{"title":"Error-Correcting Decision Diagrams for Multiple-Valued Functions","authors":"Helena Astola, S. Stankovic, J. Astola","doi":"10.1109/ISMVL.2011.33","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.33","url":null,"abstract":"Decision diagrams are an efficient way of representing switching functions and they are easily mapped to technology. The layout of a circuit is directly determined by the shape of the decision diagram. By combining the theory of error-correcting codes with decision diagrams, it is possible to form robust circuit layouts, which can detect and correct errors. The method of constructing robust decision diagrams is analogous to the decoding process of linear codes, and can be based on simple matrix and look-up operations. In this paper, we focus on error-correcting decision diagrams for multiple-valued functions, considering them for both the Hamming metric and the Lee metric. The performance of robust decision diagrams is analyzed by determining the error probabilities for such constructions. Depending on the error-correcting properties of the code used in the construction, the error probability of a circuit can be significantly decreased by a robust decision diagram.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129762308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recognition of Blurred Images Using Multilayer Neural Network Based on Multi-valued Neurons","authors":"I. Aizenberg, Shane Alexander, Jacob Jackson","doi":"10.1109/ISMVL.2011.24","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.24","url":null,"abstract":"In this paper, we consider a problem of blurred image recognition using a multilayer neural network based on multi-valued neurons (MLMVN). Recognition of blurred images is a challenging problem because it is difficult or even impossible to find any relevant space of features for solving this problem in the spatial domain. The first crucial point of our approach is the use of the frequency domain as a feature space. Since Fourier phase spectrum of a blurred image remains almost unaffected, at least in the low frequency part, it is possible to use phases corresponding to the lowest frequencies as features for recognition. To preserve the physical nature of phase, it is very important to use a machine learning tool for its analysis that treats the phase properly. MLMVN is based on multi-valued neurons whose inputs and output are located on the unit circle and are determined exactly by phase. This approach makes it possible to recognize even heavily blurred images. Our solution works even for images so degraded they cannot be recognized using traditional image recognition techniques, furthermore, even visually","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"84 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127981427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Invitation to Clone Theory with Partial Clones and Hyperclones","authors":"Hajime Machida, L. Haddad, J. Pantović","doi":"10.1109/ISMVL.2011.49","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.49","url":null,"abstract":"Clone theory is motivated by logic (multiple-valued logic), algebra (universal algebra) and computer science (switching and circuit theory). We introduce some fundamental concepts and properties which lie at the bottom of clone theory on a finite set and then present some of more recent results. Particular emphasis is put on partial clones and hyper clones.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114326840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Representation of Multiple-Valued Bent Functions Using Vilenkin-Chrestenson Decision Diagrams","authors":"S. Stankovic, M. Stankovic, J. Astola","doi":"10.1109/ISMVL.2011.62","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.62","url":null,"abstract":"Bent functions are a class of discrete functions which exhibit the highest degree of nonlinearity. As such bent functions form an essential part of cryptographic systems. Original concept of bent functions defined in GF(2) can be extended to multiple-valued case. Multiple-valued bent functions are defined in therms of properties of their Vilenkin-Chrestenson spectra. Decision diagrams are a method of compact representation of discrete functions. Special types of decision diagrams have been introduced for various types of discrete functions. In this paper we demonstrate how Vilenkin-Chrestenson decision diagrams can be used for efficient representation of multiple-valued bent functions.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"30 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128998029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Determining Minimized Galois Field Expressions for Ternary Functions","authors":"R. Stankovic, Helena Astola, J. Astola","doi":"10.1109/ISMVL.2011.26","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.26","url":null,"abstract":"The paper extends the notion of the Special Normal Form (SNF) for Boolean functions to ternary logic functions. An algorithm to minimize the generalized Galois field (GF) expressions for ternary functions by using SNF is presented.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134213595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Synthesis of Reversible Synchronous Counters","authors":"Mozammel H. A. Khan, M. Perkowski","doi":"10.1109/ISMVL.2011.25","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.25","url":null,"abstract":"Reversible logic is very important in low-power circuit design and quantum computing. Though a significant number of works has been done on reversible combinational logic synthesis, only few papers have been published on reversible sequential logic synthesis and per mutative quantum automata. The reported works on reversible sequential logic discuss designs of reversible flip-flops and suggest synthesizing reversible sequential circuits by replacing the flip-flops and combinational parts of traditional sequential circuit designs by their reversible counterparts. In this paper, we discuss direct design of reversible synchronous counters based on positive polarity Reed-Muller expressions. Design results show that the direct design method is more efficient than the replacement method. The method can be also applied to per mutative quantum automata that have quantum memories external to the circuit.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"29 28","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133651476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improved Complexity of Quantum Oracles for Ternary Grover Algorithm for Graph Coloring","authors":"Yushi Wang, M. Perkowski","doi":"10.1109/ISMVL.2011.42","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.42","url":null,"abstract":"The paper presents a generalization of the well-known Grover Algorithm to operate on ternary quantum circuits. We compare complexity of oracles and some of their commonly used components for binary and ternary cases and various sizes and densities of colored graphs. We show that ternary encoding leads to quantum circuits that have significantly less qud its and lower quantum costs. In case of serial realization of quantum computers, our ternary algorithms and circuits are also faster.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"57 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114125035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Entropies on Bounded Lattices","authors":"D. Simovici","doi":"10.1109/ISMVL.2011.18","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.18","url":null,"abstract":"We introduce the notion of entropy on arbitrary lattices and we study several of its properties. Explicit forms for entropy are obtained for entropies on graded lattices that satisfy certain regularity conditions. The relationships between entropies and metrics defined on lattices are also explored.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"47 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120905937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Contributions of Arto Salomaa to Multiple-Valued Logic","authors":"R. Stankovic, J. Astola","doi":"10.1109/ISMVL.2011.64","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.64","url":null,"abstract":"In scientific community, especially among mathematicians and computer scientists, Arto Salomaa is renowned as a founder of Automata Theory and Formal Languages. It is however less widely known that Salomaa started his research work in the area of multiple-valued logic, where he received his PhD degree in 1960 from the University of Turku, Finland. In this way, research in multiple-valued logic provided foundations for later work of Professor Salomaa. The paper presents a short summary of the work of Arto Salomaa in multiple-valued logic.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121344620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. H. Tran, S. Yanushkevich, S. Lyshevski, V. Shmerko
{"title":"Fault Tolerant Computing Paradigm for Random Molecular Phenomena: Hopfield Gates and Logic Networks","authors":"A. H. Tran, S. Yanushkevich, S. Lyshevski, V. Shmerko","doi":"10.1109/ISMVL.2011.21","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.21","url":null,"abstract":"This paper contributes to robust fault-tolerant computing for expected nano-centric processing hardware. We developed (a)techniques for fault tolerant logic network design given a library of AND, OR, NAND, and NOR Hop field gates, and (b) report experimental results on fault tolerant properties of designed networks. In particular, several hundred iterations are required to achieve correct outputs in a five-input single-output networks in the presence of 40% noise.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130219087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}