A1 Refereed original research article in a scientific journal
Alternating, private alternating, and quantum alternating realtime automata
Authors: Demirci G, Hirvensalo M, Reinhardt K, Say ACC, Yakaryilmaz A
Publisher: LOGICAL METHODS COMPUTER SCIENCE E V
Publication year: 2019
Journal: Logical Methods in Computer Science
Journal name in source: LOGICAL METHODS IN COMPUTER SCIENCE
Journal acronym: LOG METH COMPUT SCI
Article number: 22
Volume: 15
Issue: 3
Number of pages: 21
ISSN: 1860-5974
eISSN: 1860-5974
DOI: https://doi.org/10.23638/LMCS-15(3:22)2019
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/42728622
We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we present two equivalent definitions of realtime private alternating finite automata (PAFAs). We show that the emptiness problem is undecidable for PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages, including the unary squares language, which seems to be difficult even for some classical counter automata with two-way input. Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs on general alphabets, and for alternating QFAs with two alternations on unary alphabets. On the other hand, the same problem is decidable for nondeterministic QFAs on general alphabets. We also show that the unary squares language is recognized by alternating QFAs with two alternations.
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