eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-08-20
70:1
70:14
10.4230/LIPIcs.MFCS.2019.70
article
Acceptance Ambiguity for Quantum Automata
Bell, Paul C.
1
https://orcid.org/0000-0003-2620-635X
Hirvensalo, Mika
2
Department of Computer Science, Byrom Street, Liverpool John Moores University, Liverpool, L3-3AF, UK
Department of Mathematics and Statistics, University of Turku, FI-20014, Turku, Finland
We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the distribution of acceptance probabilities of such MO-QFA, which is partly motivated by similar freeness problems for matrix semigroups and other computational models. We show that determining if the acceptance probabilities of all possible input words are unique is undecidable for 32 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial configuration is defined over real algebraic numbers. We utilize properties of the skew field of quaternions, free rotation groups, representations of tuples of rationals as a linear sum of radicals and a reduction of the mixed modification Post’s correspondence problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol138-mfcs2019/LIPIcs.MFCS.2019.70/LIPIcs.MFCS.2019.70.pdf
Quantum finite automata
matrix freeness
undecidability
Post’s correspondence problem
quaternions