A complexity analysis of functional interpretations
| Autor: | Mircea-Dan Hernest, Ulrich Kohlenbach |
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| Rok vydání: | 2005 |
| Předmět: |
General Computer Science
Functionals of finite type Type (model theory) Arity Translation (geometry) Mathematical proof Theoretical Computer Science Combinatorics proof interpretation Proof-carrying code Time complexity Probabilistically checkable proof Mathematics Discrete mathematics quantitative analysis Degree (graph theory) Proof complexity Program extraction from (classical) proofs Software and systems verification Computational complexity Monotone polygon TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Proof theory Gödel's funktional interpretation Combinatorial logic Functional interpretation Proof mining Computer Science(all) |
| Zdroj: | Hernest, M-D & Kohlenbach, U 2005, ' A complexity analysis of functional interpretations ', Theoretical Computer Science, vol. 338, no. 1-3, pp. 200-246 . BRICS Report Series; No 12 (2003): RS-12 A Complexity Analysis of Functional Interpretations. BRICS Report Series; Nr. 12 (2003): RS-12 A Complexity Analysis of Functional Interpretations. Hernest, M-D & Kohlenbach, U 2003, ' A Complexity Analysis of Functional Interpretations ' B R I C S Report Series, no. RS-03-12 . |
| ISSN: | 0304-3975 1601-5355 0909-0878 |
| DOI: | 10.1016/j.tcs.2004.12.019 |
| Popis: | Summary: We give a quantitative analysis of Gödel's functional interpretation and its monotone variant. The two have been used for the extraction of programs and numerical bounds as well as for conservation results. They apply both to (semi-)intuitionistic as well as (combined with negative translation) classical proofs. The proofs may be formalized in systems ranging from weak base systems to arithmetic and analysis (and numerous fragments of these). We give upper bounds in basic proof data on the depth, size, maximal type degree and maximal type arity of the extracted terms as well as on the depth of the verifying proof. In all cases terms of size linear in the size of the proof at input can be extracted and the corresponding extraction algorithms have cubic worst-time complexity. The verifying proofs have depth linear in the depth of the proof at input and the maximal size of a formula of this proof |
| Databáze: | OpenAIRE |
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