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MPI-I-93-121

The circuit subfunction relations are $sum^P_2$-complete

Borchert, Bernd and Ranjan, Desh

May 1993, 14 pages.

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Status: available - back from printing

We show that given two Boolean circuits $f$ and $g$ the following three problems are $\Sigma^p_2$-complete: (1) Is $f$ a c-subfunction of $g$, i.e.\ can one set some of the variables of $g$ to 0 or 1 so that the remaining circuit computes the same function as $f$? (2) Is $f$ a v-subfunction of $g$, i.e. can one change the names of the variables of $g$ so that the resulting circuit computes the same function as $f$? (3) Is $f$ a cv-subfunction of $g$, i.e.\ can one set some variables of $g$ to 0 or 1 and simultanously change some names of the other variables of $g$ so that the new circuit computes the same function as $f$? Additionally we give some bounds for the complexity of the following problem: Is $f$ isomorphic to $g$, i.e. can one change the names of the variables bijectively so that the circuit resulting from $g$ computes the same function as $f$?

URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-121

Hide details for BibTeXBibTeX
@TECHREPORT{BorchertRanjan93,
  AUTHOR = {Borchert, Bernd and Ranjan, Desh},
  TITLE = {The circuit subfunction relations are $sum^P_2$-complete},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-93-121},
  MONTH = {May},
  YEAR = {1993},
  ISSN = {0946-011X},
}