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33
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 879 (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
A Knowledge Compilation Map
 Journal of Artificial Intelligence Research
, 2002
"... We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. ..."
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Cited by 162 (24 self)
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We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime.
Verification of Arithmetic Functions with Binary Moment Diagrams
 IN DESIGN AUTOMATION CONF
, 1994
"... Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitary functions from Boolean variables to real, rational, or integer values. BM ..."
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Cited by 97 (6 self)
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Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitary functions from Boolean variables to real, rational, or integer values. BMDs can thus model the functionality of data path circuits operating over word level data. Many important functions, including integer multiplication, that cannot be represented efficiently at the bit level with BDDs have simple representations at the word level with BMDs. Furthermore, BMDs can represent Boolean functions with around the same complexity as BDDs. We propose
New Advances in Compiling CNF into Decomposable Negation Normal Form
 In ECAI
, 2004
"... Abstract. We describe a new algorithm for compiling conjunctive normal form (CNF) into Deterministic Decomposable Negation Normal (dDNNF), which is a tractable logical form that permits model counting in polynomial time. The new implementation is based on latest techniques from both the SAT and OBD ..."
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Cited by 62 (14 self)
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Abstract. We describe a new algorithm for compiling conjunctive normal form (CNF) into Deterministic Decomposable Negation Normal (dDNNF), which is a tractable logical form that permits model counting in polynomial time. The new implementation is based on latest techniques from both the SAT and OBDD literatures, and appears to be orders of magnitude more efficient than previous algorithms for this purpose. We compare our compiler experimentally to state of the art model counters, OBDD compilers, and previous CNF2dDNNF compilers. 1
A Compiler for Deterministic, Decomposable Negation Normal Form
, 2002
"... We present a compiler for converting CNF formulas into deterministic, decomposable negation normal form (dDNNF). This is a ..."
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Cited by 52 (11 self)
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We present a compiler for converting CNF formulas into deterministic, decomposable negation normal form (dDNNF). This is a
A Logical Approach to Factoring Belief Networks
"... We have recently proposed a tractable logical form, known as deterministic, decomposable negation normal form (dDNNF). We have shown that dDNNF supports a number of logical operations in polynomial time, including clausal entailment, model counting, model enumeration, model minimization, and proba ..."
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Cited by 51 (11 self)
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We have recently proposed a tractable logical form, known as deterministic, decomposable negation normal form (dDNNF). We have shown that dDNNF supports a number of logical operations in polynomial time, including clausal entailment, model counting, model enumeration, model minimization, and probabilistic equivalence testing. In this paper, we discuss another major application of this logical form: the implementation of multilinear functions (of exponential size) using arithmetic circuits (that are not necessarily exponential). Specifically, we show that each multi–linear function can be encoded using a propositional theory, and that each dDNNF of the theory corresponds to an arithmetic circuit that implements the encoded multi–linear function. We discuss the application of these results to factoring belief networks, which can be viewed as multi–linear functions as has been shown recently. We discuss the merits of the proposed approach for factoring belief networks, and present experimental results showing how it can handle efficiently belief networks that are intractable to structure–based methods for probabilistic inference.
On the Tractable Counting of Theory Models and its Application to Truth Maintenance and Belief Revision
 Journal of Applied NonClassical Logics
, 2000
"... We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of ..."
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Cited by 50 (17 self)
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We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of literals S, we can simultaneously count, in time linear in the size of , the models of: [ S; [ S [ flg: for every literal l 62 S; [ S n flg: for every literal l 2 S; [ S n flg [ f:lg: for every literal l 2 S.
Efficient Boolean Manipulation with OBDD's Can be Extended to FBDD's
, 1993
"... OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient man ..."
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Cited by 37 (0 self)
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OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient manipulation of OBDD's can be extended to a more general data structure, socalled FBDD's. In detail, the advantages of using FBDD's instead of OBDD's are ffl FBDD's are generally more (sometimes even exponentially more) succinct than OBDD's, ffl FBDD's provide, similarly to OBDD's, canonical representations of Boolean functions, and ffl in terms of FBDD's basic tasks of Boolean manipulation can be performed similarly efficient as in terms of OBDD's. The power of the FBDDconcept is demonstrated by showing that the verification of the benchmark circuit design for the hidden weighted bit function HWB proposed by Bryant can be carried out efficiently in terms of FBDD's while, for princip...
A Perspective on Knowledge Compilation
 In Proc. International Joint Conference on Artificial Intelligence (IJCAI
, 2001
"... We provide a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We argue that ..."
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Cited by 28 (9 self)
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We provide a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones.
On the Relation Between BDDs and FDDs
 INFORMATION AND COMPUTATION
, 1995
"... Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called bran ..."
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Cited by 26 (12 self)
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Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called branching programs, by ordering restrictions. In the context of EXORbased logic synthesis another type of decision diagram (DD), called (ordered) functional decision diagram ((O)FDD) becomes increasingly important. We study the relation between (ordered, free) BDDs and FDDs. Both, BDDs and FDDs, result from DDs by defining the represented function in different ways. If the underlying DD is complete, the relation between both types of interpretation can be described by a Boolean transformation . This allows us to relate the FDDsize of f and the BDDsize of (f) also in the case that the corresponding DDs are free or ordered, but not (necessarily) complete. We use this property to derive...