MPI-I-93-121
The circuit subfunction relations are $sum^P_2$-complete
Borchert, Bernd and Ranjan, Desh
May 1993, 14 pages.
.
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
BibTeX
@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},
}