Determining a singleton attractor of an AND/OR Boolean network in O(1.587ⁿ) time

An O(1.587n) time algorithm for the problem is studied. The cornerstone of the algorithm, and of the algorithms, is the observation that there is a family of simple BNs (Boolean Networks) that is in one-to-one correspondence with the family of SAT formulas. The reduction to a SAT-network is accomplished by repeatedly removing nodes that do not fit the SAT-network mold. The algorithm presented achieves its superior running time by dynamically choosing which triplets or pairs of nodes to remove. It can be assumed that the Boolean network contains only OR-nodes, because AND nodes can easily be turned into OR nodes. To generate the possible assignments of the two nodes in a pair-singleton u, v the algorithm uses the fact that only 3 assignments to u and v are possible, instead of 4, because of the constraint embodied in the edge. AttractorByTriplets finds a singleton attractor of an OR Boolean network if and only if one exists.