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A syntactical analysis of non-size-increasing polynomial time computation
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Source ACM Transactions on Computational Logic (TOCL) archive
Volume 3 ,  Issue 3  (July 2002) table of contents
Pages: 383 - 401  
Year of Publication: 2002
ISSN:1529-3785
Authors
Klaus Aehlig  Universität München, Munich, Germany
Helmut Schwichtenberg  Universität München, Munich, Germany
Publisher
ACM  New York, NY, USA
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ABSTRACT

A syntactical proof is given that all functions definable in a certain affine linear typed λ-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
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Beckmann, A. and Weiermann, A. 2000. Characterizing the elementary recursive functions by a fragment of Gödel's T. Arch. Math. Logic 39, 7 (Oct.), 475--492.
 
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Bellantoni, S., Niggl, K.-H., and Schwichtenberg, H. 2000. Higher type recursion, ramification and polynomial time. Ann. Pure Appl. Logic 104, 17--30.
 
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Caseiro, V.-H. 1997. Equations for defining poly-time functions. Ph.D. thesis, Department of Computer Science, University of Oslo, Oslon, Norway. Available at www.ifi.uio.no/~ftp/publications/research-reports/.
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Gödel, K. 1958. Über eine bisher noch nicht benützte Erweiterung des finiten Standpunkts. Dialectica 12, 280--287.
 
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Hofmann, M. 1998. Typed lambda calculi for polynomial-time computation. Habilitation thesis, Mathematisches Institut, TU Darmstadt, Germany. Available under www.dcs.ed.ac.uk/home/mxh/habil.ps.gz.
 
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Hofmann, M. 2000a. Linear types and non-size-increasing polynomial time computation. Theoret. Comput. Sci. To appear.
 
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Hofmann, M. 2001. The strength of non size-increasing computation. In Proceedings of the 3rd International Workshop on Implicit Computational Complexity (ICC '01) Aarhus, Denmark, May 20--21, 2001), M. Hofmann, Ed. Number NS-01-3 in Notes Series. BRICS, Department of Computer Science, University of Aarhus, Aarhus, Denmark, 19--35.
 
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Joachimski, F. and Matthes, R. 1999. Short proofs of normalisation for the simply-typed λ-calculus, permutative conversions and Gödel's T. Arch. Math. Logic, To appear.
 
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Simmons, H. 1988. The realm of primitive recursion. Arch. Math. Logic 27, 2 (Oct.), 177--188.


Collaborative Colleagues:
Klaus Aehlig: colleagues
Helmut Schwichtenberg: colleagues