Journal article 1203 views
Uniform Proof Complexity
Journal of Logic and Computation, Volume: 15, Issue: 4, Pages: 433 - 446
Swansea University Author:
Arnold Beckmann
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DOI (Published version): 10.1093/logcom/exi035
Abstract
We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform...
| Published in: | Journal of Logic and Computation |
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| ISSN: | 0955-792X 1465-363X |
| Published: |
2005
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa1702 |
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| Abstract: |
We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are \Pi^0_1-hard and obviously in \Sigma^0_2. We also show under certain regularity conditions that each uniform reduct is closed under bounded generalisation; that in the case the language includes a symbol for exponentiation, a uniform reduct is closed under modus ponens if and only if it already contains all true bounded formulas; and that each uniform reduct contains all true \Pi^b_1(\alpha)-formulas. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
4 |
| Start Page: |
433 |
| End Page: |
446 |