### New Order-theoretic Characterisation of the Polytime Computable Functions

Martin Avanzini, Naohi Eguchi, and Georg MoserProceedings of the 10th Asian Symposium on Programming Languages and Systems (APLAS 2012), Lecture Notes in Computer Science 7705, pp. 280 – 295, 2012.

### 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 upto depth d, the (innermost) runtime complexity is polynomially bounded of degree d. This bound is tight.

### BibTeX

@inproceedings{MANEGM-APLAS12, author = "Martin Avanzini and Naohi Eguchi and Georg Moser", title = "New Order-theoretic Characterisation of the Polytime Computable Functions", booktitle = "Proceedings of the 10th Asian Symposium Programming Languages and Systems", series = "Lecture Notes in Computer Science (Programming Languages and Systems)", number = 7705, pages = "280--295", publisher = "Springer-Verlag", year = 2012 }