Binary Decision Diagrams Research Articles

Availability importance measures of components in smart electric power grid systems

The emergence of the smart grid has brought great innovation in the new distribution power system, facilitated a green and sustainable energy-based society, and mitigated the growing energy crisis. The smart grid is regarded as the next generation electrical power grid. It not only improves the power distribution systems with the techniques of distributed generation, but also makes the systems more complicated than the traditional ones. Thus it is important to evaluate the availability of smarts grids and to indicate the vulnerable parts of the systems. In this paper, a hierarchical model consisting of a layered fault tree (FT) and continuous-time Markov chains (CTMCs) is presented to model a smart grid system with two different power supply modes. We also analyze the component importance of the system, aiming to find the weak parts of the system thereby improving the system design. The importance analysis of components is based on parametric sensitivities and binary decision diagram (BDD) representation for the FTs. In a numerical illustration, we quantify the availability of the system with two power supply modes and also evaluate the importance of all components in the system.

Using Extended Logical Primitives for Efficient BDD Building

Binary Decision Diagrams (BDDs) have been used to represent logic models in a variety of research contexts, such as software product lines, circuit testing, and plasma confinement, among others. Although BDDs have proven to be very useful, the main problem with this technique is that synthesizing BDDs can be a frustratingly slow or even unsuccessful process, due to its heuristic nature. We present an extension of propositional logic to tackle one recurring phenomenon in logic modeling, namely groups of variables related by an exclusive-or relationship, and also consider two other extensions: one in which at least n variables in a group are true and another one for in which at most n variables are true. We add XOR, atLeast-n and atMost-n primitives to logic formulas in order to reduce the size of the input and also present algorithms to efficiently incorporate these constructions into the building of BDDs. We prove, among other results, that the number of nodes created during the process for XOR groups is reduced from quadratic to linear for the affected clauses. the XOR primitive is tested against eight logical models, two from industry and six from Kconfig-based open-source projects. Results range from no negative effects in models without XOR relations to performance gains well into two orders of magnitude on models with an abundance of this kind of relationship.

Satisfiability Algorithm for Syntactic Read-k-times Branching Programs

The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink. In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink. In a preliminary version of this paper, we provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time \(O\left (\text {poly}(n, m^{k^{2}})\cdot 2^{(1-4^{-k-1})n}\right )\). In this paper, we improve the bounds for k = 2. More precisely, we show that the satisfiability of syntactic read-twice branching programs can be solved in time \(O\left (\text {poly}(n, m)\cdot 2^{5n/6}\right )\). Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993].

Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time.

Circuit Lower Bounds for MCSP from Local Pseudorandom Generators

The Minimum Circuit Size Problem (MCSP) asks if a given truth table of a Boolean function f can be computed by a Boolean circuit of size at most θ, for a given parameter θ. We improve several circuit lower bounds for MCSP, using pseudorandom generators (PRGs) that are local; a PRG is called local if its output bit strings, when viewed as the truth table of a Boolean function, can be computed by a Boolean circuit of small size. We get new and improved lower bounds for MCSP that almost match the best-known lower bounds against several circuit models. Specifically, we show that computing MCSP, on functions with a truth table of length N , requires • N 3− o (1) -size de Morgan formulas, improving the recent N 2− o (1) lower bound by Hirahara and Santhanam (CCC, 2017), • N 2− o (1) -size formulas over an arbitrary basis or general branching programs (no non-trivial lower bound was known for MCSP against these models), and • 2 Ω( N 1/( d +1.01)) -size depth- d AC 0 circuits, improving the (implicit, in their work) exponential size lower bound by Allender et al. (SICOMP, 2006). The AC 0 lower bound stated above matches the best-known AC 0 lower bound (for PARITY) up to a small additive constant in the depth. Also, for the special case of depth-2 circuits (i.e., CNFs or DNFs), we get an optimal lower bound of 2 Ω( N ) for MCSP.

Reliability evaluation of avionics system with imperfect fault coverage and propagated failure mechanisms

Fault tolerance designs are essential techniques for systems that require high levels of reliability, such as aircraft or spacecraft control system. Imperfect Fault Coverage (IFC) may lead to the failure of a system or subsystem even with adequate redundancy. Previous studies of IFC mostly concentrated on evaluating Coverage Factor (CF), whereas the system failure behaviors with IFC have rarely been involved. Failures that occur in low-layer may be covered by high-layer. However, if the coverage is imperfect, uncovered failure will have functional and physical impact on the system behavior. In this thesis, the failure behavior and reliability of IFC of multi-layer systems are studied and a Binary Decision Diagram (BDD)-based modeling and simulation method are proposed to evaluate system reliability. As a case, the failure behavior of an aero engine electronic controller with IFC is studied. The results show that the IFC may impact system behavior without taking the IFC into account, the system maintenance intervals may reduce, and thus the maintenance costs will increase.

Adaptively Simulation-Secure Attribute-Hiding Predicate Encryption

This paper demonstrates how to achieve simulation-based strong attribute hiding against adaptive adversaries for predicate encryption (PE) schemes supporting expressive predicate families under standard computational assumptions in bilinear groups. Our main result is a simulation-based adaptively strongly partially-hiding PE (PHPE) scheme for predicates computing arithmetic branching programs (ABP) on public attributes, followed by an inner-product predicate on private attributes. This simultaneously generalizes attribute-based encryption (ABE) for boolean formulas and ABP's as well as strongly attribute-hiding PE schemes for inner products. The proposed scheme is proven secure for any a priori bounded number of ciphertexts and an unbounded (polynomial) number of decryption keys, which is the best possible in the simulation-based adaptive security framework. This directly implies that our construction also achieves indistinguishability-based strongly partially-hiding security against adversaries requesting an unbounded (polynomial) number of ciphertexts and decryption keys. The security of the proposed scheme is derived under (asymmetric version of) the well-studied decisional linear (DLIN) assumption. Our work resolves an open problem posed by Wee in TCC 2017, where his result was limited to the semi-adaptive setting. Moreover, our result advances the current state of the art in both the fields of simulation-based and indistinguishability-based strongly attribute-hiding PE schemes. Our main technical contribution lies in extending the strong attribute hiding methodology of Okamoto and Takashima [EUROCRYPT 2012, ASIACRYPT 2012] to the framework of simulation-based security and beyond inner products.

Minimization of Binary Decision Diagrams for Systems of Incompletely Defined Boolean Functions Using Inverse Cofactors

Minimization of Binary Decision Diagrams for Systems of Incompletely Defined Boolean Functions Using Inverse Cofactors

Dynamic study of critical factors of explosion accident in laboratory based on FTA

Laboratory safety has been widely concerned, but fire, explosion, poisoning and other accidents occur from time to time. Among them, the proportion of safety accidents, casualties and economic losses caused by explosion are relatively high. In particular, the safety, reliability and maintainability of laboratories in colleges and universities and scientific research institutes should be evaluated and optimized. Therefore, it is necessary to use efficient, reliable and economical methods to identify and monitor the key factors that will cause explosion accidents in the laboratory. In this paper, through the combination of fault tree analysis (FTA) and binary decision diagram (BDD), the three main sources of explosion accidents in laboratory (gas cylinder, pressure device and hazardous chemicals) are analyzed quantitatively. When using BDD to simplify FT operation, a variety of event sorting methods are compared. Finally, it is found that “Level” and “AND” methods can provide a more convenient and reasonable number of cut sets. Considering different methods to measure the importance of basic events, it is found that similar results can be obtained. The importance of Critical is used to identify the importance of events, combined with its change with time, the change of importance is analyzed dynamically. The key factors from four aspects of “human”, “machine”, “environment” and “management” in laboratory explosion accident are determined. It provides a new idea for the dynamic safety management and maintenance of the laboratory, and puts forward some ideas for the new research content at the end of this paper.

Dynamic programming algorithms for computing power indices in weighted multi-tier games

In weighted games each voter has a weight assigned and “yes”-voters win if the sum of each weight is greater than or equal to the quota. In weighted multi-tier games, we have several weighted games (tiers) over the same set of voters. In this article, algorithms for calculating Banzhaf and Shapley–Shubik indices for three different type of games are proposed: weighted AND-games, weighted OR-games and games where the tiers have conjunctive normal form. The presented algorithms are generalizations of known computational methods using dynamic programming technique. Finally, some applications and experiments are carried out and these algorithms are compared to a fairly new method based on binary decision diagrams.

Reversible Circuit Synthesis Time Reduction Based on Subtree-Circuit Mapping

Several works have been conducted regarding the reduction of the energy consumption in electrical circuits. Reversible circuit synthesis is considered to be one of the major efforts at reducing the amount of power consumption. The field of reversible circuit synthesis uses a large number of proposed algorithms to minimize the overall cost of circuits synthesis (represented in the line number and quantum cost), with minimal concern paid for synthesis time. However, because of the iterative nature of the synthesis optimization algorithms, synthesis time cannot be neglected as a parameter which needs to be tackled, especially for large-scale circuits which need to be realized by cascades of reversible gates. Reducing the synthesis cost can be achieved by Binary Decision Diagrams (BDDs), which are considered to be a step forward in this field. Nevertheless, the mapping of each BDD node into a cascade of reversible gates during the synthesis process is time-consuming. In this work, we implement the idea of the subtree-based mapping of BDD nodes to reversible gates instead of the classical nodal-based algorithm to effectively reduce the entire reversible circuit synthesis time. Considering Depth-First Search (DFS), we convert an entire BDD subtree in one step into a cascade of reversible gates. A look-up table for all possible combinations of subtrees and their corresponding reversible gates has been constructed, in which a hash key is used to directly access subtrees during the mapping process. This table is constructed as a result of a comprehensive study of all possible BDD subtrees and considered as a reference during the conversion process. The conducted experimental tests show a significant synthesis time reduction (around 95% on average), preserving the correctness of the algorithm in generating a circuit realizing the required Boolean function.

Reliability Dynamic Analysis by Fault Trees and Binary Decision Diagrams

New wind turbines are becoming more complex and reliability analysis of them rising in complexity. The systems are composed of many components. Fault tree is used as an useful tool to analyze these interrelations and provide a scheme of the wind turbine, to get a quick overview of the behavior of the system under certain conditions of the components. However, it is complicated and in some cases not possible, to identify the conditions that would generate a wind turbine failure. A quantitative and qualitative reliability analysis of the wind turbine is proposed in this study. Binary decision diagrams are employed as a suitable and operational method to facilitate this analysis and to get an analytical expression by the Boolean functions. The size of the binary decision diagram, i.e., the computational cost for solving the problem, has an important dependence on the order of the components or events considered. Different heuristic ranking methods are used to find an optimal order or one closed, and to validate the results: AND, level, top-down-left-right, deep-first search and breadth-first-search. Birnbaum and criticality importance measures are proposed to evaluate the relevance of each component. This analysis leads to classify the events according to their importance with respect to the probability of the top event. This analysis provides the basis for making medium and long-term maintenance strategies.

МЕТОД ЗБЕРІГАННЯ ДАНИХ РЕКОМЕНДАЦІЙНОЇ СИСТЕМИ НА ОСНОВІ БІНАРНИХ ДІАГРАМ РІШЕНЬ

Стаття присвячена дослідженню методів збереження даних рекомендаційних систем. Запропоновано та досліджено використання бінарних діаграм рішень для збереження таких даних. Внаслідок великого розміру рекомендаційних систем суттєвими є обмеження по оперативній пам'яті. Метою роботи є розробка методу зберігання даних рекомендаційної системи у формі бінарних діаграм рішень та порівняння з методами збереження на основі інших структур даних. Дані рекомендаційної системи зберігаються у вигляді графу із вершинами, які представляють користувачів системи та об'єкти системи, а ребра – дії користувачів системи, відношення подібності, зв'язки рекомендацій тощо. Для підвищення ефективності у випадку інтенсивного редагування графу запропоновано збереження даних на основі “гарячого” (хеш-таблиця) та “холодного” (бінарна діаграма рішень) сховищ.Проведено серію експериментів для перевірки ефективності розробленого способу зберігання даних, для чого розроблено програмну модель спрощеної рекомендаційної системи та описано алгоритм роботи такої системи. В чисельному експерименті пропонований спосіб зберігання даних на основі бінарних дерев рішень порівнюється із трьома іншими: на основі бітових масивів, зв'язних списків та хеш-таблиць. Розглянуто переваги та недоліки реалізації кожного із вказаних методів. В ході експерименту для різних значень кількості агентів, предметів, сесій та вподобань досліджено максимальні та мінімальні значення використаної оперативної пам'яті, а також час генерації лайків, сесій та рекомендацій. Встановлено, що у випадку застосування бінарних діаграм рішень обсяг використаної оперативної пам’яті є нижчим за інші способи при меншій швидкодії, що частково може бути компенсовано декількома застосованими оптимізаціями. Завдяки меншому використанню оперативної пам'яті можна зберігати інформацію про більшу кількість вподобань, що може виявитися корисним у випадку великих розмірів графу рекомендаційної системи. Можливість для бінарних діаграм рішень пошуку даних за частковими ключами додатково дозволяє зберігати дані більшої розмірності

Early detection and diagnosis of thermal runaway reactions using model-based approaches in batch reactors

Since the early 1990s, considerable efforts have been made in researching and applying approaches for faults detection and diagnosis in chemical processes. The occurrence of chemical accidental events due to thermal runaways has serious consequences for the human, environmental and economic and encourage these efforts. This is the main motivation for this paper that details a fault detection and diagnosis approach for exothermic reactions. The proposed approach is based on the temperature measurements. It compares the collected measurements with a reference behavior for early thermal runaway detection. Once a fault is detected, characteristic features are extracted from the successive measurements collected within a time window. The fault isolation is based on a classification of these features with respect to several faulty modes. The studied faults are the most responsible for thermal runaway events. A multiset of linear classifiers and binary decision diagrams indexed with respect to the time are used for that purpose. The synthesis of peroxyformic acid in a batch reactor is considered to validate the proposed method by numerical simulations and experiments. The performance of the proposed method is carried out in a systematic way in order to evaluate its robustness and efficiency.

Iterative Variable Reordering: Taming Huge System Families

For the verification of systems using model-checking techniques, symbolic representations based on binary decision diagrams (BDDs) often help to tackle the well-known state-space explosion problem. Symbolic BDD-based representations have been also shown to be successful for the analysis of families of systems that arise, e.g., through configurable parameters or following the feature-oriented modeling approach. The state space of such system families face an additional exponential blowup in the number of parameters or features. It is well known that the order of variables in ordered BDDs is crucial for the size of the model representation. Especially for automatically generated models from real-world systems, family models might even be not constructible due to bad variable orders. In this paper we describe a technique, called iterative variable reordering, that can enable the construction of large-scale family models. We exemplify feasibility of our approach by means of an aircraft velocity control system with redundancy mechanisms modeled in the input language of the probabilistic model checker PRISM. We show that standard reordering and dynamic reordering techniques fail to construct the family model due to memory and time constraints, respectively, while the new iterative approach succeeds to generate a symbolic family model.

Modern design approach of faults (toggling faults, bridge faults and SAT) of reduced ordered binary decision diagram based on combo & sequential blocks

In this Research we are going to develop ROBDD (Reduced Ordered Binary Decision Diagram) designs to detect toggling faults, bridge faults and SAT (Stuck at Fault), Here we are going to develop sequential blocks using ROBDD and applying to the mux to detect stuck at faults and also connecting the combo & Sequential blocks to find the toggling faults by connecting or using automatic test pattern generator. In this research we are going to develop the bridges between the blocks of ROBDD designs and converting them to and or logic to find the bridge faults of the design. Finding bridge and toggle faults are more difficult in logic designs, here we use an advance technique to find the faults of the design by calculating the path delays of the individual blocks of the design. More concentrating on the path delays by using basic stuck at faults methods to refer the faults (toggling and bridge faults) at mux output. In our research the basic design modules are ROBDD circuit of both combinational and sequential blocks are designed and tested using Multiplexer and K-map Simplification Methods. The main purpose of the research to find the faults at all levels of all logic designs which involves in both combinational and sequential blocks of the design.

ИССЛЕДОВАНИЕ ПРОЦЕССА ТЕПЛОВОГО КОНТРОЛЯ КОЛОДОЧНЫХ ТОРМОЗОВ ПОДВИЖНОГО СОСТАВА МЕТОДОМ ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ

The development of heavy speed freight train communications in the Russian Federation results in the increased thermal loading of braking system elements of rolling-stock, in particular, in shoe brakes. Taking into account the requirements of branch program documents on wheel life increase, it is evident that the further development of freight communications requires a complex application of thermal diagnostics means for auto-brake equipment of rolling-stock during a train motion. 
 The statistics shows that the fifth part of wheel pair failures is connected with thermal-mechanical damages and the situation goes on to be aggravated. In view of this hardware and software means for thermal diagnostics of shoe brakes require further improvement. The purpose of this paper is the process investigation of shoe brake thermal control by method of computer simulation and the estimate of infrared optics position impact upon control results. 
 There is considered a model for the definition of a scanning path and computation of a signal level being part of a complex simulation model of wheel thermal control. The model offered is based on the methods of solid dynamics system investigations in the basis of which there is an application of theorems on mass center motion and changes of a solid kinetic moment. 
 The model is used for finding a form and a spot area at every time moment of scanning by a solution of a problem on a dynamic spatial intersection of a wheel surface with the control area. There are considered different versions of optics orientation to an object of control for each of which for the first time there are obtained calculated thermal signals from the object under control. The analysis has shown that at the optics orientation to wheels from the outside a wheel tread appears to be in the control area that allows defining a maximum temperature of a wheel. But at the realization of emergency brake application a sharp short-time temperature increase of a tread is possible which indicates an improper operation of a brake unit. 
 The optics orientation to a wheel from its inner side allows excluding false alarm indices at emergency brake application. The correctness of the results shown in the paper is confirmed by convergence with the results of wheel heating monitoring and environmental tests of experimental complexes of thermal control means of shoe brakes.

Practical Frank–Wolfe Method with Decision Diagrams for Computing Wardrop Equilibrium of Combinatorial Congestion Games

Computation of equilibria for congestion games has been an important research subject. In many realistic scenarios, each strategy of congestion games is given by a combination of elements that satisfies certain constraints; such games are called combinatorial congestion games. For example, given a road network with some toll roads, each strategy of routing games is a path (a combination of edges) whose total toll satisfies a certain budget constraint. Generally, given a ground set of n elements, the set of all such strategies, called the strategy set, can be large exponentially in n, and it often has complicated structures; these issues make equilibrium computation very hard. In this paper, we propose a practical algorithm for such hard equilibrium computation problems. We use data structures, called zero-suppressed binary decision diagrams (ZDDs), to compactly represent strategy sets, and we develop a Frank–Wolfe-style iterative equilibrium computation algorithm whose per-iteration complexity is linear in the size of the ZDD representation. We prove that an ϵ-approximate Wardrop equilibrium can be computed in O(poly(n)/ϵ) iterations, and we improve the result to O(poly(n) log ϵ−1) for some special cases. Experiments confirm the practical utility of our method.

Winning Strategy Tree Construction for BDD-Based ATL Model Checkers

The Alternating-time Temporal Logic (ATL) is a temporal logic for formal verification of open systems, which supports selective quantification over paths. The open system can be represented as a game where the system and the environment pick their moves in turn or simultaneously. The ATL model checker Mocha has been developed by using Binary Decision Diagrams (BDDs), and successfully employed for open system verification. However, since Mocha symbolically manipulates a set of states by a BDD, it is hard to generate a winning strategy as a witness or a counter-example. In this paper, we propose a novel algorithm to efficiently construct a winning strategy tree and report that our technique has been successfully implemented on Mocha.

Solving Delete Free Planning with Relaxed Decision Diagram Based Heuristics

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.