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45
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 881 (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 159 (22 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.
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 61 (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
Probabilistic algorithms for deciding equivalence of straightline programs
 J. ACM
, 1983
"... Let Q be any algebraic structure and ~the set of all total programs over Q using the instruction set {z,, 1, z,, x + y, z,, x y, z ~ x * y, z ~ x/y}. (A program is total if no division by zero occurs during any computation) Let the equivalence problem for ~ be the problem of deciding for tw ..."
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Cited by 43 (1 self)
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Let Q be any algebraic structure and ~the set of all total programs over Q using the instruction set {z,, 1, z,, x + y, z,, x y, z ~ x * y, z ~ x/y}. (A program is total if no division by zero occurs during any computation) Let the equivalence problem for ~ be the problem of deciding for two given programs in ~whether or not they compute the same funcuon The following results are proved: (1) If Q is an inftmte field (e.g, the rauonal numbers or the complex numbers), then the equwalence problem for ~ is probabilistlcally decidable in polynomml time. The result also holds for programs with no dwlslon instructions and Q an infimte integral domain (e.g., the integers). (2) If Q is a finite field, or if Q is a fimte set of integers of cardmahty _>2, then the equivalence problem is NPhard. The case when the field Q is finite but its cardinality is a funcuon of the size of the instance to the eqmvalence problem is also considered An example is shown for which a sharp boundary between the classes NPhard and probabihsticaUy decidable exists (provided they are not identical classes).
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 38 (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 Lower Bound For Integer Multiplication With ReadOnce Branching Programs
 Proceedings of the 27th STOC
, 1998
"... . We prove that readonce branching programs computing integer multiplication require size 2 ## # n) . This is the first nontrivial lower bound for multiplication on branching programs that are not oblivious. By the appropriate problem reductions, we obtain the same lower bound for other arithmeti ..."
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Cited by 34 (0 self)
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. We prove that readonce branching programs computing integer multiplication require size 2 ## # n) . This is the first nontrivial lower bound for multiplication on branching programs that are not oblivious. By the appropriate problem reductions, we obtain the same lower bound for other arithmetic functions. Key words. multiplication, readonce, branching programs, BDD, verification AMS subject classifications. 68Q05, 68Q25, 68M15 PII. S0097539795290349 1. Introduction and background. It is well known that many functions, some of them very simple, cannot be computed by readonce branching programs of polynomial size [We88, Za84, Du85, We87, BHST87, Ju88, Kr88]. Interest in whether integer multiplication can be so computed has been created by recent developments in the field of digital design and hardware verification. 1.1. Hardware verification and branching programs. The central problem of verification is to check whether a combinational hardware circuit has been correctly designe...
Discovering affine equalities using random interpretation
 In 30th Annual ACM Symposium on Principles of Programming Languages
, 2003
"... We present a new polynomialtime randomized algorithm for discovering affine equalities involving variables in a program. The key idea of the algorithm is to execute a code fragment on a few random inputs, but in such a way that all paths are covered on each run. This makes it possible to rule out i ..."
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Cited by 33 (12 self)
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We present a new polynomialtime randomized algorithm for discovering affine equalities involving variables in a program. The key idea of the algorithm is to execute a code fragment on a few random inputs, but in such a way that all paths are covered on each run. This makes it possible to rule out invalid relationships even with very few runs. The algorithm is based on two main techniques. First, both branches of a conditional are executed on each run and at joint points we perform an affine combination of the joining states. Secondly, in the branches of an equality conditional we adjust the data values on the fly to reflect the truth value of the guarding boolean expression. This increases the number of affine equalities that the analysis discovers. The algorithm is simpler to implement than alternative deterministic versions, has better computational complexity, and has an extremely small probability of error for even a small number of runs. This algorithm is an example of how randomization can provide a tradeoff between the cost and complexity of program analysis, and a small probability of unsoundness.
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.
Modeling Design Constraints and Biasing in Simulation Using BDDs
, 1999
"... this paper we provide an alternative approach to environment modeling  we introduce a tool, SimGen, and an associated methodology which employs userspecified constraints to model the interaction between the design and its environment. Constraints are Boolean formulas involving the design signal ..."
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Cited by 27 (5 self)
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this paper we provide an alternative approach to environment modeling  we introduce a tool, SimGen, and an associated methodology which employs userspecified constraints to model the interaction between the design and its environment. Constraints are Boolean formulas involving the design signals. Note that because they can depend on state variables, they are dynamic. As an example, we have employed the following constraint in the course of using SimGen in the verification of a bus interface unit: