A new order-theoretic characterisation of the polytime computable functions

We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order (sPOP⁎ for short). This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully...

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Bibliographic Details
Published in:Theoretical computer science Vol. 585; pp. 3 - 24
Main Authors: Avanzini, Martin, Eguchi, Naohi, Moser, Georg
Format: Journal Article
Language:English
Published: Netherlands Elsevier B.V 20.06.2015
North-Holland Pub. Co
Subjects:
Asymptotic properties
Automation
Compatibility
Complexity
Complexity analysis
Implicit computational complexity
Mathematical analysis
Mathematical models
Polynomials
Recursion
Run time (computers)
Term rewriting
Term rewriting
Complexity analysis
Automation
Implicit computational complexity
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order (sPOP⁎ for short). This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully automatically: for any rewrite system compatible with sPOP⁎ that employs recursion up to depth d, the (innermost) runtime complexity is polynomially bounded of degree d. This bound is tight. Thus we obtain a direct correspondence between a syntactic (and easily verifiable) condition of a program and the asymptotic worst-case complexity of the program.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.03.003