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31
BDDbased synthesis of reversible logic for large functions
 in Design Automation Conf., 2009
"... Reversible logic is the basis for several emerging technologies such as quantum computing, optical computing, or DNA computing and has further applications in domains like lowpower design and nanotechnologies. However, current methods for the synthesis of reversible logic are limited, i.e. they a ..."
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Cited by 46 (28 self)
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Reversible logic is the basis for several emerging technologies such as quantum computing, optical computing, or DNA computing and has further applications in domains like lowpower design and nanotechnologies. However, current methods for the synthesis of reversible logic are limited, i.e. they are applicable to relatively small functions only. In this paper, we propose a synthesis approach, that can cope with Boolean functions containing more than a hundred of variables. We present a technique to derive reversible circuits for a function given by a Binary Decision Diagram (BDD). The circuit is obtained using an algorithm with linear worst case behavior regarding runtime and space requirements. Furthermore, the size of the resulting circuit is bounded by the BDD size. This allows to transfer theoretical results known from BDDs to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.
AND/OR multivalued decision diagrams (AOMDDs) for graphical models
, 2008
"... Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical model ..."
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Cited by 18 (3 self)
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Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR MultiValued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is searchbased, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inferencebased and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.
Partition Search for Nonbinary Constraint Satisfaction
 Information Sciences
, 2007
"... Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Anal ..."
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Cited by 18 (0 self)
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Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Analytical prediction of quantitative performance of partition search appears to be intractable and evaluation therefore has to be by experimental comparison with reduction search algorithms that represent the state of the art. Instead of working only with available reduction search algorithms, this paper introduces enhancements such as semijoin reduction preprocessing using Bloom filtering.
Learning and Inference in WEIGHTED LOGIC WITH APPLICATION TO NATURAL LANGUAGE PROCESSING
, 2008
"... ..."
On the Construction of MultipleValued Decision Diagrams
, 2002
"... Decision diagrams are the stateoftheart representation for logic functions, both binary and multiplevalued. Here we consider ways to improve the construction of multiplevalued decisions diagrams (MDD). Efficiency is achieved through the use of a simple computed table. We compare the use of recu ..."
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Cited by 15 (1 self)
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Decision diagrams are the stateoftheart representation for logic functions, both binary and multiplevalued. Here we consider ways to improve the construction of multiplevalued decisions diagrams (MDD). Efficiency is achieved through the use of a simple computed table. We compare the use of recursive MIN and MAX as primitive operations in multiplevalued decision diagram construction to the MVCASE primitive which is a generalization of the ifthenelse (ITE) commonly used in binary DD packages. We also consider
Design of experiments and evaluation of BDD ordering heuristics
, 2001
"... Traditional approaches to the measurement of performance for CAD algorithms involve the use of sets of socalled “benchmark circuits.” In this paper, we demonstrate that current procedures do not produce results which accuratelycharacterize the behavior of the algorithms under study. Indeed, we show ..."
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Cited by 14 (8 self)
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Traditional approaches to the measurement of performance for CAD algorithms involve the use of sets of socalled “benchmark circuits.” In this paper, we demonstrate that current procedures do not produce results which accuratelycharacterize the behavior of the algorithms under study. Indeed, we show that the apparent advances in algorithms which are documented by traditional benchmarking maywell be due to chance, and not due to anynew properties of the algorithms. As an alternative, we introduce a new methodologyfor the characterization of CAD heuristics which employs wellstudied design of experiments methods. We show through numerous examples how such methods can be applied to evaluate the behavior of heuristics used in BDD variable ordering.
Propositionalizing the EM algorithm by BDDs
"... Abstract. We propose an EM algorithm working on binary decision diagrams (BDDs). It opens a way to applying BDDs to statistical inference in general and machine learning in particular. We also present the complexity analysis of noisyOR models. 1 ..."
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Cited by 13 (5 self)
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Abstract. We propose an EM algorithm working on binary decision diagrams (BDDs). It opens a way to applying BDDs to statistical inference in general and machine learning in particular. We also present the complexity analysis of noisyOR models. 1
Firstorder decisiontheoretic planning in structured relational environments
, 2008
"... We consider the general framework of firstorder decisiontheoretic planning in structured relational environments. Most traditional solution approaches to these planning problems ground the relational specification w.r.t. a specific domain instantiation and apply a solution approach directly to the ..."
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Cited by 10 (2 self)
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We consider the general framework of firstorder decisiontheoretic planning in structured relational environments. Most traditional solution approaches to these planning problems ground the relational specification w.r.t. a specific domain instantiation and apply a solution approach directly to the resulting ground Markov decision process (MDP). Unfortunately, the space and time complexity of these solution algorithms scale linearly with the domain size in the best case and exponentially in the worst case. An alternate approach to grounding a relational planning problem is to lift it to a firstorder MDP (FOMDP) specification. This FOMDP can then be solved directly, resulting in a domainindependent solution whose space and time complexity either do not scale with domain size or can scale sublinearly in the domain size. However, such generality does not come without its own set of challenges and the first purpose of this thesis is to explore exact and approximate solution techniques for practically solving FOMDPs. The second purpose of this thesis is to extend the FOMDP specification to succinctly capture factored actions and additive rewards while extending the exact and approximate solution techniques to directly exploit this structure. In addition, we provide a proof of correctness of the firstorder symbolic dynamic programming approach w.r.t. its wellstudied ground MDP
Augmented Sifting of MultipleValued Decision Diagrams
, 2003
"... Discrete functions are now commonly represented by binary (BDD) and multiplevalued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of ..."
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Cited by 9 (3 self)
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Discrete functions are now commonly represented by binary (BDD) and multiplevalued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of BDD sifting where XOR operations involving adjacent variable pairs augment adjacent variable interchange leading to further reduction in the node count. In this paper, we consider the extension of this approach to MDDs. In particular, we show that the XOR operation of linear sifting can be extended to a variety of operations. We term the resulting approach augmented sifting. Experimental results are presented showing sifting and augmented sifting can be quite effective in reducing the size of MDDs for certain types of functions.
Interactive Cost Configuration Over Decision Diagrams
 Journal of Artificial Intelligence Research (JAIR
"... Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackf ..."
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Cited by 6 (1 self)
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Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackfree user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDDbased configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multivalued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is nonadditive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiplecost configuration is NPhard in the input MDD. However, for solving twocost configuration we develop a pseudopolynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over realworld configuration models and productcatalogue datasets. Response times are generally within a fraction of a second even for very large instances.