Complexity Bounds of ConstantSpace Quantum Computation
Abstract
We realize constantspace quantum computation by measuremany twoway quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In particular, we show that, when the automata halt "in finite steps" along all computation paths, they must terminate in worstcase liner time. In the boundederror probability case, the acceptance of the automata depends only on the computation paths that terminate within exponentially many steps even if not all computation paths may terminate. We also present a classical simulation of those automata on twoway multihead probabilistic finite automata with cut points. Moreover, we discuss how the recognition power of the automata varies as the automata's acceptance criteria change to error free, onesided error, bounded error, and unbounded error by comparing the complexity of their computational powers. We further note that, with the use of arbitrary complex transition amplitudes, twoway unboundederror quantum finite automata and twoway boundederror 2head quantum finite automata can recognize certain nonrecursive languages, whereas twoway errorfree quantum finite automata recognize only recursive languages.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 arXiv:
 arXiv:1606.08764
 Bibcode:
 2016arXiv160608764Y
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Computational Complexity;
 Quantum Physics
 EPrint:
 A4, 10pt, pp.26. This is a complete version of an extended abstract that appeared in the Proceedings of the 19th International Conference on Developments in Language Theory (DLT 2015), Liverpool, United Kingdom, July 2730, 2015, Lecture Notes in Computer Science, Springer, vol.9168, pp.426438, 2015