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A Combination Framework for Complexity
Martin Avanzini,Georg Moser +1 more
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TL;DR: In this article, a combination framework for polynomial complexity analysis of term rewrite systems is presented, which covers both derivational and runtime complexity analysis, including a generalisation of complexity pairs and dependency pairs.
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Abstract: 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.
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Citations
Towards automatic resource bound analysis for OCaml
Jan Hoffmann,Ankush Das,Shu-Chun Weng +2 more
- 01 Jan 2017
TL;DR: In this article, the authors present a multivariate automatic amortized resource analysis (AARA) for OCaml programs with user-defined inductive types. But their analysis is based on linear AARA for higher-order programs with first-order lists and binary trees.
136
The Termination and Complexity Competition
Jürgen Giesl,Albert Rubio,Christian Sternagel,Johannes Waldmann,Akihisa Yamada +4 more
- 06 Apr 2019
TL;DR: The terminated and complexity competition (termCOMP) focuses on automated termination and complexity analysis for various kinds of programming paradigms, including categories for term rewriting, integer transition systems, imperative programming, logic programming, and functional programming.
•Posted Content
Bounded Expectations: Resource Analysis for Probabilistic Programs
TL;DR: In this paper, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning based on weakest preconditions is presented.
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•Posted Content
Analysing the Complexity of Functional Programs: Higher-Order Meets First-Order (Long Version).
TL;DR: It is shown how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalised versions of them, and feeding the result to existing tools for the complexity analysis of first-order term rewrite systems.
44
Raising expectations: automating expected cost analysis with types
Di Wang,David M. Kahn,Jan Hoffmann +2 more
- 02 Aug 2020
TL;DR: In this article, a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs is presented, which is based on the potential method of amortized analysis.
References
•Book
Term rewriting and all that
Franz Baader,Tobias Nipkow +1 more
- 01 Jan 1998
TL;DR: This chapter discusses abstract reduction systems, universal algebra, and Grobner bases and Buchberger's algorithm, and a bluffer's guide to ML Bibliography Index.
2.8K
Term rewriting and all that
TL;DR: Term Rewriting and All That is a self-contained introduction to the field of term rewriting and covers all the basic material including abstract reduction systems, termination, confluence, completion, and combination problems.
1K
Tyrolean Termination Tool 2
Martin Korp,Christian Sternagel,Harald Zankl,Aart Middeldorp +3 more
- 19 Apr 2005
TL;DR: The Tyrolean Termination tool is described, the successor of the Tsukuba Termination Tool, and the differences between the two are described and the new features are explained, some of which are not (yet) available in any other termination tool, in some detail.
Automating the dependency pair method
Nao Hirokawa,Aart Middeldorp +1 more
- 25 May 2005
TL;DR: New ideas to overcome obstacles to overcome termination of term rewrite systems that resist traditional techniques based on simplification orders are presented.