We propose a model called priority branching trees (pBT ) for backtracking and dynamic
programming algorithms. Our model generalizes both the priority model of Borodin, Nielson
and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence
spans a wide spectrum of algorithms. After witnessing the ... more >>>

Lovasz and Schrijver described a generic method of tightening the LP and SDP relaxation for any 0-1 optimization problem. These tightened relaxations were the basis of several celebrated approximation algorithms (such as for MAX-CUT, MAX-3SAT, and SPARSEST CUT).

We prove strong nonapproximability results in this model for well-known problems such ... more >>>

DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satisfiability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatisfiable formulas are equivalent to tree-like resolution proofs. Therefore, lower bounds for tree-like resolution (which ... more >>>

We analyze the efficiency of the random walk algorithm on random 3CNF instances, and prove em linear upper bounds on the running time
of this algorithm for small clause density, less than 1.63. Our upper bound matches the observed running time to within a multiplicative factor. This is the ... more >>>

This paper gives two distinct proofs of an exponential separation
between regular resolution and unrestricted resolution.
The previous best known separation between these systems was
quasi-polynomial.

We call a pseudorandom generator $G_n:\{0,1\}^n\to \{0,1\}^m$ {\em
hard} for a propositional proof system $P$ if $P$ can not efficiently
prove the (properly encoded) statement $G_n(x_1,\ldots,x_n)\neq b$ for
{\em any} string $b\in\{0,1\}^m$. We consider a variety of
``combinatorial'' pseudorandom generators inspired by the
Nisan-Wigderson generator on the one hand, and ... more >>>

We study space complexity in the framework of
propositional proofs. We consider a natural model analogous to
Turing machines with a read-only input tape, and such
popular propositional proof systems as Resolution, Polynomial
Calculus and Frege systems. We propose two different space measures,
corresponding to the maximal number of bits, ... more >>>