23 research outputs found
Termination Proofs in the Dependency Pair Framework May Induce Multiple Recursive Derivational Complexity
We study the derivational complexity of rewrite systems whose termination is
provable in the dependency pair framework using the processors for reduction
pairs, dependency graphs, or the subterm criterion. We show that the
derivational complexity of such systems is bounded by a multiple recursive
function, provided the derivational complexity induced by the employed base
techniques is at most multiple recursive. Moreover we show that this upper
bound is tight.Comment: 22 pages, extended conference versio
A Combination Framework for Complexity
In this paper we present a combination framework for polynomial complexity
analysis of term rewrite systems. The framework covers both derivational and
runtime complexity analysis. We present generalisations of powerful complexity
techniques, notably a generalisation of complexity pairs and (weak) dependency
pairs. Finally, we also present a novel technique, called dependency graph
decomposition, that in the dependency pair setting greatly increases
modularity. We employ the framework in the automated complexity tool TCT. TCT
implements a majority of the techniques found in the literature, witnessing
that our framework is general enough to capture a very brought setting
First-order formative rules
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints that need to be solved during a termination proof. Compared to the higher-order definition, the first-order setting allows for significant improvements of the technique
Modular Complexity Analysis for Term Rewriting
All current investigations to analyze the derivational complexity of term
rewrite systems are based on a single termination method, possibly preceded by
transformations. However, the exclusive use of direct criteria is problematic
due to their restricted power. To overcome this limitation the article
introduces a modular framework which allows to infer (polynomial) upper bounds
on the complexity of term rewrite systems by combining different criteria.
Since the fundamental idea is based on relative rewriting, we study how matrix
interpretations and match-bounds can be used and extended to measure complexity
for relative rewriting, respectively. The modular framework is proved strictly
more powerful than the conventional setting. Furthermore, the results have been
implemented and experiments show significant gains in power.Comment: 33 pages; Special issue of RTA 201
Automated Amortised Resource Analysis for Term Rewrite Systems
Based on earlier work on amortised resource analysis, we establish a novel automated amortised resource analysis for term rewrite systems. The method is presented in an inference system akin to a type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term rewrite system. Our analysis does not restrict the input rewrite system in any way. This facilitates integration in a general framework for resource analysis of programs. In particular, we have implemented the method and integrated it into our tool TCT.(VLID)2581042Accepted versio
The Derivational Complexity Induced by the Dependency Pair Method
We study the derivational complexity induced by the dependency pair method,
enhanced with standard refinements. We obtain upper bounds on the derivational
complexity induced by the dependency pair method in terms of the derivational
complexity of the base techniques employed. In particular we show that the
derivational complexity induced by the dependency pair method based on some
direct technique, possibly refined by argument filtering, the usable rules
criterion, or dependency graphs, is primitive recursive in the derivational
complexity induced by the direct method. This implies that the derivational
complexity induced by a standard application of the dependency pair method
based on traditional termination orders like KBO, LPO, and MPO is exactly the
same as if those orders were applied as the only termination technique