Fully Lattice Linear Algorithms

Abstract: This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they induce a partial order among all states and form \textit{multiple lattices}. An initial state locks in one of these lattices. We present a lattice linear self-stabilizing algorithm for minimal dominating set.