Affiliations: Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany. kutrib@informatik.uni-giessen.de | Laboratoire I3S, Université Nice Sophia Antipolis, 06903 Sophia Antipolis Cedex, France. julien.provillard@i3s.unice.fr | Department of Computer Science, University of Debrecen, 4028 Debrecen, Kassai út 26, Hungary. vaszil.gyorgy@inf.unideb.hu | Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany. matthias.wendlandt@informatik.uni-giessen.de
Note: [] Address for correspondence: Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany
Note: [] The author acknowledges the support of the Hungarian Scientific Research Fund, “OTKA”, grant no. K75952, and the European Union through the TÁMOP-4.2.2.C-11/1/KONV-2012-0001 project which is co-financed by the European Social Fund.
Abstract: Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.
