A note on the size of Craig Interpolants

Mundici considered the question of whether the interpolant of two propositional formulas of the form F G can always have a short circuit description, and showed that if this is the case then every problem in NP co-NP would have polynomial size circuits. In this note we observe further consequences of the interpolant having short circuit descriptions, namely that UP 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.

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Uwe Schöning, Jacobo Torán
• Keywords: DAGSTUHL 2006, DAGSTUHL 2007, Polynomial Size Circuits, Short Circuit Descriptions, Single Valued Np