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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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
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Abstract	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.
AbstractList	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. We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the ([Formula: see text] 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 [Formula: see text] that employs recursion up to depth , the (innermost) runtime complexity is polynomially bounded of degree . 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. We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order ( 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 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. We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order ([Formula: see text] 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 [Formula: see text] 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.We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order ([Formula: see text] 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 [Formula: see text] 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.
Author	Moser, Georg Eguchi, Naohi Avanzini, Martin
AuthorAffiliation	Institute of Computer Science, University of Innsbruck, Austria
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Keywords	Term rewriting Complexity analysis Automation Implicit computational complexity
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Snippet	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⁎... We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the ([Formula: see text] for short).... We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order ( for... We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order...
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SubjectTerms	Asymptotic properties Automation Compatibility Complexity Complexity analysis Implicit computational complexity Mathematical analysis Mathematical models Polynomials Recursion Run time (computers) Term rewriting
Title	A new order-theoretic characterisation of the polytime computable functions
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