We introduce a linear algebraic model of computation, the Span Program, and prove several upper and lower bounds on it. These results yield the following applications in complexit...
We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ ...
We show that a combinatorial question which has been studied in connection with lower bounds for the knapsack problem by Brimkov and Dantchev (2001) is related to threshold graphs...
or representation theory of groups), and even borrows abstract geometrical concepts like Euler characteristic or Grothendieck ring. However, the most stimulating for proof complexi...