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37
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.
Characterizing Diagnoses
, 1988
"... Most approaches to modelbased diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms. In order to characterize the typically very large number of diagnoses, usually only the minimal such sets of failing components are represented. This method of charac ..."
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Cited by 43 (4 self)
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Most approaches to modelbased diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms. In order to characterize the typically very large number of diagnoses, usually only the minimal such sets of failing components are represented. This method of characterizing all diagnoses is inadequate in general, in part because not every superset of the faulty components of a diagnosis necessarily provides a diagnosis. In this paper we analyze the notion of diagnosis in depth exploiting the notions of implicate/implicant and prime implicate/implicant. We use these notions to propose two alternative approaches for addressing the inadequacy of the concept of minimal diagnosis. First, we propose a new concept, that of kernel diagnosis, which is free of the problems of minimal diagnosis. Second, we propose to restrict the axioms used to describe the system to ensure that the concept of minimal diagnosis is adequate.
Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms
 ACM Transactions on Graphics
, 1989
"... Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the t ..."
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Cited by 29 (9 self)
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Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone 2 that represents the region of space where changes to A affect the solid represented by S, and we use a representation of 2 instead of S for setmembership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (nullset) detection, and for graphic shading.
Assassin: A synthesis system for asynchronous control circuits
 Tech. Rep., IMEC, User and Tutorial manual
, 1994
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Propositional DAGs: a new graphbased language for representing Boolean functions
 KR’06, 10TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING, LAKE DISTRICT
, 2006
"... This paper continues the line of research on knowledge compilation in the context of Negation Normal Forms (NNF) and Binary Decision Diagrams (BDD). The idea is to analyze different target languages according to their succinctness and the classes of queries and transformations supported in polytime. ..."
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Cited by 21 (8 self)
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This paper continues the line of research on knowledge compilation in the context of Negation Normal Forms (NNF) and Binary Decision Diagrams (BDD). The idea is to analyze different target languages according to their succinctness and the classes of queries and transformations supported in polytime. We identify a new property called simplenegation, which is an implicit restriction of all NNFs and BDDs. The removal of this restriction leads to Propositional Directed Acyclic Graphs (PDAG), a more general family of graphbased languages for representing Boolean functions or propositional theories. With respect to certain NNFbased languages, we will show that corresponding PDAGbased languages are at least as succinct and support the same transformations. The most interesting language even supports the same queries and an additional transformation, making it more flexible.
Multistate Directed Acyclic Graphs
 In Proc. Canadian AI
, 2007
"... Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and ..."
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Cited by 9 (3 self)
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Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and to explicitly represent them in their most natural way. The resulting representation languages are analyzed according to their succinctness, supported queries, and supported transformations. The paper shows that most results from PDAGs, NNFs, and BDDs can be generalized to their corresponding multistate extension. This implies that the entire knowledge compilation map is extensible from propositional to multistate variables. 1
New Views of Transfer Function Based Performance Analysis of Coded Modulations
, 1999
"... Transfer function methods are attractive in performance analysis of coded modulations since they allow averaging of all possible error event probabilities. However, they can be computationally intensive when the code has large number of states. In this paper, a method to reduce the complexity of the ..."
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Cited by 8 (1 self)
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Transfer function methods are attractive in performance analysis of coded modulations since they allow averaging of all possible error event probabilities. However, they can be computationally intensive when the code has large number of states. In this paper, a method to reduce the complexity of the transfer function method is proposed. In addition, transfer function methods for computing the upper bound to bit error probability in flat fading channel are presented. These bounds are simple and tight at high SNR. KeywordsRayleigh Fading, Performance Analysis, Transfer Function. I. Introduction P ERFORMANCE analysis of digital communications systems in a variety of channels has been an area of longtime interest. The performance analysis of coded modulations often utilizes the union bound obtained by averaging the probability of all possible error events. Transfer function method introduced in [1] is attractive in the sense that it is possible to enumerate all error events and the...
The inference based on molecular computing
 INTERNATIONAL JOURNAL OF CYBERNETICS AND SYSTEMS
, 2000
"... Molecular computing is a new paradigm to perform calculations using nanotechnology. This paper presents the overall research direction from which molecular inference and expert systems are emerging. It introduces the subject matter and a general description of the problems involved. This includes ..."
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Cited by 7 (0 self)
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Molecular computing is a new paradigm to perform calculations using nanotechnology. This paper presents the overall research direction from which molecular inference and expert systems are emerging. It introduces the subject matter and a general description of the problems involved. This includes selected methods of knowledge representation by DNA oligonucleotides, strategies of the inference mechanism, concept of the inference engine based on circular DNA molecules, particularly derived from plasmids, practical experience in DNA inference engine implementation, and discussion of the experimental results. The approach allows evaluating logical statements and drawing inferences for generating other statements via DNA computing. Series of experiments have been conducted to confirm practical utility of this approach. In these experiments, parameters of biochemical reactions were varied to determine truth/false recognition accuracy. In addition, we discuss the fundamental issues of inference engine and try to enhance physical insight into the dominating features of the approach proposed.
Adding Numbers with DNA
, 2000
"... The new algorithm of DNA computing for adding binary integer numbers is p resented. It requi res the un ique representat ion o f b i ts p laced in tes t tubes t reated as reg is ters. Ampl i f i ca t ion s tep used for the carry operat ion a l lows in theory to add numbers at the same quant i ty of ..."
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Cited by 7 (1 self)
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The new algorithm of DNA computing for adding binary integer numbers is p resented. It requi res the un ique representat ion o f b i ts p laced in tes t tubes t reated as reg is ters. Ampl i f i ca t ion s tep used for the carry operat ion a l lows in theory to add numbers at the same quant i ty of e lementary operat ions ~ regard less o f a number o f b i ts used for representat ion. New notat ion proposed in th is paper a l lows for ef f ic ient and abst rac t descr ip t ion o f the techn ica l operations on DNA.
On the Adders with Minimum Tests
 Proc. 5th Asian Test Symp
, 1997
"... This paper considers two types of nbit adders, ripple carry adders and cascaded carry lookahead adders, with minimum tests for stuckat fault models. In the first part, we present two types of full adders consisting of five gates, and show their minimality. We also prove that one of the full adder ..."
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Cited by 5 (0 self)
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This paper considers two types of nbit adders, ripple carry adders and cascaded carry lookahead adders, with minimum tests for stuckat fault models. In the first part, we present two types of full adders consisting of five gates, and show their minimality. We also prove that one of the full adders can be tested by only three test patterns for single stuckat faults. We also present two types of 4bit carry lookahead adders and their minimum tests. In the second part, we consider the tests for the cascaded adders, an nbit ripple carry adder and a 4mbit cascaded carry lookahead adders. These tests are considerably smaller than previously published ones. In this paper, we consider two types of nbit adders with minimum tests for stuckat fault models: Ripple carry adders and cascaded carry lookahead adders. First, we show the minimality of full adders shown in Fig. 1. They contain the minimum number of gates among adders consisting of only 2input gates. We also show that the sizes of the minimum tests for single stuckat faults in the full adders of Fig. 1A and 1B are five and three, respectively. To our knowledge, the full