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Register automata (RAs) are finite automata extended with a finite set ofregisters to store and compare data from an infinite domain. We study theconcept of synchronizing data words in RAs: does there exist a data word thatsends all states of the RA to a single state?  For deterministic RAs with k registers (k-DRAs), we prove that inputting datawords with 2k+1 distinct data from the infinite data domain is sufficient tosynchronize. We show that the synchronization problem for DRAs is in generalPSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministicRAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of theRA) might be necessary to synchronize. The synchronization problem for NRAs isin general undecidable, however, we establish Ackermann-completeness of theproblem for 1-NRAs.  Another main result is the NEXPTIME-completeness of the length-boundedsynchronization problem for NRAs, where a bound on the length of thesynchronizing data word, written in binary, is given. A variant of this lastconstruction allows to prove that the length-bounded universality problem forNRAs is co-NEXPTIME-complete.

Synchronizing Data Words for Register Automata