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# Actual arithmetic and feasibility

1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper presents a methodology for reasoning about the computational complexity of functional programs. We introduce a first order arithmetic $\StrictTa$ which is a syntactic restriction of Peano arithmetic. We establish that the set of functions which are provably total in $\StrictTa$, is exactly the set of polynomial time functions.The cut-elimination process is polynomial time computable. Compared to others feasible arithmetics, $\StrictTa$ is conceptually simpler. The main feature of $\StrictTa$ concerns the treatment of the quantification. The range of quantifiers is restricted to the set of {\em actual terms} which is the set of constructor terms with variables. The inductive formulas are restricted to conjunctions of atomic formulas.
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Conference papers
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https://hal.inria.fr/inria-00100424
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Submitted on : Tuesday, September 26, 2006 - 2:43:37 PM
Last modification on : Friday, February 4, 2022 - 3:32:25 AM

### Identifiers

• HAL Id : inria-00100424, version 1

### Citation

Jean-Yves Marion. Actual arithmetic and feasibility. International Workshop on Computer Science Logic - CSl'2001, 2001, Paris, France, pp.115--129. ⟨inria-00100424⟩

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