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125
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.
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 1022 (13 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 ..."
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Cited by 71 (3 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 ..."
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Cited by 51 (10 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 37 (32 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.
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 33 (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
P.: A Constraint Store Based on Multivalued Decision Diagrams
 Principles and Practice of Constraint Programming (CP 2007). Lecture Notes in Computer Science
, 2007
"... Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limitedwidth multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is on ..."
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Cited by 32 (12 self)
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Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limitedwidth multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time. 1
Dependability Assessment Using Binary Decision Diagrams (BDDs)
"... ... algorithm which incorporates coverage modeling into a BDD solution of a combinatorial model. BDDs, which do not use cutsets to generate system unreliability, may be used to nd exact solutions for extremely large systems. The DREDD algorithm takes advantage of the e ciency of the BDD solution app ..."
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Cited by 24 (2 self)
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... algorithm which incorporates coverage modeling into a BDD solution of a combinatorial model. BDDs, which do not use cutsets to generate system unreliability, may be used to nd exact solutions for extremely large systems. The DREDD algorithm takes advantage of the e ciency of the BDD solution approach and increases the accuracy of a combinatorial model by including consideration of (possibly) imperfect coverage. The usefulness of combinatorial models, long appreciated for their logical structure and concise representational form, is extended to include many fault tolerant systems previously thought to require more complicated analysis techniques in order to include coverage modeling. In this paper, the DREDD approach is presented and applied to the analysis of two sample systems, the F18 ight control system and a fault tolerant multistage interconnection network.