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16
Generalized ReedMuller canonical form of a multiplevalued algebra
 MultipleValued Logic  An International Journal
, 1996
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Evaluation of Toggle Coverage for MVL Circuits Specified in the
"... Designing modern circuits comprised of millions of gates is a very challenging task. Therefore new directions are investigated for efficient modeling and verification of such systems. Recently, a new language, SystemVerilog, was introduced and became an IEEE standard. SystemVerilog extends the hardw ..."
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Designing modern circuits comprised of millions of gates is a very challenging task. Therefore new directions are investigated for efficient modeling and verification of such systems. Recently, a new language, SystemVerilog, was introduced and became an IEEE standard. SystemVerilog extends the hardware description language Verilog by including higher abstraction levels and integrated verification features. In this paper, we first present the concept of modeling multiple valued logic circuits in SystemVerilog. We demonstrate that this approach allows for efficient simulation of complex multiple valued logic systems. Secondly, we show how SystemVerilog can be used to ensure functional correctness. A generalization of binary toggle coverage for the multiple valued logic domain is presented and evaluated. As a test case, a scalable multiple valued logic arithmetic unit is modeled and experimental results for multiple valued logic toggle coverage are given. 1.
Modeling MultiValued Circuits in SystemC
"... The complexity of todays hardware systems steadily increases. Due to this fact new ways of efficiently describing systems are investigated. A very promising approach in this area is SystemC which is a C++library. To take advantage of SystemC in the multivalued domain, the concept of multivalued l ..."
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The complexity of todays hardware systems steadily increases. Due to this fact new ways of efficiently describing systems are investigated. A very promising approach in this area is SystemC which is a C++library. To take advantage of SystemC in the multivalued domain, the concept of multivalued logic has to be embedded in SystemC.
Representation of MultipleValued Functions with Modp Decision Diagrams
 In Proceedings of IEEE/ACM International Workshop on Logic Synthesis (IWLS2000), Dana Point
, 2000
"... Multiplevalued logic allows us to formulate problems by using symbolic variables which are often more naturally associated with the problem speci cation than the variables obtained by a binary encoding. In this paper we present a data structure for representation and manipulation of multiplevalued ..."
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Multiplevalued logic allows us to formulate problems by using symbolic variables which are often more naturally associated with the problem speci cation than the variables obtained by a binary encoding. In this paper we present a data structure for representation and manipulation of multiplevalued functions  Modp Decision Diagrams (ModpDDs). ModpDDs differ from conventional MultipleValued Decision Diagrams (MDDs) in that they contain not only branching nodes but also functional nodes, labeled by addition modulo p operation, p  prime. ModpDDs are potentially much more spaceecient than MDDs. However, they are not a canonical representation and thus, the equivalence test of two ModpDDs is more difficult then the test of two MDDs. To overcome this problem, we design a fast probabilistic equivalence test for ModpDDs that requires time linear in the number of nodes.
Modp decision diagrams: A data structure for multiplevalued functions
 In Proceedings of the 30th IEEE International Symposium on MultipleValued Logic (ISMVL 2000
, 2000
"... Multiplevalued decision diagrams (MDDs) give a way of approaching problems by using symbolic variables which are often more naturally associated with the problem statement than the variables obtained by a binary encoding. We present a more general class of MDDs, containing not only branching nodes ..."
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Multiplevalued decision diagrams (MDDs) give a way of approaching problems by using symbolic variables which are often more naturally associated with the problem statement than the variables obtained by a binary encoding. We present a more general class of MDDs, containing not only branching nodes but also functional nodes, labeled by addition modulo operation, prime, and give algorithms for their manipulation. Such decision diagrams have a potential of being more spaceefficient than MDDs. However, they are not a canonical representation of multiplevalued functions and thus the equivalence test of two ModDDs is more difficult then the test of two MDDs. To overcome this problem, we design a fast probabilistic equivalence test for ModDDs that requires time linear in the number of nodes. 1
NonSilicon NonBinary Computing: Why not?
"... Nonsilicon based computing technologies open new possibilities for designing electronic circuits which employ more than two discrete levels of signal. Such circuits, called multiplevalued logic circuits, have a number of theoretical advantages over standard binary circuits. In this paper, we give ..."
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Nonsilicon based computing technologies open new possibilities for designing electronic circuits which employ more than two discrete levels of signal. Such circuits, called multiplevalued logic circuits, have a number of theoretical advantages over standard binary circuits. In this paper, we give an introduction to alternative to binary number representations and multiplevalued logic. We discuss possibilities for implementing multiplevalued functions using chemically assembled electronic nanotechnology.
Evaluation of mvalued Fixed Polarity Generalizations of ReedMuller Canonical Form
 Proc. 29th Int. Symp. on MultipleValued Logic
, 1999
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Multivalued Logic Mapping of Neurons in Feedforward Networks
"... A common view of feedforward neural networks is that of a black box since the knowledge embedded in the connection weights of a feedforward neural network is generally considered incomprehensible. Many researchers have addressed this deficiency of neural networks by suggesting schemes to obtain a Bo ..."
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A common view of feedforward neural networks is that of a black box since the knowledge embedded in the connection weights of a feedforward neural network is generally considered incomprehensible. Many researchers have addressed this deficiency of neural networks by suggesting schemes to obtain a Boolean logic representation for the output of a neuron based on its connection weights. However, these schemes mostly assume binary inputs to the neural network. Since it is not uncommon to find multivalued discrete inputs to neurons, we present in this paper a weight mapping scheme that is capable of generating a multivalued logic representation for the output of a neuron. Such a logic representation is also useful for continuous inputs through multilevel quantization. Two examples are presented to illustrate the use of multivalued logic representation in understanding the knowledge incorporated in the connection strengths of neurons in feedforward networks.
Evaluation ofvalued Fixed Polarity Generalizations of ReedMuller Canonical Form
"... This paper compares the complexity of three different fixed polarity generalizations of ReedMuller canonical form to multiplevalued logic: the Galois Fieldbased expansion introduced by Green and Taylor, the ReedMullerFourier form of Stanković and Moraga, and the expansion over addition modulo, ..."
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This paper compares the complexity of three different fixed polarity generalizations of ReedMuller canonical form to multiplevalued logic: the Galois Fieldbased expansion introduced by Green and Taylor, the ReedMullerFourier form of Stanković and Moraga, and the expansion over addition modulo, minimum and the set of all literal operators introduced by the author and Muzio. An algorithm for computing the minimal canonical forms for these generalizations is implemented and applied to a set of encoded 4valued benchmark functions, 3 and 4valued adders and multipliers. The experimental results show that, for the benchmark functions, the ReedMullerFourier form and our expansion yield a comparable number of products on average. They have 40 % less products on average than the expansion of Green and Taylor. The ReedMullerFourier form gives a compact representation for adders, while our expansion seems to be suitable for multipliers. 1.