A note on the size of Craig Interpolants

Schöning, Uwe; Torán, Jacobo

doi:10.4230/DagSemProc.06451.3

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A note on the size of Craig Interpolants

Authors Uwe Schöning, Jacobo Torán

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 6451
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2007-04-23

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DOI: 10.4230/DagSemProc.06451.3
URN: urn:nbn:de:0030-drops-9735

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Keywords

Interpolant
non-uniform complexity

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Abstract

Mundici considered the question of whether the interpolant of two
propositional formulas of the form $F
ightarrow G$ can always have
a short circuit description, and showed that if this is the case then
every problem in NP $cap$ co-NP would have polynomial size circuits.
In this note we observe  further consequences of the interpolant having
short circuit descriptions, namely that
UP $subseteq$ P$/$poly, and that every single valued NP function has a
total extension in FP$/$poly.  We also relate
this question with other
Complexity Theory assumptions.

Cite As Get BibTex

Uwe Schöning and Jacobo Torán. A note on the size of Craig Interpolants. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 6451, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007) https://doi.org/10.4230/DagSemProc.06451.3

Author Details

Uwe Schöning

Jacobo Torán

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