The authors of this book cast the problem as solving abstract equations over language and study the most general (largest) solutions under the synchronous and parallel composition operators. They also apply such equations to languages associated with important classes of automata used for modeling systems, e.g., regular languages as counterparts of finite automata, FSM languages as counterparts of FSMs. The authors investigate the largest subsets of solutions closed with respect to various language properties; in particular, classes of the largest compositional solutions (defined by properties exhibited by the composition of the solution and of the context). The first algorithm to compute the largest compositionally progressive solution of synchronous equations is provided. This approach unifies in a seamless frame previously reported techniques.