An efficient variable partitioning approach for functional decomposition of circuits

Muthukumar, Venkatesan; Bignall, Robert J; Selvaraj, Henry

doi:10.1016/j.sysarc.2006.07.001

Cited by 7 publications

(8 citation statements)

References 16 publications

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“…Due to the huge solution space for larger functions, these methods are not practical. To overcome this difficulty, several heuristic methods have been suggested in the literature to avoid an exhausted search, like the methods represented in [21,16,22,13,3]. Among them in [16], the authors have proposed a method to search for the best solution.…”

Section: Discussionmentioning

confidence: 99%

“…The subsets Z 1 and Z 2 are called bound and free sets, respectively. A few papers deal with the search for the partition {Z 1 , Z 2 } at which this problem has a solution [2,9,18,29,21,16,7,19]. In this paper, the main attention is paid to the search for subsets Z 1 and Z 2 in a particular way.…”

Section: Definitions and Preliminary Stagesmentioning

confidence: 99%

“…It is important to find a successful solution for this problem, because it has a direct influence on the quality and cost of digital devices at the design process. It has been shown in [8,18] that a considerable number of papers have been already published on this topic and it is still interesting for the research [21,16,28,6,14,23,19]. The motivation is reducing the complexity of the problem by divide and conquer approach to find an appropriate set of sub-circuits.…”

Section: Introductionmentioning

confidence: 99%

“…The motivation is reducing the complexity of the problem by divide and conquer approach to find an appropriate set of sub-circuits. Efficiency and usefulness of functional decomposition have been demonstrated in theoretical papers [2,9,16,23]. It can be applied in many fields of modern engineering and science, such as combinational and sequential logic synthesis for VLSI systems, machine learning, decision systems, databases, data mining, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, several heuristic methods have been proposed in the literature to avoid an exhaustive search [21,16,22]. Although, heuristic approaches cannot guarantee the quality of the obtained results, sometimes they are the only way to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

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An input variable partitioning algorithm for functional decomposition of a system of Boolean functions based on the tabular method

Afshord

Pottosin

Arasteh

2015

Discrete Applied Mathematics

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a b s t r a c tFunctional decomposition is a fundamental method for the optimization of multi-level logic circuits by breaking down a complex circuit into smaller and hopefully simpler subcircuits. The problem of searching for an appropriate partition of input variables is the first step in the decomposition process, and it is a challenging task in the logic synthesis. The serial, two-block disjoint decomposition of a system of completely specified Boolean functions is investigated. An input variable partitioning algorithm is proposed, which is used for functional decomposition along with a tabular method. It is based on using the ternary matrix cover approach. A method for constructing the cover map that has the structure of the Karnaugh map is also presented. It is used in a step of the tabular method during the decomposition. There is a chance in a decomposable system, to choose such a solution of the task to reduce the circuit size exponentially. The paper emphasizes on obtaining the best possible partition in an efficient manner. A set of experiments has been carried out on the generated systems of Boolean functions and standard benchmarks. The results confirm the efficiency and effectiveness of the suggested algorithm along with the ternary matrix cover approach. The obtained solutions are optimal in the most cases, according to a certain criterion.

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