We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions ... more >>>

Chvatal-Gomory (CG) cuts and the Bienstock-Zuckerberg hierarchy capture useful linear programs that the standard bounded degree Lasserre/Sum-of-Squares (SOS) hierarchy fails to capture.

In this paper we present a novel polynomial time SOS hierarchy for 0/1 problems with a custom subspace of high degree polynomials (not the standard subspace of low-degree ... more >>>

The complexity of Iterated Matrix Multiplication is a central theme in Computational Complexity theory, as the problem is closely related to the problem of separating various complexity classes within $\mathrm{P}$. In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show ... more >>>