Unary Probabilistic and Quantum Automata on Promise Problems [chapter]

Aida Gainutdinova, Abuzer Yakaryılmaz
2015 Lecture Notes in Computer Science  
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs
more » ... be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs. ⋆ The arXiv number is 1502.01462. ⋆⋆ Yakaryılmaz was partially supported by CAPES with grant 88881.030338/2013-01.
doi:10.1007/978-3-319-21500-6_20 fatcat:ass5dzddyvap3ilx2bakmryelq