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Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329)

20-22 May 1999

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  • Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329)

    Publication Year: 1999
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (254 KB)

    Conference proceedings front matter may contain various advertisements, welcome messages, committee or program information, and other miscellaneous conference information. This may in some cases also include the cover art, table of contents, copyright statements, title-page or half title-pages, blank pages, venue maps or other general information relating to the conference that was part of the ori... View full abstract»

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  • Author index

    Publication Year: 1999, Page(s): 302
    Request permission for commercial reuse | PDF file iconPDF (120 KB)
    Freely Available from IEEE
  • The number of cascade functions

    Publication Year: 1999, Page(s):131 - 135
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB)

    Cascade function is a Boolean function which can be implemented by a so-called cascade network. An n input cascade network is a circuit built with n-1 two-input-one-output gates (i.e., dyadic operations) such that at least one input of each gate is a network input. By arranging the inputs in a proper order these networks can be presented in a “cascade” shape, which is the origin of the... View full abstract»

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  • Clarifying the axioms of Kleene algebra based on the method of indeterminate coefficients

    Publication Year: 1999, Page(s):125 - 130
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (112 KB)

    After introducing the method of indeterminate coefficients, by which we can derive all finite models satisfying a given set of axioms, we derive all models of 8 elements of Kleene algebra by using the method, and find out many examples of a set of independent and complete axioms of Kleene algebra by checking whether each axiom in Kleene algebra is independent from others or not based on the method View full abstract»

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  • A super switch algebra for quantum device based systems

    Publication Year: 1999, Page(s):118 - 124
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1184 KB)

    In this paper a multiple-valued algebra, super switch algebra, is formalized. The algebra is well suited for the design of quantum device based multiple-valued systems. A minimization algorithm based on this algebra is proposed. This new algebraic algorithm has some advantages over the existing map-based procedure and subfunction-based algorithm. Benchmark functions are minimized and the results a... View full abstract»

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  • Logical model for representing uncertain statuses of multiple-valued logic systems realized by min, max and literals

    Publication Year: 1999, Page(s):110 - 115
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1704 KB)

    This paper discusses a logical model which is suitable for representing uncertain statuses existing in multiple-valued logic systems realized by minimum, maximum and literals. Then, some of the mathematical properties of functions defined by the logical model are presented View full abstract»

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  • The output permutation for the multiple-valued logic minimization with universal literals

    Publication Year: 1999, Page(s):105 - 109
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (40 KB)

    This paper shows the effectiveness of an output permutation for the implementation of current-mode CMOS circuits. A combination of a simple function and an output permutation can realize a difficult function and cost for the combination will be lower than the cost for a difficult function. The output permutation can be realized by a universal literal and we can calculate the cost. We first examine... View full abstract»

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  • Ternary multiplication circuits using 4-input adder cells and carry look-ahead

    Publication Year: 1999, Page(s):174 - 179
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1076 KB)

    We introduce a new implementation of a ternary adder with four inputs and two outputs. This ternary adder reduces the number of digits in a multiplication compared with a binary multiplication. One advantage of the ternary adder is that four instead of three inputs within a binary representation will be summed up. In this paper we will compare the complexity of binary against ternary multipliers. ... View full abstract»

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  • Multiple-valued minimization to optimize PLAs with output EXOR gates

    Publication Year: 1999, Page(s):99 - 104
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (100 KB)

    This paper considers an optimization method of programmable logic arrays (PLAs), which have two-input EXOR gate at the outputs. The PLA realizes an EXOR of two sum-of-products expressions (EX-SOP) for multiple-valued input two-valued output functions. We present techniques to minimize EX-SOPs, which is an extension of Dubrova-Miller-Muzio's AOXMIN algorithm. We conjecture that, when n is sufficien... View full abstract»

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  • Semirigidity problems in k-valued logic

    Publication Year: 1999, Page(s):256 - 260
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (108 KB)

    The study of semirigid sets arose from the classification of bases. In this complex problem-fully solved only for |A|=2, 3-one of the task is to find all minimal nontrivial intersections of systems of maximal clones. Most of the clones are determined by reflexive relations (binary or of higher arities) and so we need to determine subsets R of these relations such that every function preserving all... View full abstract»

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  • Probabilistic and truth-functional many-valued logic programming

    Publication Year: 1999, Page(s):236 - 241
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (160 KB)

    We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-valu... View full abstract»

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  • Shared multiple-valued decision diagrams for multiple-output functions

    Publication Year: 1999, Page(s):166 - 172
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB)

    In this paper, we propose a method to represent multiple-output functions using shared multiple-valued decision diagrams (SMDDs). We show an algorithm for pairing the input variables of binary decision diagrams (BDDs). We also present the pair sifting that moves pairs of 4-valued input variables to speed up the normal sifting, and to produce compact SMDDs. The size of the SMDD is the total number ... View full abstract»

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  • Evaluation of m-valued fixed polarity generalizations of Reed-Muller canonical form

    Publication Year: 1999, Page(s):92 - 98
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (108 KB)

    This paper compares the complexity of three different fixed polarity generalizations of Reed-Muller canonical form to multiple-valued logic. The Galois field-based expansion introduced by D.H. Green and I.S. Taylor (1974), the Reed-Muller-Fourier form of R.S. Stankovic and C. Moraga (1998), and the expansion over addition modulo m, minimum and the set of all literal operators introduced by the aut... View full abstract»

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  • B-ternary logic based asynchronous micropipeline

    Publication Year: 1999, Page(s):214 - 219
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (152 KB)

    In this paper, a B-ternary logic based asynchronous pipeline is presented. The pipeline processes binary dates elastically. It has high speed operation potential an spite of having an idle phase, because the stages of the pipeline operate concurrently. The mechanism for correct pipeline behavior and the designed circuits are provided View full abstract»

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  • Structural and behavioral modeling with monadic logics

    Publication Year: 1999, Page(s):142 - 151
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (328 KB)

    Logic offers the possibility of modeling and reasoning about hardware and software. But which logic? We propose monadic logics of strings and trees as good candidates for many kinds of discrete systems. These logics are natural, decidable, yet substantially more expressive, extensions of Boolean logic. We motivate their applicability through examples View full abstract»

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  • Multivalued binary relations and Post algebras

    Publication Year: 1999, Page(s):10 - 17
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2004 KB)

    This paper deals with a multivalued extension of the concept of a binary relation on a set E. If R is such an r-valued relation on E, far every (x, y)∈E2, there exists exactly one i∈{0, 1, ..., r-1} such that the degree of comparability of (x, y) with respect to R is equal to i. The set of all r-valued relations on E is then equipped with an order relation ⩽ and turns out ... View full abstract»

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  • Highly testable Boolean ring logic circuits

    Publication Year: 1999, Page(s):268 - 274
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (192 KB)

    In this paper we show how Boolean Ring logic, a group-based logic, leads to a circuit implementation that is highly testable. We develop Boolean Ring based expressions, which we call Generalized-Literal Boolean-Ring Sum-of-Products (GL-BRSOP) and Universal-Literal Boolean-Ring Sum-of-Products (UL-BRSOP) to represent (powers of 2)-valued MVL functions. Our BRSOPs: allow MVL functions to be implemen... View full abstract»

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  • Transformations between signed and classical clause logic

    Publication Year: 1999, Page(s):248 - 255
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (164 KB)

    In the last years two automated reasoning techniques for clause normal form arose in which the use of labels are prominently featured: signed logic and annotated logic programming, which can be embedded into the first. The underlying basic idea is to generalise the classical notion of a literal by adorning an atomic formula with a sign or label which in general consists of a possibly ordered set o... View full abstract»

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  • Information relationships and measures in application to logic design

    Publication Year: 1999, Page(s):228 - 235
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (140 KB)

    In this paper, the theory of information relationships and relationship measures is considered and its application to logic design is discussed. This theory makes operational the famous theory of partitions and set systems of Hartmanis. The information relationships and measures enable us to analyze relationships between the modeled information streams and constitute an important analysis apparatu... View full abstract»

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  • Synthesis of multiple-valued decision diagrams using current-mode CMOS circuits

    Publication Year: 1999, Page(s):160 - 165
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (176 KB)

    In this paper, an algorithm for generating modular designs of Ordered Multiple Decision Diagrams (OMDDs) for Current-Mode CMOS Logic (CMCL) implementation is introduced. The OMDD structures for a set of twelve benchmark circuits from the LGSynth93 using radices ranging from r=2 to r=10 are generated and compared in terms of size and speed. It is observed that MODDs with radices r∈(2, 4, 8) re... View full abstract»

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  • Multiple-valued content-addressable memory using metal-ferroelectric-semiconductor FETs

    Publication Year: 1999, Page(s):30 - 35
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1388 KB)

    This paper presents a design of a non-volatile multiple-valued content-addressable memory (MVCAM) using metal-ferroelectric-semiconductor (MFS) FETs. An MFSFET is an important device with a non-destructive read scheme. Multiple-valued stored data are directly represented by remnant polarization states that correspond to threshold voltages of an MFSFET. Since one-digit comparison between multiple-v... View full abstract»

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  • Partial clones and their generating sets

    Publication Year: 1999, Page(s):85 - 90
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB)

    We present some of our recent results on partial clones. Let A be a non singleton finite set. For every maximal clone C on A, we find the maximal partial clone on A that contains C. We also construct families of finitely generated maximal partial clones as well as a family of not finitely generated maximal partial clones on A. Furthermore, we study the pairwise intersections of all maximal partial... View full abstract»

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  • On the number of multilinear partitions and the computing capacity of multiple-valued multiple-threshold perceptrons

    Publication Year: 1999, Page(s):208 - 213
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB)

    We introduce the concept of multilinear partition of a point set V⊂Rn and the concept of multilinear separability of a function f:V→K={0, ..., k-1}. Based on well known relationships between linear partitions and minimal pairs, we derive formulae for the number of multilinear partitions of a point set in general position and of the set K2. The (n, k, s)-perceptrons p... View full abstract»

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  • A generalization of Shestakov's function decomposition method

    Publication Year: 1999, Page(s):66 - 71
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (140 KB)

    Shestakov expresses an incompletely specified Boolean function f(x 1, ..., xn) in terms of Boolean functions gu , gv and h in the form h(gu(u1, ..., ur), gv(v1, ..., vs)), where {u1, ..., ur}∪{v1, ..., vs}={x1, ..., xn}.... View full abstract»

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  • Research on the similarity among precomplete sets preserving m-ary relations in partial k-valued logic

    Publication Year: 1999, Page(s):136 - 139
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (64 KB)

    In multiple-valued logic theories, the characterization of Sheffer functions is an important problem, it includes the decision and construction for Sheffer functions in Pk and Pk*. The solution of these problems depends on the solution of the decision problem for completeness in Pk and Pk*, and reduced to determining the minimal coverings of precomplete ... View full abstract»

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