We present two results in structural complexity theory concerned with the following interrelated
topics: computation with postselection/restarting, closed timelike curves (CTCs), and
approximate counting. The first result is a new characterization of the lesser known complexity
class BPP_path in terms of more familiar concepts. Precisely, BPP_path is the class of ... more >>>

We ask, and answer, the question of what's computable by Turing machines equipped with time travel into the past: that is, closed timelike curves or CTCs (with no bound on their size). We focus on a model for CTCs due to Deutsch, which imposes a probabilistic consistency condition to avoid ... more >>>

We consider the problem of commutative rank computation of a given matrix space, $\mathcal{B}\subseteq\mathbb{F}^{n\times n}$. The problem is fundamental, as it generalizes several computational problems from algebra and combinatorics. For instance, checking if the commutative rank of the space is $n$, subsumes problems such as testing perfect matching in graphs ... more >>>