This chapter introduces a design framework based on matching, in which the matching automaton is considered. The matching automaton is obtained by viewing the stable marriage problem as an automaton. The motivations for the matching automaton are three-fold: A design framework with degeneracy; a discrete model for a matching process; and one of a self-action model where the action is rewiring. The background is also explained, introducing the related paradigms of matching problems and rewiring networks. Other related fields such as game theory, network sciences (with graph theory and statistics), social agents, molecular design and reliability theory are also briefly explained.