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TR98-067 | 12th November 1998 00:00
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#### Propositional Proof Complexity: Past, Present and Future

TR98-067
Authors:

Paul Beame
Publication: 1st December 1998 10:18

Downloads: 1942

Keywords:

**Abstract:**
Proof complexity, the study of the lengths of proofs in

propositional logic, is an area of study that is fundamentally connected

both to major open questions of computational complexity theory and

to practical properties of automated theorem provers. In the last

decade, there have been a number of significant advances in proof

complexity lower bounds. Moreover, new connections between proof

complexity and circuit complexity have been uncovered, and the interplay

between these two areas has become quite rich. In addition, attempts

to extend existing lower bounds to ever stronger proof systems of proof

have spurred the introduction of new and interesting proof systems,

adding both to the practical aspects of proof complexity as well as

to a rich theory.

This note attempts to survey these developments

and to lay out some of the open problems in the area.

This is an updated version of our article appearing in

the Computational Complexity Column of the Bulletin of

the EATCS, 1998.