Prop ositional Pro of Complexity Past Present
and Future
Paul Beame and Toniann Pitassi
Abstract Pro of complexity the study of the lengths of pro ofs in
prop ositional logic is an area of study that is fundamentally connected
b oth to ma jor op en questions of computational complexity theory and
to practical prop erties of automated theorem provers In the last decade
there have b een a number of signi cant advances in pro of complexity
lower b ounds Moreover new connections b etween pro of complexity
and circuit complexity have b een uncovered and the interplay b etween
these two areas has b ecome quite rich In addition attempts to extend
existing lower b ounds to ever stronger systems of pro of have spurred the
introduction of new and interesting pro of systems adding b oth to the
practical asp ects of pro of complexity as well as to a rich theory This
note attempts to survey these developments and to lay out some of the
op en problems in the area