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Electronic Colloquium on Computational Complexity

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All reports by Author Soren Riis:

TR09-014 | 7th February 2009
Soren Riis

On the asymptotic Nullstellensatz and Polynomial Calculus proof complexity

We show that the asymptotic complexity of uniformly generated (expressible in First-Order (FO) logic) propositional tautologies for the Nullstellensatz proof system (NS) as well as for Polynomial Calculus, (PC) has four distinct types of asymptotic behavior over fields of finite characteristic. More precisely, based on some highly non-trivial work by ... more >>>

TR97-048 | 13th October 1997
Soren Riis, Meera Sitharam

Non-constant Degree Lower Bounds imply linear Degree Lower Bounds

The semantics of decision problems are always essentially independent of the
underlying representation. Thus the space of input data (under appropriate
indexing) is closed
under action of the symmetrical group $S_n$ (for a specific data-size)
and the input-output relation is closed under the action of $S_n$.
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