Polynomial Path Orders: A Maximal Model

This paper is concerned with the automated complexity analysis of term rewrite systems (TRSs for short) and the ramification of these in implicit computational complexity theory (ICC for short). We introduce a novel path order with multiset status, the polynomial path order POP*. Essentially relying on the principle of predicative recursion as proposed by Bellantoni and Cook, its distinct feature is the tight control of resources on compatible TRSs: The (innermost) runtime complexity of compatible TRSs is polynomially bounded. We have implemented the technique, as underpinned by our experimental evidence our approach to the automated runtime complexity analysis is not only feasible, but compared to existing methods incredibly fast. As an application in the context of ICC we provide an order-theoretic characterisation of the polytime computable functions. To be precise, the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*

TcT: Tyrolean Complexity Tool

International audienceIn this paper we present TcT v3.0, the latest version of our fully automated complexity analyser.TcT implements our framework for automated complexity analysis and focuses on extensibility and automation. TcT is open with respect to the input problem under investigation and the resource metric in question.It is the most powerful tool in the realm of automated complexity analysis of term rewrite systems. Moreover it provides an expressive problem-independent strategy language that facilitates proof search.We give insights about design choices, the implementation of the framework and report different case studies where we have applied TcT successfully