arXiv subjects
Publications and source records attributed to Giorgio Camerani.
We orchestrate a randomized algorithm for #$k$-SAT which counts the exact number of satisfying assignments in $2^{o(n)}$ time. The existence of such algorithm signifies that the #ETH is hereby refuted, and so are $\oplus$ETH, ETH, #SETH, $\oplus$SETH and SETH.
We furnish solid evidence, both theoretical and empirical, towards the existence of a deterministic algorithm for random sparse $\#Ω(\log n)$-SAT instances, which computes the exact counting of satisfying assignments in sub-exponential time. The algorithm uses a nice combinatorial property that every CNF formula has, which relates its number of unsatisfying assignments to the space of its monotone sub-formulae.
Let G=(V,E) be a graph. Let k < |V| be an integer. Let O_k be the number of edge induced subgraphs of G having k vertices and an odd number of edges. Let E_k be the number of edge induced subgraphs of G having k vertices and an even number of edges. Let D_k = O_k - E_k. The ODD EVEN DELTA problem consists in computing D_k, given G and k. We show that such problem is #P-hard, even on 3-regular bipartite planar graphs.