1,275 research outputs found
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
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
On Complexity Bounds and Confluence of Parallel Term Rewriting
We revisit parallel-innermost term rewriting as a model of parallel
computation on inductive data structures and provide a corresponding notion of
runtime complexity parametric in the size of the start term. We propose
automatic techniques to derive both upper and lower bounds on parallel
complexity of rewriting that enable a direct reuse of existing techniques for
sequential complexity. Our approach to find lower bounds requires confluence of
the parallel-innermost rewrite relation, thus we also provide effective
sufficient criteria for proving confluence. The applicability and the precision
of the method are demonstrated by the relatively light effort in extending the
program analysis tool AProVE and by experiments on numerous benchmarks from the
literature.Comment: Under submission to Fundamenta Informaticae. arXiv admin note:
substantial text overlap with arXiv:2208.0100
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*
Analysing Parallel Complexity of Term Rewriting
We revisit parallel-innermost term rewriting as a model of parallel
computation on inductive data structures and provide a corresponding notion of
runtime complexity parametric in the size of the start term. We propose
automatic techniques to derive both upper and lower bounds on parallel
complexity of rewriting that enable a direct reuse of existing techniques for
sequential complexity. The applicability and the precision of the method are
demonstrated by the relatively light effort in extending the program analysis
tool AProVE and by experiments on numerous benchmarks from the literature.Comment: Extended authors' accepted manuscript for a paper accepted for
publication in the Proceedings of the 32nd International Symposium on
Logic-based Program Synthesis and Transformation (LOPSTR 2022). 27 page
Certification of Complexity Proofs using CeTA
Nowadays certification is widely employed by automated termination tools for term rewriting, where certifiers support most available techniques. In complexity analysis, the situation is quite different. Although tools support certification in principle, current certifiers implement only the most basic technique,
namely, suitably tamed versions of reduction orders. As a consequence, only a small fraction of the proofs generated by state-of-the-art complexity tools can be certified. To improve upon this situation, we formalized a framework for the certification
of modular complexity proofs and incorporated it into CeTA. We
report on this extension and present the newly supported techniques
(match-bounds, weak dependency pairs, dependency tuples, usable rules, and usable replacement maps), resulting in a significant increase in the number of certifiable complexity proofs. During our work we detected conflicts in theoretical results as well as bugs in
existing complexity tools
Polynomial Path Orders
This paper is concerned with the complexity analysis of constructor term
rewrite systems and its ramification in implicit computational complexity. We
introduce a path order with multiset status, the polynomial path order POP*,
that is applicable in two related, but distinct contexts. On the one hand POP*
induces polynomial innermost runtime complexity and hence may serve as a
syntactic, and fully automatable, method to analyse the innermost runtime
complexity of term rewrite systems. On the other hand POP* provides an
order-theoretic characterisation of the polytime computable functions: the
polytime computable functions are exactly the functions computable by an
orthogonal constructor TRS compatible with POP*.Comment: LMCS version. This article supersedes arXiv:1209.379
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