On a new Boolean function with applications

Luccio, Fabrizio; Pagli, Linda

doi:10.1109/12.754996

Cited by 67 publications

(69 citation statements)

References 14 publications

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“…Prime pseudoproducts characterize SPP with a minimum number of XOR gates [LP99] rather than minimum SPP formulae as defined in this paper. Still, they are important to the study of SPP formulae, so we consider the complexity of determining whether a pseudoproduct is prime.…”

Section: Definition 22 (Prime Pseudoproduct)mentioning

confidence: 99%

“…Little has been known about the formal complexity of SPP minimization. Characterizing the complexity of SPP minimization is important, as SPPs are well-suited for use in practical situations such as representation of arithmetic functions [LP99,JSA97].…”

Section: Definition 12 (Pseudoproduct) a Pseudoproduct Is The Conjumentioning

confidence: 99%

“…More recently, the constant depth version for all constants greater than 2 as well as the unlimited depth version were proven to be hard for the second level of the PH under Turing reductions in [BU08]. More recently, three-level formula minimization in which the first level is an OR gate, the second level is AND gates, and the third level is composed of XOR gates, has been introduced [LP99]. Such a formula is referred to as a Sum of Pseudoproducts (SPP) in the literature.…”

Section: Introductionmentioning

confidence: 99%

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The Complexity of SPP Formula Minimization

Buchfuhrer

2008

Algorithms and Computation

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Circuit minimization is a useful procedure in the field of logic synthesis. Recently, it was proven that the minimization of (∨, ∧, ¬) formulae is hard for the second level of the polynomial hierarchy [BU08]. The complexity of minimizing more specialized formula models was left open, however. One model used in logic synthesis is a three-level model in which the third level is composed of parity gates, called SPPs. SPPs allow for small representations of Boolean functions and have efficient heuristics for minimization. However, little was known about the complexity of SPP minimization. Here, we show that SPP minimization is complete for the second level of the Polynomial Hierarchy under Turing reductions.

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Section: Definition 22 (Prime Pseudoproduct)mentioning

confidence: 99%

Section: Definition 12 (Pseudoproduct) a Pseudoproduct Is The Conjumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Complexity of SPP Formula Minimization

Buchfuhrer

2008

Algorithms and Computation

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“…Apseudoproduct of a Boolean function is prime iff no other -pseudoproduct of exists such that . Observe that, unlike products, is not always obtained from by deleting one or more factors (for more details see [9,4]). For example, the 2-pseudoproduct is contained, among others, not only in , but also in and .…”

Section: -Spp Networkmentioning

confidence: 99%

“…Here we continue the investigation of three-level EXOR-AND-OR forms, introduced in [9,4]. They are a direct generalization of AND-OR forms, obtained generalizing cubes to pseudocubes where literals in cubes may be replaced by EXOR factors in pseudocubes.…”

Section: Introductionmentioning

confidence: 99%

Efficient Minimization of Fully Testable 2-SPP Networks

Bernasconi

Ciriani

Drechsler

et al. 2006

Proceedings of the Design Automation &Amp; Test in Europe Conference

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Stuck-At-Fault Testability of SPP Three-Level Logic Forms

Ciriani

Bernasconi

Drechsler

IFIP International Federation for Information Processing

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Recently introduced, three-level logic Sum of Pseudoproducts (SPP) forms al- low the representation of Boolean functions with much shorter expressions than standard two-level Sum of Products (SOP) forms, or other three-level logic forms. In this paper the testability of circuits derived from SPPs is analyzed. We study testability under the Stuck-At Fault Model (S AFM). For SPP networks several minimal forms can be considered. While full testability can be proved for some classes, others are shown to contain redundancies. Experimental results are given to demonstrate the efficiency of the approach

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On a new Boolean function with applications

Cited by 67 publications

References 14 publications

The Complexity of SPP Formula Minimization

The Complexity of SPP Formula Minimization

Efficient Minimization of Fully Testable 2-SPP Networks

Stuck-At-Fault Testability of SPP Three-Level Logic Forms

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