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 active line of research in proof complexity over the last decade has been the study of
proof space and trade-offs between size and space. Such questions were originally …

This paper is intended as an informal and accessible survey of proof complexity for non-
experts, focusing on some comparatively weak proof systems of particular interest in …

Pebble games were extensively studied in the 1970s and 1980s in a number of different
contexts. The last decade has seen a revival of interest in pebble games coming from the …

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in
width w but require resolution proofs of size n Ω (w). This shows that the simple counting …

We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to
monotone span program size by Pitassi and Robere (2018) so that it works for any gadget …

Semialgebraic proof systems have been studied extensively in proof complexity since the
late 1990s to understand the power of Gröbner basis computations, linear and semidefinite …

We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus
resolution (PCR) proof systems. These are the first true size-space trade-offs in any …

We show quadratic lower bounds on the total space used in resolution refutations of random
k-CNFs over n variables and of the graph pigeonhole principle and the bit pigeonhole …

Algebraic proof systems, such as Polynomial Calculus (PC) and Polynomial Calculus with
Resolution (PCR), refute contradictions using polynomials. Space complexity for such …