TY - GEN
T1 - A purely democratic characterization of W[1]
AU - Fellows, Michael
AU - Hermelin, Danny
AU - Müller, Moritz
AU - Rosamond, Frances
PY - 2008/6/9
Y1 - 2008/6/9
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/44649122259
U2 - 10.1007/978-3-540-79723-4_11
DO - 10.1007/978-3-540-79723-4_11
M3 - Conference contribution
AN - SCOPUS:44649122259
SN - 354079722X
SN - 9783540797227
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 103
EP - 114
BT - Parameterized and Exact Computation - Third International Workshop, IWPEC 2008, Proceedings
T2 - 3rd International Workshop on Parameterized and Exact Computation, IWPEC 2008
Y2 - 14 May 2008 through 16 May 2008
ER -