High Accuracy Asymptotic Bounds on the BDD Size and Weight of the Hardest Functions

Lozhkin, S. A.; Shiganov, Alexander E.

doi:10.3233/fi-2010-347

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…In our research we consider ROBDD sizes for a fixed variable order. Lozhkin et al [LS10] extends the work of Shannon [Sha49] in examining sizes when allowed to seek a better variable ordering.…”

Section: Related Workmentioning

confidence: 99%

“…We wish to examine the question of whether the Common Lisp run-time type reflection can be improved by searching for better ordering of the type specifiers at compile-time. The work of Lozhkin [LS10] and Shannon [Sha49] may give insight into how much improvement is possible, and hence whether it is worth dedicating compilation time to it. CUDD, as well as the system described by Brace et al [BRB90], both provide a subsystem for cache management.…”

Section: Future Workmentioning

confidence: 99%

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A Theoretical and Numerical Analysis of the Worst-Case Size of Reduced Ordered Binary Decision Diagrams

Newton

Verna

2019

ACM Trans. Comput. Logic

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Binary Decision Diagrams (BDDs) and in particular ROBDDs (Reduced Ordered BDDs) are a common data structure for manipulating Boolean expressions, integrated circuit design, type inferencers, model checkers, and many other applications. Although the ROBDD is a lightweight data structure to implement, the behavior, in terms of memory allocation, may not be obvious to the program architect. We explore experimentally, numerically, and theoretically the typical and worst-case ROBDD sizes in terms of number of nodes and residual compression ratios, as compared to unreduced BDDs. While our theoretical results are not surprising, as they are in keeping with previously known results, we believe our method contributes to the current body of research by our experimental and statistical treatment of ROBDD sizes. In addition, we provide an algorithm to calculate the worst-case size. Finally, we present an algorithm for constructing a worst-case ROBDD of a given number of variables. Our approach may be useful to projects deciding whether the ROBDD is the appropriate data structure to use, and in building worst-case examples to test their code.

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Section: Related Workmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

A Theoretical and Numerical Analysis of the Worst-Case Size of Reduced Ordered Binary Decision Diagrams

Newton

Verna

2019

ACM Trans. Comput. Logic

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“…, y t ) that essentially depends on all its variables. From [1,2,3] it follows that for Boolean function ψ and partition Δ of the cube B n there always exist Boolean functions…”

Section: Generalized Decomposition and Universal Sets Of Boolean Funcmentioning

confidence: 99%

“…It is shown in [1] (see also [2]) that described earlier selector vectors of internal Boolean functions of the generalized decomposition and universal sets of Boolean functions of the form (7) may be implemented substantially simpler than similar standard sets. The mentioned simplification is the larger, the smaller the entropy H(D) of the utilized partition D (see [1]):…”

Section: Generalized Decomposition and Universal Sets Of Boolean Funcmentioning

confidence: 99%

Synthesis of asymptotically size-optimal Boolean circuits protected from functionality inference

Lozhkin¹,

Shupletsov²,

Данилов³

et al. 2017

Матем. вопр. криптогр.

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“…В работах [1,2,4,5,11] рассмотрены и другие примеры классов схем, в которых для соответствующих «сложностных» функций Шеннона удалось получить асимптотические оценки высокой степени точности. 170 С. А. ЛОЖКИН Напомним, что в [1]…”

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Refined bounds on Shannon's function for complexity of circuits of some classes

Lozhkin

2023

MVK

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Earlier the author proposed rather general approaches and methods for obtaining high accuracy and close to high accuracy asymptotic bounds on Shannon's function for complexity in various classes of circuits. Most of the results obtained with their aid were published in a number of papers, except perhaps for the close to the high accuracy asymptotic bounds on Shannon's function for the complexity of circuits without restrictions on their structure. This paper fills this gap and presents a modified and simplified version of the above-mentioned method -- the synthesis method of circuits in arbitrary basis, that nevertheless allows to obtain the bounds with the required level of accuracy at the account of "effective" usage of the outputs branching of gates with minimal reduced "weight".

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High Accuracy Asymptotic Bounds on the BDD Size and Weight of the Hardest Functions

Cited by 5 publications

References 6 publications

A Theoretical and Numerical Analysis of the Worst-Case Size of Reduced Ordered Binary Decision Diagrams

A Theoretical and Numerical Analysis of the Worst-Case Size of Reduced Ordered Binary Decision Diagrams

Synthesis of asymptotically size-optimal Boolean circuits protected from functionality inference

Refined bounds on Shannon's function for complexity of circuits of some classes

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