This chapter gives an overview of proof complexity and connections to SAT solving, focusing
on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes …

An argument that the meaning of written or auditory linguistic signals is not derived from the
input but results from the brain's internal construction process. When we read a text or listen …

Computational complexity theory is a subfield of theoretical computer science one of whose
primary goals is to classify and compare the practical difficulty of solving problems about …

The range avoidance problem (denoted by Avoid) asks to find a string outside of the range
of a given circuit C:{0, 1} n→{0, 1} m, where m> n. Although at least half of the strings of …

Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for
the performance of important QBF solvers. However, the proof complexity of these proof …

We study the logical complexity of proofs in cyclic arithmetic (CA), as introduced by Simpson
in [Sim17], in terms of quantifier alternations of formulae occurring. Writing CΣn for (the …

Modern QBF solvers typically use two different paradigms, conflict-driven clause learning
(CDCL) solving or expansion solving. Proof systems for quantified Boolean formulas (QBFs) …

Several calculi for quantified Boolean formulas (QBFs) exist, but relations between them are
not yet fully understood. This paper defines a novel calculus, which is resolution-based and …

As a natural extension of the SAT problem, an array of proof systems for quantified Boolean
formulas (QBF) have been proposed, many of which extend a propositional proof system to …

We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on
bit strings of length n. In 1995 Razborov showed that many can be proved in PV 1, a …