Turing Machines with One-sided Advice and Acceptance of the co-RE Languages

0427248 - ÚI 2018 RIV NL eng J - Journal Article
van Leeuwen, J. - Wiedermann, Jiří
Turing Machines with One-sided Advice and Acceptance of the co-RE Languages.
Fundamenta Informaticae. Roč. 153, č. 4 (2017), s. 347-366. ISSN 0169-2968. E-ISSN 1875-8681
Grant - others:GA ČR(CZ) GA15-04960S
Institutional support: RVO:67985807
Keywords : advice functions * co-RE languages * machine models * Turing machines
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 0.725, year: 2017

We resolve an old problem, namely to design a ‘natural’ machine model for accepting the complements of recursively enumerable languages. The model we present is based on nondeterministic Turing machines with ‘one-sided’ advice. We prove that these machines precisely accept the co-RE languages, without restriction on the advice functions that are used. We show that for accepting a co-RE language, one-sided advice is as powerful as arbitrary advice, but also that linearly bounded one-sided advice is sufficient. However, ‘long’ sublinear advice can make Turing machines with one-sided advice accept more co-RE languages than ‘short’ sublinear advice. We prove that infinite proper hierarchies of language classes inside co-RE can be devised, using suitable increasing sequences of bounding functions for the allowed advice. The machine model and the results dualize for the family of recursively enumerable languages.
Permanent Link: http://hdl.handle.net/11104/0232839