Unweighted and Weighted Hyper-Minimization

Hyper-minimization of deterministic nite automata (dfa) is a recently introduced state reduction technique that allows a nite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semi elds is presented, which allows the recognized weighted language to di er for nitely many input strings. First, the structure of hyper-minimal deterministic weighted nite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an e cient hyper-minimization algorithm, which runs in time O(n logn), is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal dfa, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.