presented: The Reed-Muller-Fourier tran... more The Reed-Muller-Fourier is reviewed and a new property is presented: The Reed-Muller-Fourier transform of an n-place p-valued function preserves any permutation of the arguments. This leads to the additional result that the Reed-Muller-Fourier spectrum of an n-place p-valued symmetric function is also symmetric. Furthermore, the Reed-Muller and the Vilenkin-Chrestenson spectra of an n-place p-valued symmetric function are also symmetric.
In this paper we propose a method for optimization of fixed polarity arithmetic expressions (FPAE... more In this paper we propose a method for optimization of fixed polarity arithmetic expressions (FPAEs) based on dual polarity. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using dual polarity route. Conversion from one FPAE to another one is carried out using one-bit checking i.e. by using a very simple rule. Therefore, the proposed method is efficient. Experimental results show this.
Artificial neural networks (ANN) have received a great deal of attention in many fields of engine... more Artificial neural networks (ANN) have received a great deal of attention in many fields of engineering and science. Inspired by the study of brain architecture, ANN represent a class of non-linear models capable of learning from data. ANN have been applied in many areas where statistical methods are traditionally employed. They have been used in pattern recognition, classification, prediction and process control. The purpose of this paper is to discuss ANN and compare them to non-linear time series models. We begin exploring recent developments in time series forecasting with particular emphasis on the use of non-linear models. Thereafter we include a review of recent results on the topic of ANN. The relevance of ANN models for the statistical methods is considered using time series prediction problems. Finally we construct asymptotic prediction intervals for ANN and show how to use prediction intervals to choose the number of nodes in the ANN.
Proceedings 31st IEEE International Symposium on Multiple-Valued Logic, 2000
... Radomir S. Stankovic Claudio Moraga Milena Stankovic Dept. ... are word-level PKDDs with vari... more ... Radomir S. Stankovic Claudio Moraga Milena Stankovic Dept. ... are word-level PKDDs with variables ordered in descend-ing values of indices, the leftmost nodes determined as the Walsh nodes [13], and the other nodes as the integer counterparts of the Shannon nodes. ...
This paper discusses methods for efficient implementation of algorithms for determination of Fixe... more This paper discusses methods for efficient implementation of algorithms for determination of Fixed-polarity Galois field (FPGF) expressions for q-valued logic functions (p- prime). Calculations of coefficients in FPGF expressions can be most efficiently performed in terms of space and time, if conversion of an expression for a given polarity into the expression for another polarity is done along the so-called
In the paper a procedure for linearization of Ternary Decision Diagrams is proposed. Linearizatio... more In the paper a procedure for linearization of Ternary Decision Diagrams is proposed. Linearization is based on the properties of the Polynomial Chrestenson spectral coefficients of the considered function. In the cases of some functions, by using the proposed procedure, linearized TDDs are reduced when compared with the original TDDs.
It is shown in this paper that a model of multiplevalued logic over the field of complex numbers ... more It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids). Thus, it is possible to consider the genetic code as a partially defined multiple-valued function of a 20-valued logic. Consideration of the genetic code within the proposed mathematical model makes it possible to learn the code using a multilayer neural network based on multi-valued neurons (MLMVN). MLMVN is a neural network with traditional feedforward architecture, but with a highly efficient derivativefree learning algorithm and higher functionality than the one of the traditional feedforward neural networks and a variety of kernel-based networks. It is shown that the genetic code multiple-valued function can be easily trained by a significantly * Based on "The Genetic Code as a Multiple-Valued Function and its Implementation Using
Linguistic variables are reviewed and some aspects of the original definition revisited, showing ... more Linguistic variables are reviewed and some aspects of the original definition revisited, showing that they provide a first formal frame to do computing with words in a "narrow sense". A two-levels hierarchy of languages is discussed in order to move to simple cases of computing with words in natural language, supported by linguistic variables.
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Papers by Claudio Moraga