Abstract
In contrast to most kinds of computability studied in mathematical logic, feedback computability has a non-degenerate notion of parallelism. Here we study parallelism for the most basic kind of feedback, namely that of Turing computability. We investigate several different possible definitions of parallelism in this context, with an eye toward specifying what is so computable. For the deterministic notions of parallelism identified we are successful in this analysis; for the non-deterministic notion, not completely.
Keywords
Thanks are due to Nate Ackerman, Cameron Freer, and Anil Nerode for their consultation during the preparation of this work.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ackerman, N., Freer, C., Lubarsky, R.: Feedback turing computability, and turing computability as feedback. In: Proceedings of LICS 2015, Kyoto, Japan (2015). Accessed https://math.fau.edu/lubarsky/pubs.html
Lubarsky, R.: ITTMs with feedback. In: Schindler, R. (ed.) Ways of Proof Theory, pp. 341–354. Ontos (2010). Accessed http://math.fau.edu/lubarsky/pubs.html
Lubarsky, R.: \(\mu \)-definable set of integers. J. Symbolic Log. 58(1), 291–313 (1993)
Moschovakis, Y.: Descriptive Set Theory. First edition North Holland (1987); second edition AMS (2009)
Richter, W., Aczel, P.: Inductive definitions and reflecting properties of admissible ordinals. In: Fenstad, H. (eds.) Generalized Recursion Theory, pp. 301–381. North-Holland (1974)
Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)
Sacks, G.: Higher Recursion Theory. Springer, New York (1990)
Tanaka, H.: On analytic well-orderings. J. Symbolic Log. 35(2), 198–204 (1970)
Tanaka, K.: The Galvin-Prikry theorem and set existence axioms. Ann. Pure Appl. Log. 42(1), 81–104 (1989)
Tanaka, K.: Weak axioms of determinacy and subsystems of analysis II (\({\Sigma ^{0}_{2}}\) Games). Ann. Pure Appl. Log. 52(1–2), 181–193 (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Lubarsky, R.S. (2016). Parallel Feedback Turing Computability. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-27683-0_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27682-3
Online ISBN: 978-3-319-27683-0
eBook Packages: Computer ScienceComputer Science (R0)