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Journal articles on the topic 'Algebaic Decision Diagram'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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1

Rauzy, Antoine, and Yang. "Decision Diagram Algorithms to Extract Minimal Cutsets of Finite Degradation Models." Information 10, no. 12 (2019): 368. http://dx.doi.org/10.3390/info10120368.

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In this article, we propose decision diagram algorithms to extract minimal cutsets of finite degradation models. Finite degradation models generalize and unify combinatorial models used to support probabilistic risk, reliability and safety analyses (fault trees, attack trees, reliability block diagrams…). They formalize a key idea underlying all risk assessment methods: states of the models represent levels of degradation of the system under study. Although these states cannot be totally ordered, they have a rich algebraic structure that can be exploited to extract minimal cutsets of models, w

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2

DJIDJEV, HRISTO N., and ANDRZEJ LINGAS. "ON COMPUTING VORONOI DIAGRAMS FOR SORTED POINT SETS." International Journal of Computational Geometry & Applications 05, no. 03 (1995): 327–37. http://dx.doi.org/10.1142/s0218195995000192.

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We show that the Voronoi diagram of a finite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time. In contrast, we observe that the problem of computing the Voronoi diagram of a finite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires Ω(n log n) operations in the algebraic decision tree model. As a corollary from the first result, we show that the bounded Voronoi diagrams of simple n-vertex polygons which can be efficiently cut into

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Dudek, Jeffrey, Vu Phan, and Moshe Vardi. "ADDMC: Weighted Model Counting with Algebraic Decision Diagrams." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (2020): 1468–76. http://dx.doi.org/10.1609/aaai.v34i02.5505.

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We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the main data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We then compare ADDMC to four state-of-the-art weighted model counters (Cachet, c2d, d4, and miniC2D) on 1914 standard model counting benchmarks and show that ADDMC significantly improves the virtual best solver.

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Bibilo, P. N., and V. I. Romanov. "Experimental Study of Algorithms for Minimization of Binary Decision Diagrams using Algebraic Representations of Cofactors." Programmnaya Ingeneria 13, no. 2 (2022): 51–67. http://dx.doi.org/10.17587/prin.13.51-67.

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BDD (Binary Decision Diagram) is used for technology-independent optimization, performed as the first stage in the synthesis of logic circuits in the design of ASIC (application-specific integrated circuit). BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph is associated with the complete or reduced Shannon expansion formula. Binary decision diagrams with mutually inverse subfunctions (cofac-tors) are considered. We have developed algorithms for finding algebraic representations of cofactors of the same BDD level in the form of a di

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Pralet, C., G. Verfaillie, and T. Schiex. "An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities." Journal of Artificial Intelligence Research 29 (August 23, 2007): 421–89. http://dx.doi.org/10.1613/jair.2151.

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Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we firs

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Bibilo, P. N. "Disjunctive and conjunctive decompositions of incompletely defined Boolean functions in a Binary Decision Diagram." Informatics 22, no. 1 (2025): 40–65. https://doi.org/10.37661/1816-0301-2025-22-1-40-65.

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Objectives. The problems of minimizing the number of cofactors (subfunctions) of the Shannon expansions located at the same level of the BDD, representing a system of incompletely defined (partial) Boolean functions, are considered. To reduce the number of functions, it is proposed to find a subset of such functions that can be expressed as algebraic decompositions of disjunctions or conjunctions of other predefined partial functions, while the directed graph of function occurrences in decompositions should not contain contours.Methods. Finding disjunctive and conjunctive decompositions requir

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Joshi, S., and R. Khardon. "Probabilistic Relational Planning with First Order Decision Diagrams." Journal of Artificial Intelligence Research 41 (June 21, 2011): 231–66. http://dx.doi.org/10.1613/jair.3205.

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Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of decision diagrams (FODD) and developed a value iteration algorithm for this representation. This paper develops several improvements to the FODD algorithm that make the approach practical. These include,

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8

Falkowski, B. J., and Chip-Hong Chang. "Efficient calculation of Gray code-ordered Walsh spectra through algebraic decision diagrams." Electronics Letters 34, no. 9 (1998): 848. http://dx.doi.org/10.1049/el:19980606.

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9

Speck, David, Florian Geißer, and Robert Mattmüller. "Symbolic Planning with Edge-Valued Multi-Valued Decision Diagrams." Proceedings of the International Conference on Automated Planning and Scheduling 28 (June 15, 2018): 250–58. http://dx.doi.org/10.1609/icaps.v28i1.13890.

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Symbolic representations have attracted significant attention in optimal planning. Binary Decision Diagrams (BDDs) form the basis for symbolic search algorithms. Closely related are Algebraic Decision Diagrams (ADDs), used to represent heuristic functions. Also, progress was made in dealing with models that take state-dependent action costs into account. Here, costs are represented as Edge-valued Multi-valued Decision Diagrams (EVMDDs), which can be exponentially more compact than the corresponding ADD representation. However, they were not yet considered for symbolic planning. In this work, w

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10

Van den Broeck, Guy, Ingo Thon, Martijn Van Otterlo, and Luc De Raedt. "DTProbLog: A Decision-Theoretic Probabilistic Prolog." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (2010): 1217–22. http://dx.doi.org/10.1609/aaai.v24i1.7755.

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We introduce DTProbLog, a decision-theoretic extension of Prolog and its probabilistic variant ProbLog. DTProbLog is a simple but expressive probabilistic programming language that allows the modeling of a wide variety of domains, such as viral marketing. In DTProbLog, the utility of a strategy (a particular choice of actions) is defined as the expected reward for its execution in the presence of probabilistic effects. The key contribution of this paper is the introduction of exact, as well as approximate, solvers to compute the optimal strategy for a DTProbLog program and the decision problem

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Friedl, Katalin, and László Kabódi. "Storing the Quantum Fourier Operator in the QuIDD Data Structure." Acta Cybernetica 23, no. 2 (2017): 503–12. http://dx.doi.org/10.14232/actacyb.23.2.2017.5.

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Quantum algorithms can be simulated using classical computers, but the typical time complexity of the simulation is exponential. There are some data structures which can speed up this simulation to make it possible to test these algorithms on classical computers using more than a few qubits. One of them is QuIDD by Viamontes et al., which is an extension of the Algebraic Decision Diagram. In this paper, we examine the matrix of Fourier operator and its QuIDD representation. To utilize the structure of the operator we propose two orderings (reversed column variables and even-odd order), both re

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Ibănescu, Radu, and Cătălin Ungureanu. "Lagrange's Equations versus Bond Graph Modeling Methodology by an Example of a Mechanical System." Applied Mechanics and Materials 809-810 (November 2015): 914–19. http://dx.doi.org/10.4028/www.scientific.net/amm.809-810.914.

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The bond graph modeling method was discovered by Henry Painter in 1959 and has quickly become a wide spread method all over the modeling engineering world. The method is based on the analysis of power circulation in systems and has some indisputable advantages over other modeling methods, based in principle on mathematical aspects. The paper proposes a comparison between the bond graph method and Lagrange's equations method, by applying both methods to model a mechanical system. The bond graph model is a graphical model. There are three possibilities to exploit the bond-graph diagram. The firs

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Cramer, Claes. "Problem-solving a lesson from relativity in physics education." Physics Education 57, no. 4 (2022): 045010. http://dx.doi.org/10.1088/1361-6552/ac5641.

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Abstract The principle of relativity is of fundamental importance in practice when we are solving problems in physics since the axiom states that the result of any physical experiment is the same when performed with identical initial conditions relative to any inertial coordinate system. Hence, conceptual knowledge of coordinate systems is central in any physics problem-solving framework. This opens up the question whether upper secondary school students should be taught to set up coordinate systems and apply basic coordinate transformations systematically when solving problems or if it should

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14

Bibilo, P. N., and V. I. Romanov. "Minimization of Binary Decision Diagrams for Systems of Completely Defined Boolean Functions using Algebraic Representations of Cofactors." INFORMACIONNYE TEHNOLOGII 27, no. 8 (2021): 395–408. http://dx.doi.org/10.17587/it.27.395-408.

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In design systems for digital VLSI (very large integrated circuits), the BDD is used for VLSI verification, as well as for technologically independent optimization, performed as the first stage in the synthesis of logic circuits in various technological bases. BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph corresponds to the complete or reduced Shannon expansion formula. Having constructed BDD representation for systems of Boolean functions, it is possible to perform additional logical optimization based on the proposed method of

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15

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.

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Bibilo, P. N. "Minimizing Binary Decision Diagrams for Systems of Incompletely Defined Boolean Functions Using Algebraic Cofactor Expansions." Journal of Computer and Systems Sciences International 61, no. 4 (2022): 539–66. http://dx.doi.org/10.1134/s1064230722030029.

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17

Bibilo, P. N., and V. I. Romanov. "Experimental Study of Algorithms for Minimization of Binary Decision Diagrams Using Algebraic Representations of Cofactors." Programming and Computer Software 49, no. 4 (2023): 268–85. http://dx.doi.org/10.1134/s0361768823040035.

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Bibilo, P. N., and V. I. Romanov. "Minimization of binary decision diagrams for systems of completely defined Boolean functions using Shannon expansions and algebraic representations of cofactors." Informatics 18, no. 2 (2021): 7–32. http://dx.doi.org/10.37661/1816-0301-2021-18-2-7-32.

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In the systems of digital VLSI design (Very Large Integrated Circuits), the BDD (Binary Decision Diagram) is used for VLSI verification, as well as for technologically independent optimization as the first stage in the synthesis of logic circuits in various technological bases. The BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph corresponds to the complete or reduced Shannon expansion formula. When BDD representation for systems of Boolean functions is constructed, it is possible to perform additional logical optimization based on

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19

Kumar, Arvind, and Hiroaki Wagatsuma. "A Kamm’s Circle-Based Potential Risk Estimation Scheme in the Local Dynamic Map Computation Enhanced by Binary Decision Diagrams." Sensors 22, no. 19 (2022): 7253. http://dx.doi.org/10.3390/s22197253.

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Autonomous vehicles (AV) are a hot topic for safe mobility, which inevitably requires sensors to achieve autonomy, but relying too heavily on sensors will be a risk factor. A high-definition map (HD map) reduces the risk by giving geographical information if it covers dynamic information from moving entities on the road. Cooperative intelligent transport systems (C-ITS) are a prominent approach to solving the issue and local dynamic maps (LDMs) are expected to realize the ideal C-ITS. An actual LDM implementation requires a fine database design to be able to update the information to represent

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20

Salmani, Bahare, and Joost-Pieter Katoen. "Automatically Finding the Right Probabilities in Bayesian Networks." Journal of Artificial Intelligence Research 77 (August 27, 2023): 1637–96. http://dx.doi.org/10.1613/jair.1.14044.

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This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, w

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Bibilo, P. N., Yu Yu Lankevich, and V. I. Romanov. "Logical Minimization of Multilevel Representations of Boolean Function Systems." Informacionnye Tehnologii 29, no. 2 (2023): 59–71. http://dx.doi.org/10.17587/it.29.59-71.

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A decisive influence on complexity and speed of a combinational logic circuit of library CMOS elements is exerted by the preliminary stage of technologically independent optimization of the implemented system of Boolean functions. At present, the main methods of such optimization in the logical synthesis of custom CMOS VLSI blocks are methods for minimizing binary decision diagrams — Binary Decision Diagrams (BDD) or their modifications. Graphical representations of BDD are built on the basis of the Shannon expansions of Boolean functions. A BDD graph corresponds to a set of interrelated Shann

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22

Sanner, Scott, and Ehsan Abbasnejad. "Symbolic Variable Elimination for Discrete and Continuous Graphical Models." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (2021): 1954–60. http://dx.doi.org/10.1609/aaai.v26i1.8406.

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Probabilistic reasoning in the real-world often requires inference incontinuous variable graphical models, yet there are few methods for exact, closed-form inference when joint distributions are non-Gaussian. To address this inferential deficit, we introduce SVE -- a symbolic extension of the well-known variable elimination algorithm to perform exact inference in an expressive class of mixed discrete and continuous variable graphical models whose conditional probability functions can be well-approximated as piecewise combinations of polynomials with bounded support. Using this representation,

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23

Dudek-Dyduch, Ewa, Zbigniew Gomolka, Boguslaw Twarog, and Ewa Zeslawska. "Intelligent ALMM System - implementation assumptions for its Knowledge Base." ITM Web of Conferences 21 (2018): 00002. http://dx.doi.org/10.1051/itmconf/20182100002.

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The paper introduces the concept of implementation assumptions about the Knowledge Base (KB) system cooperating with intelligent information system for the discrete optimization of problem solving, named Intelligent ALMM System. This system utilizes a modeling paradigm named Algebraic Logical Meta Model of Multistage Decision Processes (ALMM) and its theory, both developed by Dudek-Dyduch E. The system solves combinatorial and discrete optimization problems including NP-hard problems with possible user assistance. The models of problems are stored in a Problem Model Library. In this paper the

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Yang, Suwei, and Kuldeep S. Meel. "Engineering an Exact Pseudo-Boolean Model Counter." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 8200–8208. http://dx.doi.org/10.1609/aaai.v38i8.28660.

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Model counting, a fundamental task in computer science, involves determining the number of satisfying assignments to a Boolean formula, typically represented in conjunctive normal form (CNF). While model counting for CNF formulas has received extensive attention with a broad range of applications, the study of model counting for Pseudo-Boolean (PB) formulas has been relatively overlooked. Pseudo-Boolean formulas, being more succinct than propositional Boolean formulas, offer greater flexibility in representing real-world problems. Consequently, there is a crucial need to investigate efficient

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Gossen, Frederik, and Bernhard Steffen. "Algebraic aggregation of random forests: towards explainability and rapid evaluation." International Journal on Software Tools for Technology Transfer, September 29, 2021. http://dx.doi.org/10.1007/s10009-021-00635-x.

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AbstractRandom Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise the outcome of their predictions. However, this comes at a cost: it is increasingly difficult to understand why a Random Forest made a specific choice, and its running time for classification grows linearly with the size (number of trees). In this paper, we propose a method to aggregate large Random Forests into a single, semantically equivalent decision diagram which has the following two effects: (1) minimal, sufficient explanations for Random Forest-based classifications

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Mladenov, Martin, Vaishak Belle, and Kristian Kersting. "The Symbolic Interior Point Method." Proceedings of the AAAI Conference on Artificial Intelligence 31, no. 1 (2017). http://dx.doi.org/10.1609/aaai.v31i1.10699.

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Numerical optimization is arguably the most prominent computational framework in machine learning and AI. It can be seen as an assembly language for hard combinatorial problems ranging from classification and regression in learning, to computing optimal policies and equilibria in decision theory, to entropy minimization in information sciences. Unfortunately, specifying such problems in complex domains involving relations, objects and other logical dependencies is cumbersome at best, requiring considerable expert knowledge, and solvers require models to be painstakingly reduced to standard for

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27

Shtrakov, Slavcho. "Minor complexity of discrete functions." Applied Computing and Informatics ahead-of-print, ahead-of-print (2020). http://dx.doi.org/10.1016/j.aci.2018.07.003.

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In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram. When assigning values to some variables in a function the resulting functions are called subfunctions, and when identifying some variables the resulting functions are called minors. The sets of essential variables in subfunctions of f are called separable in f.We examine the maximal separable subsets of variables and their conjugates, introduced in the paper, proving that each such set has at least one conjugate. The essential a

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28

Vianna, Luis, Leliane De Barros, and Scott Sanner. "Real-Time Symbolic Dynamic Programming." Proceedings of the AAAI Conference on Artificial Intelligence 29, no. 1 (2015). http://dx.doi.org/10.1609/aaai.v29i1.9651.

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Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tot

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29

Béaur, Pierre, and Jarkko Kari. "Effective Projections on Group Shifts to Decide Properties of Group Cellular Automata." International Journal of Foundations of Computer Science, July 19, 2023, 1–24. http://dx.doi.org/10.1142/s0129054123480040.

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Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases include finite fields, finite commutative rings and finite commutative groups. In this paper, we provide methods to generalize these results to the broader case of group cellular automata, that is, the case where the state set is a finite (possibly non-commutative) finite group. The configuration space is not even necessarily the full shift but a subshift — ca

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30

Klarlund, Nils. "An n log n Algorithm for Online BDD Refinement." BRICS Report Series 2, no. 29 (1995). http://dx.doi.org/10.7146/brics.v2i29.19931.

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Binary Decision Diagrams are in widespread use in verification systems<br />for the canonical representation of Boolean functions. A BDD representing<br />a function phi : B^nu -> N can easily be reduced to its canonical form in<br />linear time.<br />In this paper, we consider a natural online BDD refinement problem<br />and show that it can be solved in O(n log n) if n bounds the size of the<br />BDD and the total size of update operations.<br />We argue that BDDs in an algebraic framework should be understood<br />as minimal fixed points su

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31

Mahmoud, Ahmed, and Jaka Sunarso. "A mixed integer nonlinear programming approach for integrated bio-refinery and petroleum refinery topology optimization." Chemical Product and Process Modeling, July 20, 2020. http://dx.doi.org/10.1515/cppm-2019-0124.

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AbstractThe conversion of biomass into gasoline and diesel in bio-refinery process is an attractive process given its carbon neutral and sustainable nature. The economics of bio-refinery can be improved via integration with petroleum refinery, whereby bio-refinery intermediates can be processed into gasoline and diesel in the well-established petroleum refinery processing units, i. e., hydrocracking (HC) and fluidized catalytic cracking (FCC) units. However, the integration of the new bio-refinery into the existing petroleum refinery may not give the optimum solution given the capacities const

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Kinsner, Witold, Dario Schor, Samantha Olson, and Mount First Ng. "LEARNING HOW TO DESIGN A GRAPHICS PROCESSOR." Proceedings of the Canadian Engineering Education Association (CEEA), June 20, 2012. http://dx.doi.org/10.24908/pceea.v0i0.4716.

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This paper describes the design and implementation of a rudimentary graphics processor, called GRAFIX, intended for use in a simple handheld gaming console. The processor is a part of a laboratory in an undergraduate course on Digital Systems Design 2 (DSD2) [1-2]. The GRAFIX processor can perform two different operations: (a) drawing an individual pixel, and (b) drawing a line using the Bresenham line drawing algorithm.The DSD2 course provides foundational material on discrete mathematics and the theory of modern very-large switching circuits. It presents computer engineering students with a

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Anzar. "AN EFFICIENT PSO OPTIMIZED INTEGRATION WEIGHT ESTIMATION USING D-PRIME STATISTICS FOR A MULTIBIOMETRIC SYSTEM." September 28, 2012. https://doi.org/10.5121/ijbb.2012.2304.

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International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.3, September 2012 DOI : 10.5121/ijbb.2012.2304 31 AN EFFICIENT PSO OPTIMIZED INTEGRATION WEIGHT ESTIMATION USING D-PRIME STATISTICS FOR A MULTIBIOMETRIC SYSTEM S. M. Anzar1 and P. S. Sathidevi2 1Department of Electronics & Communication Engineering, National Institute of Technology, Calicut, India, 673601 p090004ec@nitc.ac.in 2Department of Electronics & Communication Engineering, National Institute of Technology, Calicut, India, 673601 sathi@nitc.ac.in ABSTRACT The efficiency of a multibiometric system can be i

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