期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2001
卷号：2001
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：Valiant (SIAM Journal on Computing 8, pages 410--421) showed that the roblem of counting the number of s-t paths in graphs (both in the case of directed graphs and in the case of undirected graphs) is complete for #P under polynomial-time one-Turing reductions (namely, some post-computation is needed to recover the value of a #P-function). Valiant then asked whether the problem of counting the number of self-avoiding walks of length n in the two-dimensional grid is complete for #P1, i.e., the tally-version of #P. This paper offers a partial answer to the question. It is shown that a number of versions of the problem of computing the number of self-avoiding walks in two-dimensional grid graphs (graphs embedded in the two-dimensional grid) is polynomial-time one-Turing complete for #P.
