DagSemProc.06451.3.pdf
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A note on the size of Craig Interpolants
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Dagstuhl Seminar Proceedings, Volume 6451
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-04-23
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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
https://doi.org/10.4230/DagSemProc.06451.3
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.
Keywords
- Interpolant
- non-uniform complexity
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