# Boolean approximate counting CSPs with weak conservativity, and implications for ferromagnetic two-spin

@article{Backens2020BooleanAC, title={Boolean approximate counting CSPs with weak conservativity, and implications for ferromagnetic two-spin}, author={Miriam Backens and Andrei Bulatov and Leslie Ann Goldberg and Colin McQuillan and Stanislav Zivny}, journal={J. Comput. Syst. Sci.}, year={2020}, volume={109}, pages={95-125} }

Abstract We analyse the complexity of approximate counting constraint satisfactions problems # CSP ( F ) , where F is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is known if F contains arbitrary unary functions. We strengthen this result by fixing any permissive strictly increasing unary function and any permissive strictly decreasing unary function, and requiring only those to be in F . The resulting classification is employed to characterise… CONTINUE READING

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## Holant Clones and the Approximability of Conservative Holant Problems

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