Characterizing Arithmetic Circuit Classes by Constraint Satisfaction Problems - (Extended Abstract)

We explore the expressivity of constraint satisfaction problems (CSPs) in the arithmetic circuit model. While CSPs are known to yield VNP-complete polynomials in the general case, we show that for different restrictions of the structure of the CSPs we get characterizations of different arithmetic circuit classes. In particular we give the first natural non-circuit characterization of VP, the class of polynomial families efficiently computable by arithmetic circuits. Acknowledgements. I am very grateful to my supervisor Peter Bürgisser for many helpful discussions and his support in making the presentation of this paper much clearer. I would also like to thank the organizers of the Dagstuhl Seminar 10481 “Computational Counting” where some of the results in this paper were conceived. ? supported by the Research Training Group GK-693 of the Paderborn Institute for Scientific Computation (PaSCo) and DFG grant BU 1371/3-1