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A theory for Log-Space and NLIN versus co-NLIN

Published online by Cambridge University Press:  12 March 2014

Chris Pollett
Chris Pollett*
Affiliation:
214 Macquarrie Hall, Department of Computer Science, San Jose State University, 1 Washington Square, San Jose CA 95192, USA, E-mail: pollett@cs.sjsu.edu
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Abstract

The use of Nepomnjaščiǐ's Theorem in the proofs of independence results for bounded arithmetic theories is investigated. Using this result and similar ideas, it is shown that at least one of S1 or TLS does not prove the Matiyasevich-Robinson-Davis-Putnam Theorem. It is also established that TLS does not prove a statement that roughly means nondeterministic linear time is equal to co-nondeterministic linear time. Here S1 is a conservative extension of the well-studied theory IΔ0 and TLS is a theory for LOGSPACE reasoning.

Keywords

bounded arithmeticindependence resultsMRDP
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1082 - 1090
Copyright
Copyright © Association for Symbolic Logic 2003

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