AN EXTENSION OF KHRAPCHENKO THEOREM
UNSPECIFIED (1991) AN EXTENSION OF KHRAPCHENKO THEOREM. INFORMATION PROCESSING LETTERS, 37 (4). pp. 215-217. ISSN 0020-0190Full text not available from this repository.
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|
|Date:||28 February 1991|
|Number of Pages:||3|
|Page Range:||pp. 215-217|
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