We show that derandomizing Polynomial Identity Testing is, essentially, equivalent to
proving circuit lower bounds for NEXP. More precisely, we prove that if one can test in …

In order to study circuit complexity classes within NC 1 in a uniform setting, we need a
uniformity condition which is more restrictive than those in common use. Two such …

Bodlaender's Theorem states that for every k there is a linear-time algorithm that decides
whether an input graph has tree width k and, if so, computes a width-k tree composition …

It is generally conjectured that there is an exponential separation between Frege and
extended Frege systems. This paper reviews and introduces some candidates for families of …

Bounded numeric planning, where each numeric variable domain is bounded, is PSPACE-
complete, but such a complexity result does not capture how hard it really is, since the same …

Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the
determinant is characterized by the complexity ofeounting the number ofaccepting …

We observe that many important computational problems in NC1 share a simple self-
reducibility property. We then show that, for any problem A having this self-reducibility …

In this paper, we analyze the computational limitations of Mamba and State-space Models
(SSMs) by using the circuit complexity framework. Despite Mamba's stateful design and …

Fixed-parameter tractability of NP optimization problems is studied by relating it to
approximability of the problems. It is shown that an NP optimization problem is fixed …

The parameterized complexity of a problem is generally considered “settled” once it has
been shown to be fixed-parameter tractable or to be complete for a class in a parameterized …