The set of minimal braids is co-NP-complete

The Set of Minimal Braids is co-NP-Complete

Braids ñàï Üå represented as two-dimenSional diagrams showing the crossings of strings or as words over the generators of à braid group. À minimal braid is îïå with the fewest crossings (or the shortest words) among all possible repre~entations topologically equivalent to that braid. ÒÜå main result of this paper is that the set of minimal braids is co-NP-complete. Algorithmic problems in braid...

Irreversible 2-conversion set is NP-complete

An irreversible k-threshold process is a process on a graph where vertices change color from white to black if they have at least k black neighbors. An irreversible k-conversion set is a subset S of vertices of a graph G such that the irreversible k-threshold process changes all vertices of G to black if S is the initial set of black vertices. We show that deciding the existence of an irreversi...

P-matrix recognition is co-NP-complete

This is a summary of the proof by G.E. Coxson [1] that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn [5].

Minimal Controllability of Conjunctive Boolean Networks is NP-Complete

Given a conjunctive Boolean network (CBN) with n state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is controllable. We give a necessary and sufficient condition for controllability of a CBCN; an O(n)-time algorithm for testing controllability; and prove that nonet...

The Minimal Logically-Defined NP-Complete Problem