Modeling and Analyzing Distributed Computation in Monotone Spaces with Structural Map

Distributed computation follows the models of discrete structures in combinatorial forms. In higher-dimensions, the simplex structures of topological spaces as well as homology are employed to model and analyze distributed asynchronous computations. However, the monotone spaces are the general forms of topological spaces and can be effectively employed to analyze distributed computation. This paper proposes an analytical model of distributed computation in monotone spaces. It is illustrated that, the modeling of distributed computation in monotone spaces helps in determining consistent cuts under closure and convergence of computation. Furthermore, a connective mapping between the simplexes and monotone is constructed.