In 1969, Strassen shocked the computational world with his subcubic algorithm for
multiplying matrices. Attempting to understand the best possible algorithm for this problem …

The subrank of a tensor measures how much a tensor can be diagonalized. We determine
this parameter precisely for essentially all (ie, generic) tensors. Namely, we prove for generic …

In the world of space-bounded complexity, there is a strain of results showing that space
can, somewhat paradoxically, be used for multiple purposes at once. Touchstone results …

The Tree Evaluation Problem (TreeEval)(Cook et al. 2009) is a central candidate for
separating polynomial time (P) from logarithmic space (L) via composition. While space …

An m-catalytic branching program (Girard, Koucký, McKenzie 2015) is a set of m distinct
branching programs for f which are permitted to share internal (ie non-source non-sink) …

Determining the Shannon capacity of graphs is a long-standing open problem in information
theory, graph theory and combinatorial optimization. Over decades, a wide range of upper …

A catalytic machine is a model of computation where a traditional space-bounded machine
is augmented with an additional, significantly larger," catalytic" tape, which, while being …

In this paper, we study the asymptotic nonnegative rank of matrices, which characterizes the
asymptotic growth of the nonnegative rank of fixed nonnegative matrices under the …

Abstract The Tree Evaluation Problem (TreeEval)(Cook et al. 2009) is a central candidate for
separating polynomial time (P) from logarithmic space (L) via composition. While space …

CCCatalytic branching programs (catalytic bps) compute the same n-bit Boolean function f at
multiple entry points that need to be remembered at the exit nodes of the branching program …