Affiliation:
1. Universität Leipzig, Germany
2. CNRS, IRIF, and University of Oxford, UK
Abstract
Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data from an infinite domain. We study the concept of synchronizing data words in RAs: does there exist a data word that sends all states of the RA to a single state?
For deterministic RAs with
k
registers (
k
-DRAs), we prove that inputting data words with 2
k
+1 distinct data from the infinite data domain is sufficient to synchronize. We show that the synchronization problem for DRAs is in general PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic RAs (NRAs), we show that Ackermann(
n
) distinct data (where
n
is the size of the RA) might be necessary to synchronize. The synchronization problem for NRAs is in general undecidable; however, we establish Ackermann-completeness of the problem for 1-NRAs. Another main result is the NEXPTIME-completeness of the length-bounded synchronization problem for NRAs, where a bound on the length of the synchronizing data word, written in binary, is given. A variant of this last construction allows to prove that the length-bounded universality problem for NRAs is co-NEXPTIME-complete.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
2 articles.
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1. Synchronizing words under LTL constraints;Information Processing Letters;2023-08
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