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Multiple-Valued Logic, 2007. ISMVL 2007. 37th International Symposium on

Date 13-16 May 2007

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  • 37th International Symposium on Multiple-Valued Logic - Cover

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  • 37th International Symposium on Multiple-Valued Logic - Title page

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  • 37th International Symposium on Multiple-Valued Logic - Copyright notice

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  • 37th International Symposium on Multiple-Valued Logic - TOC

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  • Message from the Chair

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  • Message from the Program Chair

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  • Conference Committee

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  • Program Committee

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  • Reviewers

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  • Grand Challenges of Nanoelectronics and Possible Architectural Solutions: What Do Shannon, von Neumann, Kolmogorov, and Feynman Have to do with Moore

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    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (595 KB) |  | HTML iconHTML  

    This presentation discuss the many challenges faced by the design of future tera-scale integrated circuits that result from the use of nano-scale electronic devices. The relations among these challenges was studied, and a relative ranking was proposed. Afterwards, we shall delve into the most difficult challenges. Finally, possible solutions was also be suggested. View full abstract»

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  • The Ternary Calculating Machine of Thomas Fowler

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    In 1840, Thomas Fowler, a self-taught English mathematician and inventor, created a unique ternary calculating machine. Until recently, all detail of this machine was lost. A research project begun in 1997 uncovered sufficient information to enable the recreation of a physical concept model of Fowler's machine. View full abstract»

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  • Automated Reasoning in Some Local Extensions of Ordered Structures

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    We give a uniform method for automated reasoning in several types of extensions of ordered algebraic structures (definitional extensions, extensions with boundedness axioms or with monotonicity axioms). We show that such extensions are local and, hence, efficient methods for hierarchical reasoning exist in all these cases. View full abstract»

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  • Reading the Sampling Theorem in Multiple-Valued Logic: A Journey from the (Shannong) Sampling Theorem to the Shannon Decomposition Rule

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    Signals described by functions of continuous and discrete variables can be uniformly studied in a group theoretic framework. This paper presents a consideration which shows that in the case of multiple-valued (MV) functions, the notion of bandwidth relates to the concept of essential variables. Sampling conditions convert into requirements for periodicity and regularity in the truth-vectors of MV functions. Due to that, by starting from the sampling theorem, we derive generalized Shannon decomposition rules for MV functions that include the classical Shannon decomposition rule in binary-valued logic as a particular case. It follows from these considerations that the sampling theorem provides a regular way for the decomposition of a MV function into subfunctions of smaller numbers of variables. In circuit synthesis, this allows decomposition of a network to realize a function into subnetworks realizing subfunctions depending on subsets of variables, where the cardinality of the subsets is determined by the bandwidth selected. As there are no convergence problems, the sampling theorem for discrete functions can be formulated in terms of a class of Fourier-like transforms with certain properties provided. Due to that, different decompositions of a given function can be determined by selecting various Fourier-like transforms. View full abstract»

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  • Model-Characterizing Formulas and Normal Forms in Godel Logics

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    This paper focuses on three kinds of normal forms: the weak conjunctive normal form, the weak disjunctive normal form and the weak implicational normal form. The existence of these normal forms in Godel logics is investigated, and two kinds of reduction methods for them are presented, one of which is based on model-characterizing formulas and the other on rewriting systems. As byproducts of these investigations, three kinds of model-characterizing formulas are obtained. In the end, the complexities of reductions to these normal forms are also studied. View full abstract»

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  • Spectral Analysis of Special Properties of Ternary Functions

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    This paper shows that particular classes of linear combinations of the coefficients of the circular Chrestenson-Vilenkin spectrum of ternary functions characterize whether cofactors of the function are constant or balanced. These results may be applied to take decisions related to hardware implementations or to simplify ternary decision diagrams. View full abstract»

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  • Representations of Elementary Functions Using Edge-Valued MDDs

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    This paper proposes a method to represent elementary functions such as trigonometric, logarithmic, square root, and reciprocal functions using edge-valued multi-valued decision diagrams (EVMDDs). We introduce a new class of integer functions, Mp-monotone increasing functions, and derive an upper bound on the number of nodes in an edge-valued binary decision diagram (EVBDD) for the Mp-monotone increasing function. The upper bound shows that EVBDDs represent Mp-monotone increasing functions more compactly than other decision diagrams when p is small. Experimental results using 16-bit precision elementary functions show that: 1) standard elementary functions can be converted into Mp-monotone increasing functions with p = 1 or p = 2, or their linear transformations. And, they can be compactly represented by EVBDDs. 2) EVMDDs represent elementary functions with, on average, only 11% of the memory size needed for binary moment diagrams (BMDs), and only 69% of the memory size needed for EVBDDs. View full abstract»

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  • Experimental Studies on SAT-Based ATPG for Gate Delay Faults

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    The clock rate of modern chips is still increasing and at the same time the gate size decreases. As a result, already slight variations during the production process may cause a functional failure. Therefore, dynamic fault models like the gate delay fault model are becoming more important. Meanwhile classical algorithms for test pattern generation reach their limits regarding run time and memory needs. In this work, a SAT-based approach to calculate test patterns for gate delay faults is presented. The basic transformation is explained in detail. The application to industrial circuits - where multi-valued logic has to be considered - is studied and experimental results are reported. View full abstract»

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  • Polynomials as Generators of Minimal Clones

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    A minimal clone is an atom of the lattice of clones. A minimal function is a function which generates a minimal clone. We consider the base set with k elements, for a prime k, as a finite field and treat functions as polynomials. Starting from binary minimal functions over GF(3), we generalize some of them and obtain binary minimal functions, as polynomials, over GF(k) for any prime k ges 3. View full abstract»

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  • Restriction-Closed Hyperclones

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    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (226 KB) |  | HTML iconHTML  

    The sets of multi-valued operations closed with respect to compositions and restrictions, called restriction- closed hyperclones, defined on the finite set E(k)={0, 1,..., k-1} (kges2) are investigated. The set of all maximal restriction-closed pre-hyperclones (composition without projections) is obtained. Based on it the analogue of Slupecki completeness criteria in restriction-closed pre-hyperclones is established. Next the problem of classification of restriction-closed hyperclones according to their single-valued clone component is considered. View full abstract»

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  • Monoidal Intervals of Partial Clones

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    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (132 KB) |  | HTML iconHTML  

    Let 2 = {0,1} and let M be a monoid on 2. The monoidal interval determined by M is the set of all partial clones on 2 whose foundation is M. We study monoidal intervals determined by several monoids on 2. Among other things, we show that if M is a monoid of total functions and contains a non-trivial unary function on 2, then the monoidal interval determined by M consists of total clones on 2. Moreover, we exhibit 4 monoids on 2 each of which determines a monoidal interval of continuum cardinality on 2. View full abstract»

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  • Variable Reordering and Sifting for QMDD

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    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (227 KB) |  | HTML iconHTML  

    This paper considers variable reordering for quantum multiple-valued decision diagrams (QMDD) used to represent the matrices describing reversible and quantum gates and circuits. An efficient method for adjacent variable interchange is presented and this method is employed to implement sifting of QMDDs. Experimental results are presented showing the effectiveness of the proposed techniques. View full abstract»

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  • GF(4) Based Synthesis of Quaternary Reversible/Quantum Logic Circuits

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    Galois field sum of products (GFSOP) has been found to be very promising for reversible/quantum implementation of multiple-valued logic. In this paper, we show ten quaternary Galois field expansions, using which quaternary Galois field decision diagrams (QGFDD) can be constructed. Flattening of the QGFDD generates quaternary GFSOP (QGFSOP). These QGFSOP can be implemented as cascade of quaternary 1-qudit gates and multi-qudit Feynman and Toffoli gates. We also show the realization of quaternary Feynman and Toffoli gates using liquid ion-trap realizable 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates. Besides the quaternary functions, this approach can also be used for synthesis of encoded binary functions by grouping 2-bits together into quaternary value. For this purpose, we show binary-to-quaternary encoder and quaternary-to- binary decoder circuits using quaternary 1-quidit gates and 2-qudit Muthukrishnan-Stroud gates. View full abstract»

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  • A Generalization of the Deutsch-Jozsa Algorithm to Multi-Valued Quantum Logic

    Page(s): 12
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    We generalize the binary Deutsch-Jozsa algorithm to n- valued logic using the quantum Fourier transform. Our algorithm is not only able to distinguish between constant and balanced Boolean functions in a single query, but can also find closed expressions for classes of affine functions in quantum oracles, accurate to a constant term. View full abstract»

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  • The Genetic Code as a Multiple-Valued Function and Its Implementation Using Multilayer Neural Network Based on Multi-Valued Neurons

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    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. It is shown in the paper that a model of multiple-valued logic over the field of complex numbers is the most appropriate for the representation of the genetic code. Furthermore, consideration of the genetic code within this model makes it possible to learn it using a multilayer neural network based on multi-valued neurons (MLMVN). The functionality of MLMVN is higher than the ones of the traditional feedforward and kernel-based networks and its backpropagation learning algorithm is derivative-free. It is shown that the genetic code multiple-valued function can be easily trained by a significantly smaller MLMVN in comparison with a classical feedforward neural network. View full abstract»

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  • Non-deterministic Multi-valued Matrices for First-Order Logics of Formal Inconsistency

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    Paraconsistent logic is the study of contradictory yet non-trivial theories. One of the best-known approaches to designing useful paraconsistent logics is da Costa's approach, which has led to the family of logics of formal inconsistency (LFIs), where the notion of inconsistency is expressed at the object level. In this paper we use non- deterministic matrices, a generalization of standard multivalued matrices, to provide simple and modular finite-valued semantics for a large family of first-order LFIs. The modular approach provides new insights into the semantic role of each of the studied axioms and the dependencies between them. For instance, four of the axioms of LFII*, a first-order system designed in [8] for treating inconsistent databases, are shown to be derivable from the rest of its axioms. We also prove the effectiveness of our semantics, a crucial property for constructing counterexamples, and apply it to show a non-trivial proof-theoretical property of the studied LFIs. View full abstract»

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