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 …

We use critical block sensitivity, a new complexity measure introduced by Huynh and
Nordström (STOC 2012), to study the communication complexity of search problems. To …

A secret-sharing scheme enables a dealer to share a secret s among n parties such that
only authorized subsets of parties, specified by a monotone access structure f:{0, 1} n→{0 …

A secret-sharing scheme allows to distribute a secret s among n parties such that only some
predefined “authorized” sets of parties can reconstruct the secret, and all other …

Separations: We introduce a monotone variant of Xor-Sat and show it has exponential
monotone circuit complexity. Since Xor-Sat is in NC^ 2, this improves qualitatively on the …

We characterize the size of monotone span programs computing certain “structured”
boolean functions by the Nullstellensatz degree of a related unsatisfiable Boolean formula …

A secret-sharing scheme allows to distribute a secret s among n parties such that only some
predefined “authorized” sets of parties can reconstruct the secret, and all other …

We survey lower-bound results in complexity theory that have been obtained via newfound
interconnections between propositional proof complexity, boolean circuit complexity, and …

Query-to-communication lifting theorems translate lower bounds on query complexity to
lower bounds for the corresponding communication model. In this paper, we give a …

We study the amortized circuit complexity of boolean functions. Given a circuit model F and a
boolean function f:{0,1\}^n→{0,1\}, the F-amortized circuit complexity is defined to be the size …