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Equality of streams is a Π0 over 2-complete problem

Published:16 September 2006Publication History
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Abstract

This paper gives a precise characterization for the complexity of the problem of proving equal two streams defined with a finite number of equations: Π0 over 2. Since the Π 0 over 2 class includes properly both the reursively enumerable and the corecursively enumerable classes, this result implies that neither the set of pairs of equal streams nor the set of pairs of unequal streams is recursively enumerable. Consequently, one can find no algorithm for determining equality of streams, as well as no algorithm for determining inequality of streams. In particular, there is no complete proof system for equality of streams and no complete system for inequality of streams.

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        • Published in

          cover image ACM SIGPLAN Notices
          ACM SIGPLAN Notices  Volume 41, Issue 9
          Proceedings of the 2006 ICFP conference
          September 2006
          296 pages
          ISSN:0362-1340
          EISSN:1558-1160
          DOI:10.1145/1160074
          Issue’s Table of Contents
          • cover image ACM Conferences
            ICFP '06: Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming
            September 2006
            308 pages
            ISBN:1595933093
            DOI:10.1145/1159803
            • General Chair:
            • John Reppy,
            • Program Chair:
            • Julia Lawall

          Copyright © 2006 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 16 September 2006

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