Relevant bibliographies by topics / Reduced ordered binary decision diagram

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Reduced ordered binary decision diagram'

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Published: 3 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Reduced ordered binary decision diagram"

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Dvořák, Václav. "Bounds on Size of Decision Diagrams." JUCS - Journal of Universal Computer Science 3, no. (1) (1997): 2–22. https://doi.org/10.3217/jucs-003-01-0002.

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Known upper bounds on the number of required nodes (size) in the ordered binary and multiple-valued decision diagram (DD) for representation of logic functions are reviewed and reduced by a small constant factor. New upper bounds are derived for partial logic functions containing don t cares and also for complete Boolean functions specified by Boolean expressions. The evaluation of upper bounds is based on a bottom-up algorithm for constructing efficient ordered DDs developed by the author.
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Lai, Yong, Dayou Liu, and Shengsheng Wang. "Reduced ordered binary decision diagram with implied literals: a new knowledge compilation approach." Knowledge and Information Systems 35, no. 3 (2012): 665–712. http://dx.doi.org/10.1007/s10115-012-0525-6.

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Prihozhy, Anatoly A. "Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (December 14, 2021): 84–97. http://dx.doi.org/10.33581/2520-6508-2021-3-84-97.

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The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the method consists in extending the Shannon and Davio expansions of a Boolean function on a single variable to the expansions of the same Boolean function on another function with obtaining decomposition products that are represented by incompletely defined Boolean functions. Uncertainty in the decomposition products gives remarkable opportunities for minimising the graph representation of the specified function. Instead of two outgoing branches of the binary diagram vertex, three outgoing branches of the if-diagram vertex are generated, which increase the level of parallelism in reversible and quantum circuits. For each transformation step, appropriate mapping rules are proposed that reduce the number of lines, gates and the depth of the reversible and quantum circuit. The comparison of new results with the results given by the known method of mapping the vertices of binary decision diagram into cascades of reversible and quantum gates shows a significant improvement in the quality of quantum circuits that are synthesised by the proposed method.
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Dong, Rongsheng, Yangyang Zhu, Zhoubo Xu, and Fengying Li. "Decision Diagram Based Symbolic Algorithm for Evaluating the Reliability of a Multistate Flow Network." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/6908120.

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Evaluating the reliability of Multistate Flow Network (MFN) is an NP-hard problem. Ordered binary decision diagram (OBDD) or variants thereof, such as multivalued decision diagram (MDD), are compact and efficient data structures suitable for dealing with large-scale problems. Two symbolic algorithms for evaluating the reliability of MFN, MFN_OBDD and MFN_MDD, are proposed in this paper. In the algorithms, several operating functions are defined to prune the generated decision diagrams. Thereby the state space of capacity combinations is further compressed and the operational complexity of the decision diagrams is further reduced. Meanwhile, the related theoretical proofs and complexity analysis are carried out. Experimental results show the following: (1) compared to the existing decomposition algorithm, the proposed algorithms take less memory space and fewer loops. (2) The number of nodes and the number of variables of MDD generated in MFN_MDD algorithm are much smaller than those of OBDD built in the MFN_OBDD algorithm. (3) In two cases with the same number of arcs, the proposed algorithms are more suitable for calculating the reliability of sparse networks.
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Das, Apangshu, Akash Debnath, and Sambhu Nath Pradhan. "Reduced ordered binary decision diagram-based combinational circuit synthesis for optimising area, power and temperature." International Journal of Nanoparticles 11, no. 2 (2019): 94. http://dx.doi.org/10.1504/ijnp.2019.099181.

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Pradhan, Sambhu Nath, Akash Debnath, and Apangshu Das. "Reduced ordered binary decision diagram-based combinational circuit synthesis for optimising area, power and temperature." International Journal of Nanoparticles 11, no. 2 (2019): 94. http://dx.doi.org/10.1504/ijnp.2019.10020325.

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Radmanovic, Milos. "A study of binary decision diagram characteristics of bent Boolean functions." Facta universitatis - series: Electronics and Energetics 36, no. 2 (2023): 285–98. http://dx.doi.org/10.2298/fuee2302285r.

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Bent Boolean functions exist only for an even number of variables, moreover, they are unbalanced. Therefore, they are used in coding theory and in many areas of computer science. General form of bent functions is still unknown. One way of representing Boolean functions is with a reduced ordered binary decision diagram (ROBDD). The strength of ROBDDs is that they can represent Boolean functions data with a high level of redundancy in a compact form, as long as the data is encoded in such a way that the redundancy is exposed. This paper investigates characteristics of bent functions with focus on their ROBDD parameters. Decision diagram experimental framework has been used for implementation of a program for calculation of the ROBDD parameters. The results presented in this paper are intended to be used to create methods for the construction of bent functions using a ROBDD as a data structure from which the bent functions can be discovered.
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Ali, Muhammad Ali Rushdi, and Mohammad Alturki Alaa. "Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams." British Journal of Mathematics & Computer Science 22, no. 3 (2017): 1–9. https://doi.org/10.9734/BJMCS/2017/33642.

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A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We demonstrate that the AR algorithm is, in fact, both a recursive and an iterative implementation of the strategy of Reduced Ordered Binary Decision Diagrams (ROBDDs). The underlying ROBDD for the AR recursive algorithm is represented by a compact Signal Flow Graph (SFG) that is used to deduce AR iterative algorithms of quadratic temporal complexity and linear spatial complexity. Extensions of the AR algorithm for (single or scalar) threshold, double-threshold, vector-threshold, and k-to-<em>l</em>-out-of-n systems have similar ROBDD interpretations.
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Wille, Robert, Görschwin Fey, and Rolf Drechsler. "Building free Binary Decision Diagrams using SAT solvers." Facta universitatis - series: Electronics and Energetics 20, no. 3 (2007): 381–94. http://dx.doi.org/10.2298/fuee0703381w.

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Free Binary Decision Diagrams (FBDDs) are a data structure for the representation of Boolean functions. In contrast to Ordered Binary Decision Diagrams (OBDDs) FBDDs allow different variable orderings along each path. Thus, FBDDs are the more compact representation while most of the properties of OBDDs are kept. However, how to efficiently build small FBDDs for a given function is still an open question. In this work we propose FBDD construction with the help of SAT solvers. "Recording" the single steps of a SAT solver during the search process leads to an FBDD. Furthermore, by exploiting approaches for identifying isomorphic sub-graphs, i.e. cutlines or cutsets reduced FBDDs are constructed.
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Rushdi, Ali, and Alaa Alturki. "Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams." British Journal of Mathematics & Computer Science 22, no. 3 (2017): 1–9. http://dx.doi.org/10.9734/bjmcs/2017/33642.

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Dissertations / Theses on the topic "Reduced ordered binary decision diagram"

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Fernández-Díaz, Álvaro, Christel Baier, Clara Benac-Earle, and Lars-Åke Fredlund. "Static Partial Order Reduction for Probabilistic Concurrent Systems." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-121261.

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Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.
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Fernández-Díaz, Álvaro, Christel Baier, Clara Benac-Earle, and Lars-Åke Fredlund. "Static Partial Order Reduction for Probabilistic Concurrent Systems." Technische Universität Dresden, 2012. https://tud.qucosa.de/id/qucosa%3A26083.

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Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.
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"On efficient ordered binary decision diagram minimization heuristics based on two-level logic." 1999. http://library.cuhk.edu.hk/record=b5889831.

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by Chun Gu.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.<br>Includes bibliographical references (leaves 69-71).<br>Abstract also in Chinese.<br>Chapter 1 --- Introduction --- p.3<br>Chapter 2 --- Definitions --- p.7<br>Chapter 3 --- Some Previous Work on OBDD --- p.13<br>Chapter 3.1 --- The Work of Bryant --- p.13<br>Chapter 3.2 --- Some Variations of the OBDD --- p.14<br>Chapter 3.3 --- Previous Work on Variable Ordering of OBDD --- p.16<br>Chapter 3.3.1 --- The FIH Heuristic --- p.16<br>Chapter 3.3.2 --- The Dynamic Variable Ordering --- p.17<br>Chapter 3.3.3 --- The Interleaving method --- p.19<br>Chapter 4 --- Two Level Logic Function and OBDD --- p.21<br>Chapter 5 --- DSCF Algorithm --- p.25<br>Chapter 6 --- Thin Boolean Function --- p.33<br>Chapter 6.1 --- The Structure and Properties of thin Boolean functions --- p.33<br>Chapter 6.1.1 --- The construction of Thin OBDDs --- p.33<br>Chapter 6.1.2 --- Properties of Thin Boolean Functions --- p.38<br>Chapter 6.1.3 --- Thin Factored Functions --- p.49<br>Chapter 6.2 --- The Revised DSCF Algorithm --- p.52<br>Chapter 6.3 --- Experimental Results --- p.54<br>Chapter 7 --- A Pattern Merging Algorithm --- p.59<br>Chapter 7.1 --- Merging of Patterns --- p.60<br>Chapter 7.2 --- The Algorithm --- p.62<br>Chapter 7.3 --- Experiments and Conclusion --- p.65<br>Chapter 8 --- Conclusions --- p.67
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"Transmission System Restoration Strategies in Real Time." Doctoral diss., 2010. http://hdl.handle.net/2286/R.I.8701.

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abstract: After a power system blackout, system restoration is the most important task for the operators. Most power systems rely on an off&ndashline; restoration plan and the experience of operators to select scenarios for the black start path. Using an off&ndashline; designed restoration plan based on past experience may not be the most reliable approach under changing network configurations and loading levels. Hence, an objective restoration path selection procedure, including the option to check constraints, may be more responsive in providing directed guidance to the operators to identify the optimal transmission path to deliver power to other power plants or to pick up load as needed. After the system is subjected to a blackout, parallel restoration is an efficient way to speed up the restoration process. For a large scale power system, this system sectionalizing problem is quite complicated when considering black&ndashstart; constraints, generation/load balance constraints and voltage constraints. This dissertation presents an ordered binary decision diagram (OBDD) &ndashbased; system sectionalizing method, by which the splitting points can be quickly found. The simulation results on the IEEE 39 and 118&ndashbus; system show that the method can successfully split the system into subsystems satisfying black&ndashstart; constraints, generation/load balance constraints and voltage constraints. A power transfer distribution factor (PTDF)&ndashbased; approach will be described in this dissertation to check constraints while restoring the system. Two types of restoration performance indices are utilized considering all possible restoration paths, which are then ranked according to their expected performance characteristics as reflected by the restoration performance index. PTDFs and weighting factors are used to determine the ordered list of restoration paths, which can enable the load to be picked up by lightly loaded lines or relieve stress on heavily loaded lines. A transmission path agent can then be formulated by performing the automatic path selection under different system operating conditions. The proposed restoration strategy is tested on the IEEE&ndash39; bus system and on the Western region of the Entergy system. The testing results reveal that the proposed strategy can be used in real time.<br>Dissertation/Thesis<br>Ph.D. Electrical Engineering 2010
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Book chapters on the topic "Reduced ordered binary decision diagram"

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Saglietti, Francesca. "Dynamic Decision on Checkpointing by Use of Reduced Ordered Binary Decision Diagrams." In Safe Comp 97. Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0997-6_27.

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Lu, Kuan, Ramin Yahyapour, Edwin Yaqub, and Constantinos Kotsokalis. "Structural Optimization of Reduced Ordered Binary Decision Diagrams for SLA Negotiation in IaaS of Cloud Computing." In Service-Oriented Computing. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34321-6_18.

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Bryant, Randal E., and Marijn J. H. Heule. "Generating Extended Resolution Proofs with a BDD-Based SAT Solver." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72016-2_5.

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AbstractIn 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in theextended resolutionlogical framework. Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability. Such proofs indicate that the formula is truly unsatisfiable without requiring the user to trust the BDD package or the SAT solver built on top of it.We extend their work to enable arbitrary existential quantification of the formula variables, a critical capability for BDD-based SAT solvers. We demonstrate the utility of this approach by applying a prototype solver to obtain polynomially sized proofs on benchmarks for the mutilated chessboard and pigeonhole problems—ones that are very challenging for search-based SAT solvers.
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Jacobs, Swen, and Mouhammad Sakr. "AIGEN: Random Generation of Symbolic Transition Systems." In Computer Aided Verification. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81688-9_20.

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AbstractAIGEN is an open source tool for the generation of transition systems in a symbolic representation. To ensure diversity, it employs a uniform random sampling over the space of all Boolean functions with a given number of variables. AIGEN relies on reduced ordered binary decision diagrams (ROBDDs) and canonical disjunctive normal form (CDNF) as canonical representations that allow us to enumerate Boolean functions, in the former case with an encoding that is inspired by data structures used to implement ROBDDs. Several parameters allow the user to restrict generation to Boolean functions or transition systems with certain properties, which are then output in AIGER format. We report on the use of AIGEN to generate random benchmark problems for the reactive synthesis competition SYNTCOMP 2019, and present a comparison of the two encodings with respect to time and memory efficiency in practice.
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Arge, Lars. "The I/O-complexity of Ordered Binary-Decision Diagram manipulation." In Algorithms and Computations. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0015411.

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Tani, Seiichiro, and Hiroshi Imai. "A reordering operation for an ordered binary decision diagram and an extended framework for combinatorics of graphs." In Algorithms and Computation. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58325-4_225.

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Gange Graeme, Lagoon Vitaly, and Stuckey Peter J. "Fast Set Bounds Propagation using BDDs." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2008. https://doi.org/10.3233/978-1-58603-891-5-505.

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Set bounds propagation is the most popular approach to solving constraint satisfaction problems (CSPs) involving set variables. The use of reduced ordered Binary Decision Diagrams (BDDs) to represent and solve set CSPs is well understood and brings the advantage that propagators for arbitrary set constraints can be built. This can substantially improve solving. The disadvantages of BDDs is that creating and manipulating BDDs can be expensive. In this paper we show how we can perform set bounds propagation using BDDs in a much more efficient manner by generically creating set constraint predicates, and using a marking approach to propagation. The resulting system can be significantly faster than competing approaches to set bounds propagation.
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Benamira, Adrien, Tristan Guérand, Thomas Peyrin, and Hans Soegeng. "Neural Network-Based Rule Models with Truth Tables." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2023. http://dx.doi.org/10.3233/faia230274.

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Understanding the decision-making process of a machine/deep learning model is crucial, particularly in security-sensitive applications. In this study, we introduce a neural network framework that combines the global and exact interpretability properties of rule-based models with the high performance of deep neural networks. Our proposed framework, called Truth Table rules (TT-rules), is built upon Truth Table nets (TTnets), a family of deep neural networks initially developed for formal verification. By extracting the set of necessary and sufficient rules R from the trained TTnet model (global interpretability), yielding the same output as the TTnet (exact interpretability), TT-rules effectively transforms the neural network into a rule-based model. This rule-based model supports binary classification, multi-label classification, and regression tasks for tabular datasets. Furthermore, our TT-rules framework optimizes the rule set R into Ropt by reducing the number and size of the rules. To enhance model interpretation, we leverage Reduced Ordered Binary Decision Diagrams (ROBDDs) to visualize these rules effectively. After outlining the framework, we evaluate the performance of TT-rules on seven tabular datasets from finance, healthcare, and justice domains. We also compare the TT-rules framework to state-of-the-art rule-based methods. Our results demonstrate that TT-rules achieves equal or higher performance compared to other interpretable methods while maintaining a balance between performance and complexity. Notably, TT-rules presents the first accurate rule-based model capable of fitting large tabular datasets, including two real-life DNA datasets with over 20K features. Finally, we extensively investigate a rule-based model derived from TT-rules using the Adult dataset.
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Pliego, Alberto, and Fausto Pedro García Márquez. "Big Data and Web Intelligence." In Big Data. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9840-6.ch012.

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The growing amount of available data generates complex problems when they need to be treated. Usually these data come from different sources and inform about different issues, however, in many occasions these data can be interrelated in order to gather strategic information that is useful for Decision Making processes in multitude of business. For a qualitatively and quantitatively analysis of a complex Decision Making process is critical to employ a correct method due to the large number of operations required. With this purpose, this chapter presents an approach employing Binary Decision Diagram applied to the Logical Decision Tree. It allows addressing a Main Problem by establishing different causes, called Basic Causes and their interrelations. The cases that have a large number of Basic Causes generate important computational costs because it is a NP-hard type problem. Moreover, this chapter presents a new approach in order to analyze big Logical Decision Trees. However, the size of the Logical Decision Trees is not the unique factor that affects to the computational cost but the procedure of resolution can widely vary this cost (ordination of Basic Causes, number of AND/OR gates, etc.) A new approach to reduce the complexity of the problem is hereby presented. It makes use of data derived from simpler problems that requires less computational costs for obtaining a good solution. An exact solution is not provided by this method but the approximations achieved have a low deviation from the exact.
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Pliego, Alberto, and Fausto Pedro García Márquez. "Big Data and Web Intelligence." In Handbook of Research on Trends and Future Directions in Big Data and Web Intelligence. IGI Global, 2015. http://dx.doi.org/10.4018/978-1-4666-8505-5.ch010.

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The growing amount of available data generates complex problems when they need to be treated. Usually these data come from different sources and inform about different issues, however, in many occasions these data can be interrelated in order to gather strategic information that is useful for Decision Making processes in multitude of business. For a qualitatively and quantitatively analysis of a complex Decision Making process is critical to employ a correct method due to the large number of operations required. With this purpose, this chapter presents an approach employing Binary Decision Diagram applied to the Logical Decision Tree. It allows addressing a Main Problem by establishing different causes, called Basic Causes and their interrelations. The cases that have a large number of Basic Causes generate important computational costs because it is a NP-hard type problem. Moreover, this chapter presents a new approach in order to analyze big Logical Decision Trees. However, the size of the Logical Decision Trees is not the unique factor that affects to the computational cost but the procedure of resolution can widely vary this cost (ordination of Basic Causes, number of AND/OR gates, etc.) A new approach to reduce the complexity of the problem is hereby presented. It makes use of data derived from simpler problems that requires less computational costs for obtaining a good solution. An exact solution is not provided by this method but the approximations achieved have a low deviation from the exact.
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Conference papers on the topic "Reduced ordered binary decision diagram"

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Moeinzadeh, Hossein, Mehdi Mohammadi, Hossein Pazhoumand-dar, Arman Mehrbakhsh, Navid Kheibar, and Nasser Mozayani. "Evolutionary-Reduced Ordered Binary Decision Diagram." In 2009 Third Asia International Conference on Modelling & Simulation. IEEE, 2009. http://dx.doi.org/10.1109/ams.2009.130.

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Priyadharshini, R. Indra, Priscilla Packia Slacer, A. Benila, M. Mercy Theresa, and P. Pattunna Rajam. "Detection of bridging fault using reduced ordered binary decision diagram." In RECENT TRENDS IN SCIENCE AND ENGINEERING. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0074221.

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Biswal, Pradeep Kumar. "A Concurrent Testing Scheme for Muller Circuits Using Reduced Ordered Binary Decision Diagram." In 2022 IEEE Region 10 Symposium (TENSYMP). IEEE, 2022. http://dx.doi.org/10.1109/tensymp54529.2022.9864357.

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Binder, Walter, Ion Constantinescu, and Boi Faltings. "Efficient Service Composition Using Zero-Suppressed Reduced Ordered Binary Decision Diagrams." In 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06). IEEE, 2006. http://dx.doi.org/10.1109/wi.2006.68.

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Halder, Nilimesh, A. B. M. Tariqul Islam, Mohammad Fazleh Elahi, and Ju Bin Song. "Analysis of composition techniques for combinational switching functions using reduced ordered Binary Decision Diagrams (ROBDDs)." In 2007 10th International Conference on Computer and Information Technology (ICCIT 2007). IEEE, 2007. http://dx.doi.org/10.1109/iccitechn.2007.4579401.

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Hou, Jie, Fengying Li, and Huijiao Wang. "An Ordered Binary Decision Diagram Model for Production Knowledge Representation and its Reasoning." In 2009 Third International Conference on Genetic and Evolutionary Computing (WGEC 2009). IEEE, 2009. http://dx.doi.org/10.1109/wgec.2009.103.

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Segerlind, Nathan. "On the Relative Efficiency of Resolution-Like Proofs and Ordered Binary Decision Diagram Proofs." In 2008 23rd Annual IEEE Conference on Computational Complexity. IEEE, 2008. http://dx.doi.org/10.1109/ccc.2008.34.

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Zhang, Mingwei, Liangda Fang, Zhenhao Gu, Quanlong Guan, and Yong Lai. "A Multi-Valued Decision Diagram-Based Approach to Constrained Optimal Path Problems over Directed Acyclic Graphs." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/219.

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Numerous combinatorial optimization problems can be reduced to the optimal path problem over directed acyclic graphs (DAGs). The constrained version of the optimal path problem requires the solution to satisfy a given logical constraint. BDD-constrained search (BCS) is an efficient algorithm for the constrained optimal path problem over DAGs. This algorithm considers edges as variables and constraints as Boolean functions and maintains constraints via binary decision diagrams (BDDs), a compact form of Boolean functions. However, BCS involves redundant operations during the search process. To reduce these redundant operations, we use vertices instead of edges as variables and hence represent constraints as multi-valued functions. Due to the multi-valued representation of constraints, we propose a novel algorithm, namely MDD-constrained search (MCS), by using multi-valued decision diagrams (MDDs) instead of BDDs, an efficient representation of multi-valued functions. In addition, we improve MCS via domain reduction in multi-valued functions. Experimental results prove that our proposed algorithm outperforms BCS.
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Kennedy, Lance, Issouf Kindo, and Arthur Choi. "On Training Neurons with Bounded Compilations." In 20th International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/kr.2023/39.

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Knowledge compilation offers a formal approach to explaining and verifying the behavior of machine learning systems, such as neural networks. Unfortunately, compiling even an individual neuron into a tractable representation such as an Ordered Binary Decision Diagram (OBDD), is an NP-hard problem. In this paper, we consider the problem of training a neuron from data, subject to the constraint that it has a compact representation as an OBDD. Our approach is based on the observation that a neuron can be compiled into an OBDD in polytime if (1) the neuron has integer weights, and (2) its aggregate weight is bounded. Unfortunately, we first show that it is also NP-hard to train a neuron, subject to these two constraints. On the other hand, we show that if we train a neuron generatively, rather than discriminatively, a neuron with bounded aggregate weight can be trained in pseudo-polynomial time. Hence, we propose the first efficient algorithm for training a neuron that is guaranteed to have a compact representation as an OBDD. Empirically, we show that our approach can train neurons with higher accuracy and more compact OBDDs.
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