Constrained Synchronization and Subset Synchronization Problems for Weakly Acyclic Automata

We investigate the constrained synchronization problem for weakly acyclic, or partially ordered, input automata. show that, automata of this type, is always in \(\textsf {NP}\). Furthermore, we give a full classification realizable complexities constraint with at most two states and over ternary alphabet. find that problems are PSPACE-complete general become NP-complete. However, there also exist setting but polynomial time solvable when considered acyclic related to subset synchronization, namely if exists word mapping all into given target states, one another. Both {PSPACE}\)-complete general, our former latter {NP}\)-complete.