## Quantified Propositional Calculus and a Second-Order Theory for NC¹ (2004)

by
Stephen Cook
,
Tsuyoshi Morioka

Citations: | 9 - 2 self |

### BibTeX

@MISC{Cook04quantifiedpropositional,

author = {Stephen Cook and Tsuyoshi Morioka},

title = {Quantified Propositional Calculus and a Second-Order Theory for NC¹},

year = {2004}

}

### OpenURL

### Abstract

Let H be a proof system for the quantified propositional calculus (QPC). We j -witnessing problem for H to be: given a prenex S j -formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We point out that the S witnessing problems for the systems G 1 and G 1 are complete for polynomial time and PLS (polynomial local search), respectively. We introduce