We give a novel characterization of W[1], the most important fixed-parameter intractability class in the W-hierarchy, using Boolean circuits that consist solely of majority gates. Such gates have a Boolean value of 1 if and only if more than half of their inputs have value 1. Using majority circuits, we define an analog of the W-hierarchy which we call the W̃-hierarchy, and show that W[1] = W̃[1] and W[t] ⊂ W̃[t] for all [t]. This gives the first characterization of W[1] based on the weighted satisfiability problem for monotone Boolean circuits rather than antimonotone. Our results are part of a wider program aimed at exploring the robustness of the notion of weft, showing that it remains a key parameter governing the combinatorial nondeterministic computing strength of circuits, no matter what type of gates these circuits have. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Fellows, M., Hermelin, D., Müller, M., & Rosamond, F. (2008). A purely democratic characterization of W[1]. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5018 LNCS, pp. 103–114). https://doi.org/10.1007/978-3-540-79723-4_11
Mendeley helps you to discover research relevant for your work.