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AN EXTENSION OF KHRAPCHENKO THEOREM
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UNSPECIFIED (1991) AN EXTENSION OF KHRAPCHENKO THEOREM. INFORMATION PROCESSING LETTERS, 37 (4). pp. 215-217. ISSN 0020-0190
Full text not available from this repository.Abstract
Khrapchenko's theorem is a classical result yielding lower bounds on the formula complexity of Boolean functions over the unate basis. In particular, it can yield a tight n2 lower bound on the formula complexity of the parity function. In this note we consider an extended definition of formula size in which each variable may be assigned a different cost. We then generalize Khrapchenko's theorem to cover this new definition and in particular derive a parallel-to c parallel-to 1/2 = (SIGMA-c(i)1/2)2 lower bound on the generalized formula size complexity of the parity function of n variables with cost vector c = (c1,..., c(n)). This bound is shown to be tight to within a factor of 2 by methods similar to Huffman coding. The extended definition of formula size arises naturally in cases where formulae for compound functions like closed-integral (g1,..., gn) are sought.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
| Journal or Publication Title: | INFORMATION PROCESSING LETTERS |
| Publisher: | ELSEVIER SCIENCE BV |
| ISSN: | 0020-0190 |
| Date: | 28 February 1991 |
| Volume: | 37 |
| Number: | 4 |
| Number of Pages: | 3 |
| Page Range: | pp. 215-217 |
| Publication Status: | Published |
| URI: | http://wrap.warwick.ac.uk/id/eprint/22820 |
Data sourced from Thomson Reuters' Web of Knowledge
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