Safe Recursion Over an Arbitrary Structure : PAR, PH and DPH
Identifieur interne : 000962 ( Crin/Checkpoint ); précédent : 000961; suivant : 000963Safe Recursion Over an Arbitrary Structure : PAR, PH and DPH
Auteurs : Olivier Bournez ; Felipe Cucker ; Paulin Jacobé De Naurois ; Jean-Yves MarionSource :
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Considering the Blum, Shub, and Smale computational model for real numbers, extended by Poizat to general structures, classical complexity can be considered as the restriction to finite structures of a more general notion of computability and complexity working over arbitrary structures. In a previous paper, we showed that the machine-independent characterization of Bellantoni and Cook of sequential polynomial time for classical complexity is actually the restriction to finite structures of a characterization of sequential polynomial time over arbitrary structures. In this paper, we prove that the same phenomenon happens for several other complexity classes : over arbitrary structures, parallel polynomial time corresponds to safe recursion with substitutions, and the polynomial hierarchy corresponds to safe recursion with predicative minimization. Our results yield machine-independent characterizations of several complexity classes subsuming previous ones when restricted to finite structures.
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<author><name sortKey="Jacobe De Naurois, Paulin" sort="Jacobe De Naurois, Paulin" uniqKey="Jacobe De Naurois P" first="Paulin" last="Jacobé De Naurois">Paulin Jacobé De Naurois</name>
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<front><div type="abstract" xml:lang="en" wicri:score="2507">Considering the Blum, Shub, and Smale computational model for real numbers, extended by Poizat to general structures, classical complexity can be considered as the restriction to finite structures of a more general notion of computability and complexity working over arbitrary structures. In a previous paper, we showed that the machine-independent characterization of Bellantoni and Cook of sequential polynomial time for classical complexity is actually the restriction to finite structures of a characterization of sequential polynomial time over arbitrary structures. In this paper, we prove that the same phenomenon happens for several other complexity classes : over arbitrary structures, parallel polynomial time corresponds to safe recursion with substitutions, and the polynomial hierarchy corresponds to safe recursion with predicative minimization. Our results yield machine-independent characterizations of several complexity classes subsuming previous ones when restricted to finite structures.</div>
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<BibTex type="inproceedings"><ref>bournez03b</ref>
<crinnumber>A03-R-315</crinnumber>
<category>3</category>
<equipe>PROTHEO</equipe>
<author><e>Bournez, Olivier</e>
<e>Cucker, Felipe</e>
<e>Jacobé de Naurois, Paulin</e>
<e>Marion, Jean-Yves</e>
</author>
<title>Safe Recursion Over an Arbitrary Structure : PAR, PH and DPH</title>
<booktitle>{Fifth International Workshop on Implicit Computational Complexity - ICC'2003, Ottawa, Canada}</booktitle>
<year>2003</year>
<volume>90</volume>
<number>1</number>
<series>Electronic Notes in Computer Science</series>
<month>Jun</month>
<keywords><e>complexity</e>
<e>blum shub smale model</e>
<e>safe recursion</e>
</keywords>
<abstract>Considering the Blum, Shub, and Smale computational model for real numbers, extended by Poizat to general structures, classical complexity can be considered as the restriction to finite structures of a more general notion of computability and complexity working over arbitrary structures. In a previous paper, we showed that the machine-independent characterization of Bellantoni and Cook of sequential polynomial time for classical complexity is actually the restriction to finite structures of a characterization of sequential polynomial time over arbitrary structures. In this paper, we prove that the same phenomenon happens for several other complexity classes : over arbitrary structures, parallel polynomial time corresponds to safe recursion with substitutions, and the polynomial hierarchy corresponds to safe recursion with predicative minimization. Our results yield machine-independent characterizations of several complexity classes subsuming previous ones when restricted to finite structures.</abstract>
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