# MPI-I-93-121

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

### Borchert, Bernd and Ranjan, Desh

**MPI-I-93-121**. May** **1993, 14 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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 $f$?

Acknowledgement:** **

References to related material:

To download this research report, please select the type of document that fits best your needs. | Attachement Size(s): |

MPI-I-93-121.pdf | 8225 KBytes |

Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView |

**URL to this document: **http://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},`

`}`