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Subcubic Certificates for CFL Reachability
We show that, in both scenarios, there exist succinct certificates ($O(n^2)$ in the size of the problem) and these certificates can be checked in subcubic (matrix multiplication) time.
Formal Languages and Automata Theory Computational Complexity Programming Languages
On Restricted Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative $n \times m$ matrix $M$ into a product of a nonnegative $n \times d$ matrix $W$ and a nonnegative $d \times m$ matrix $H$.
Nonnegative Matrix Factorization Requires Irrationality
Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative $n \times m$ matrix $M$ into a product of a nonnegative $n \times d$ matrix $W$ and a nonnegative $d \times m$ matrix $H$.
Approximate Counting in SMT and Value Estimation for Probabilistic Programs
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope.
