论文信息 - The complexity of β-reduction in low orders

The complexity of β-reduction in low orders

We study the complexity of β-reduction for redexes of order 2, 3 and 4. The obtained results are: evaluation of boolean expressions can be reduced to β-reduction of order 2 and β-reduction of order 2 is in O(n log n), β-reduction of order 3 is complete for PTIME, and β-reduction of order 4 is complete for PSPACE.

Aleksy Schubert

[1] John Lamping. An algorithm for optimal lambda calculus reduction , 1989, POPL '90.

[2] Harry G. Mairson. A Simple Proof of a Theorem of Statman , 1992, Theor. Comput. Sci..

[3] Paris C. Kanellakis,et al. On the expressive power of simply typed and let-polymorphic lambda calculi , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[4] Samson Abramsky,et al. Handbook of logic in computer science. , 1992 .

[5] Cosimo Laneve,et al. Interaction Systems II: The Practice of Optimal Reductions , 1993, Theor. Comput. Sci..

[6] Samuel R. Buss,et al. The Boolean formula value problem is in ALOGTIME , 1987, STOC.

[7] Helmut Schwichtenberg,et al. An upper bound for reduction sequences in the typed λ-calculus , 1991, Arch. Math. Log..

[8] Ron Dinishak. The optimal implementation of functional programming languages , 2000, SOEN.

[9] Richard Statman,et al. The typed λ-calculus is not elementary recursive , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).