The complexity of β-reduction in low orders

Authors:
Aleksy Schubert
Affiliations:
Institute of Informatics, Warsaw University
Venue:
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Year:
2001

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Abstract

This paper presents the complexity of β-reduction for redexes of order 1, 2 and 3. It concludes with the following results -- evaluation of Boolean expressions can be reduced to β-reduction of order 1 and β-reduction of order 1 is in O(n log n), β-reduction of order 2 is complete for PTIME, and β-reduction of order 3 is complete for PSPACE.