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43
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
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 225 (31 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 110 (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 80 (15 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
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 60 (19 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.
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 59 (13 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.
A compiler for deterministic, decomposable negation normal form
 In AAAI02
"... We present a compiler for converting CNF formulas into deterministic, decomposable negation normal form (dDNNF). This is a logical form that has been identified recently and shown to support a number of operations in polynomial time, including clausal entailment; model counting, minimization and e ..."
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Cited by 55 (12 self)
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We present a compiler for converting CNF formulas into deterministic, decomposable negation normal form (dDNNF). This is a logical form that has been identified recently and shown to support a number of operations in polynomial time, including clausal entailment; model counting, minimization and enumeration; and probabilistic equivalence testing. dDNNFs are also known to be a superset of, and more succinct than, OBDDs. The polytime logical operations supported by dDNNFs are a subset of those supported by OBDDs, yet are sufficient for modelbased diagnosis and planning applications. We present experimental results on compiling a variety of CNF formulas, some generated randomly and others corresponding to digital circuits. A number of the formulas we were able to compile efficiently could not be similarly handled by some stateoftheart model counters, nor by some stateoftheart OBDD compilers.
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 efficien ..."
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Cited by 36 (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 31 (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.
Binary decision diagrams in theory and practice
, 2001
"... Decision diagrams (DDs) are the stateoftheart data structure in VLSI CAD and have been successfully applied in many other fields.DDs are widely used and are also integrated in commercial tools.This special section comprises six contributed articles on various aspects of the theory and application ..."
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Cited by 31 (7 self)
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Decision diagrams (DDs) are the stateoftheart data structure in VLSI CAD and have been successfully applied in many other fields.DDs are widely used and are also integrated in commercial tools.This special section comprises six contributed articles on various aspects of the theory and application of DDs.As preparation for these contributions, the present article reviews the basic definitions of binary decision diagrams (BDDs). We provide a brief overview and study theoretical and practical aspects.Basic properties of BDDs are discussed and manipulation algorithms are described.Extensions of BDDs are investigated and by this we give a deeper insight into the basic data structure.Finally we outline several applications of BDDs and their extensions and suggest a number of articles and books for those who wish to pursue the topic in more depth.