Valiant's theory of holographic algorithms is a novel methodology
to achieve exponential speed-ups in computation. A fundamental
parameter in holographic algorithms is the dimension of the linear basis
vectors.
We completely resolve the problem of the power of higher dimensional
bases. We prove that 2-dimensional bases are universal for
holographic ... more >>>

We give a classification of block-wise symmetric signatures
in the theory of matchgate computations. The main proof technique
is matchgate identities, a.k.a. useful Grassmann-Pl\"{u}cker
identities.

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We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions.

Q1: Where does the implication [can(f) \le_m can(g) => f \le_s ... more >>>