Equisolvability of Series vs. Controller’s Topology in Synchronous Language Equations
Nina Vladimirovna Yevtushenko, Tiziano Villa, Robert K. Brayton, Alexandre Petrenko, Alberto Luigi Sangiovanni-Vincentelli · 2002
Given a plant and a specification, the largest solution of the FSM equation contains all possible discrete controllers. Often we are interested in computing the complete solutions whose composition with the plant is exactly equivalent to the specification. Not every solution contained in the largest one satisfies such property, that holds instead for the complete solutions of the series topology. We study the relation between the solvability of an equation for the series topology and of the corresponding equation for the controller’s topology. We establish that, if is a deterministic FSM, then the FSM equation is solvable for the series topology with an unknown head component iff it is solvable for the controller’s topology. Our proof is constructive, i.e., for a given solution of the series topology it shows how to build a solution of the controller’s topology and viceversa. 1