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The complexity of β-reduction in low orders

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2001) 2044 LNCS 400-414
DOI: 10.1007/3-540-45413-6_31
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Abstract

This paper presents the complexity of β-reduction for re-dexes 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.

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Schubert, A. (2001). The complexity of β-reduction in low orders. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2044 LNCS, pp. 400–414). Springer Verlag. https://doi.org/10.1007/3-540-45413-6_31

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