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| Content Provider | Springer Nature Link |
|---|---|
| Author | Terui, Kazushige |
| Copyright Year | 2007 |
| Abstract | Light Linear Logic (LLL) and Intuitionistic Light Affine Logic (ILAL) are logics that capture polynomial time computation. It is known that every polynomial time function can be represented by a proof of these logics via the proofs-as-programs correspondence. Furthermore, there is a reduction strategy which normalizes a given proof in polynomial time. Given the latter polynomial time “weak” normalization theorem, it is natural to ask whether a “strong” form of polynomial time normalization theorem holds or not. In this paper, we introduce an untyped term calculus, called Light Affine Lambda Calculus (λLA), which corresponds to ILAL. λLA is a bi-modal λ-calculus with certain constraints, endowed with very simple reduction rules. The main property of LALC is the polynomial time strong normalization: any reduction strategy normalizes a given λLA term in a polynomial number of reduction steps, and indeed in polynomial time. Since proofs of ILAL are structurally representable by terms of λLA, we conclude that the same holds for ILAL. |
| Starting Page | 253 |
| Ending Page | 280 |
| Page Count | 28 |
| File Format | |
| ISSN | 09335846 |
| Journal | Archive for Mathematical Logic |
| Volume Number | 46 |
| Issue Number | 3-4 |
| e-ISSN | 14320665 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2007-02-21 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Light logics Lambda calculus Polynomial time Algebra Mathematics Mathematical Logic and Foundations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Philosophy Logic |
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