Results 1  10
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74
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 ..."
Abstract

Cited by 2917 (46 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. Index Terms: Boolean functions, symbolic manipulation, binary decision diagrams, logic design verification 1.
Symbolic Boolean manipulation with ordered binarydecision diagrams
 ACM Computing Surveys
, 1992
"... Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as grap ..."
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Cited by 874 (11 self)
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Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD
Symbolic manipulation of boolean functions using a graphical representation
 In DAC
, 1985
"... In this paper we describe a 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 of Lee and Akers, but with further restrictions on the ordering of decision ..."
Abstract

Cited by 58 (2 self)
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In this paper we describe a 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 of Lee and Akers, 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 are quite efficient as long as the graphs being operated on do not grow too large. We present performance measurements obtained while applying these algorithms to problems in logic design verification.
BottomUp Induction of Oblivious ReadOnce Decision Graphs
, 1994
"... . We investigate the use of oblivious, readonce decision graphs as structures for representing concepts over discrete domains, and present a bottomup, hillclimbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and ..."
Abstract

Cited by 45 (8 self)
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. We investigate the use of oblivious, readonce decision graphs as structures for representing concepts over discrete domains, and present a bottomup, hillclimbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and experimental results show that it performs well on problems considered difficult for symbolic induction methods, such as the Monk's problems and parity. 1 Introduction Top down induction of decision trees [25, 24, 20] has been one of the principal induction methods for symbolic, supervised learning. The tree structure, which is used for representing the hypothesized target concept, suffers from some wellknown problems, most notably the replication problem and the fragmentation problem [23]. The replication problem forces duplication of subtrees in disjunctive concepts, such as (A B) (C D); the fragmentation problem causes partitioning of the data into fragments, when a higharity attrib...
A Cascade Realization of MultipleOutput Function for Reconfigurable Hardware
 INTERNATIONAL WORKSHOP ON LOGIC AND SYNTHESIS (IWLS01), LAKE TAHOE, CA
, 2001
"... A realization of multipleoutput logic functions using a RAM and a sequencer is presented. First, a multipleoutput function is represented by an encoded characteristic function for nonzeros (ECFN). Then, it is represented by a cascade of lookup tables (LUTs). And finally, the cascade is simulated ..."
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Cited by 30 (26 self)
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A realization of multipleoutput logic functions using a RAM and a sequencer is presented. First, a multipleoutput function is represented by an encoded characteristic function for nonzeros (ECFN). Then, it is represented by a cascade of lookup tables (LUTs). And finally, the cascade is simulated by a RAM and a sequencer. Multipleoutput functions for benchmark functions are realized by cascades of LUTs, and the number of LUTs and levels of cascades are shown. A partition method of outputs for parallel evaluation is also presented. A prototype has been developed by using RAM and FPGA.
Using ifthenelse DAGs for MultiLevel Logic Minimization
 Proc. of Advance Research in VLSI, C. Seitz Ed
, 1989
"... This article describes the use of ifthenelse dags for multilevel logic minimization. A new canonical form for ifthenelse dags, analogous to Bryant's canonical form for binary decision diagrams (bdds), is introduced. Twocuts are defined for binary decision diagrams, and a relationship is exhibi ..."
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Cited by 30 (2 self)
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This article describes the use of ifthenelse dags for multilevel logic minimization. A new canonical form for ifthenelse dags, analogous to Bryant's canonical form for binary decision diagrams (bdds), is introduced. Twocuts are defined for binary decision diagrams, and a relationship is exhibited between general ifthenelse expressions and the twocuts of a bdd for the same function. The canonical form is based on representing the lowest nontrivial twocut in the corresponding bdd, instead of the highest twocut, as in Bryant's canonical form. The definitions of prime and irredundant expressions are extended to ifthenelse dags.
Abstract interpretation of cellular signalling networks
 4905 of LNCS
, 2008
"... Abstract. Cellular signalling pathways, where proteins can form complexes and undergo a large array of post translational modifications are highly combinatorial systems sending and receiving extracellular signals and triggering appropriate responses. Processcentric languages seem apt to their repr ..."
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Cited by 23 (7 self)
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Abstract. Cellular signalling pathways, where proteins can form complexes and undergo a large array of post translational modifications are highly combinatorial systems sending and receiving extracellular signals and triggering appropriate responses. Processcentric languages seem apt to their representation and simulation [1–3]. Rulecentric languages such as κ [4–8] and BNG [9, 10] bring in additional ease of expression. We propose in this paper a method to enumerate a superset of the reachable complexes that a κ rule set can generate. This is done via the construction of a finite abstract interpretation. We find a simple criterion for this superset to be the exact set of reachable complexes, namely that the superset is closed under swap, an operation whereby pairs of edges of the same type can permute their ends. We also show that a simple syntactic restriction on rules is sufficient to ensure the generation of a swapclosed set of complexes. We conclude by showing that a substantial rule set (presented in Ref. [4]) modelling the EGF receptor pathway verifies that syntactic condition (up to suitable transformations), and therefore despite its apparent complexity has a rather simple set of reachables. 1
Efficient Calculation of Spectral Coefficients and Their Applications
 IEEE Trans. on CAD/ICAS
, 1995
"... Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficient ..."
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Cited by 21 (6 self)
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Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficients with polynomial complexity. Usually, the computation of the spectral coefficients involves the evaluation of inner products of vectors of exponential length. In the new approach, it is not necessary to compute inner products, rather, each spectral coefficient is expressed in terms of a measure of correlation between two Boolean functions. This formulation coupled with compact BDD representations of the functions reduces the overall complexity. Further, some computer aided design applications are presented that can make use of the new spectrum evaluation approach. In particular, the basis for a synthesis method that allows spectral coefficients to be computed in an iterative manner ...
On the Power of Randomized Branching Programs
 IN PROCEEDINGS OF THE ICALP'96, LECTURE NOTES IN COMPUTER SCIENCE
, 1996
"... We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function fn for which we prove that: 1) f n can be computed by polynomial size randomized readonce ordered branching program with a small onesided ..."
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Cited by 19 (9 self)
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We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function fn for which we prove that: 1) f n can be computed by polynomial size randomized readonce ordered branching program with a small onesided error; 2) fn cannot be computed in polynomial size by deterministic readonce branching programs; 3) fn cannot be computed in polynomial size by deterministic read ktimes ordered branching program for k = o(n= log n) (the required deterministic size is exp \Gamma\Omega \Gamma n k \Delta\Delta ).