Abstract
In a discussion on the computational complexity of approximately solving Boolean counting constraint satisfaction problems (or #CSPs), we demonstrate the approximability of two constant unary constraints by an arbitrary nonempty set of real-valued constraints. A use of auxiliary free unary constraints has proven to be useful in establishing a complete classification of weighted #CSPs. Using our approximability result, we can clarify the role of such auxiliary free unary constraints by constructing approximation-preserving reductions from #SAT to #CSPs with symmetric real-valued constraints of arbitrary arities.
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References
Cai, J., Lu, P.: Holographic algorithms: from arts to science. J. Comput. System Sci. 77, 41–61 (2011)
Cai, J., Lu, P., Xia, M.: Holant problems and counting CSP. In: STOC 2009, pp. 715–724 (2009)
Creignou, N.: A dichotomy theorem for maximum generalized satisfiability problems. J. Comput. System Sci. 51, 511–522 (1995)
Creignou, N., Hermann, M.: Complexity of generalized satisfiability counting problems. Inform. Comput. 125, 1–12 (1996)
Dalmau, V., Ford, D.K.: Generalized Satisfiability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 358–367. Springer, Heidelberg (2003)
Dyer, M., Goldberg, L.A., Greenhill, C., Jerrum, M.: The relative complexity of approximating counting problems. Algorithmica 38, 471–500 (2004)
Dyer, M., Goldberg, L.A., Jerrum, M.: The complexity of weighted Boolean #CSP. SIAM J. Comput. 38, 1970–1986 (2009)
Dyer, M., Goldberg, L.A., Jerrum, M.: An approximation trichotomy for Boolean #CSP. J. Comput. System Sci. 76, 267–277 (2010)
Schaefer, T.J.: The complexity of satisfiability problems. In: STOC 1978, pp. 216–226 (1978)
Yamakami, T.: Approximate counting for complex-weighted Boolean constraint satisfaction problems. Inform. Comput. 219, 17–38 (2012)
Yamakami, T.: A dichotomy theorem for the approximation complexity of complex-weighted bounded-degree Boolean #CSPs. Thoer. Comput. Sci. 447, 120–135 (2012)
Yamakami, T.: Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 454–463. Springer, Heidelberg (2011)
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Yamakami, T. (2012). Constant Unary Constraints and Symmetric Real-Weighted Counting CSPs. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_27
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DOI: https://doi.org/10.1007/978-3-642-35261-4_27
Publisher Name: Springer, Berlin, Heidelberg
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