Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Quantum computers that can be simulated classically in polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A Dichotomy Theorem for Polynomial Evaluation
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Small Space Analogues of Valiant's Classes and the Limitations of Skew Formulas
Computational Complexity
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In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H. We show that this family is computable by arithmetic circuits in constant depth if H has a loop or no edges and that it is hard otherwise (i.e., complete for VNP, the arithmetic class related to #P). We also demonstrate the hardness over ℚ of cut eliminator, a polynomial defined by Bürgisser which is known to be neither VP nor VNP-complete in $\mathbb F_2$, if VP ≠ VNP (VP is the class of polynomials computable by arithmetic circuits of polynomial size).