Analyzing Runtime Complexity via Innermost Runtime Complexity

Frohn, Florian; Giesl, Jürgen

doi:10.29007/1nbh

Cited by 4 publications

(4 citation statements)

References 21 publications

(56 reference statements)

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“…Similar to us, Frohn and Giesl [12] also relate different complexity properties. They identify a sufficient criterion to identify TRSs where runtime complexity of innermost rewriting and of full rewriting coincide.…”

Section: Related Worksupporting

confidence: 58%

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Transforming Derivational Complexity of Term Rewriting to Runtime Complexity

Fuhs

2019

Frontiers of Combining Systems

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Derivational complexity of term rewriting considers the length of the longest rewrite sequence for arbitrary start terms, whereas runtime complexity restricts start terms to basic terms. Recently, there has been notable progress in automatic inference of upper and lower bounds for runtime complexity. We propose a novel transformation that allows an offthe-shelf tool for inference of upper or lower bounds for runtime complexity to be used to determine upper or lower bounds for derivational complexity as well. Our approach is applicable to derivational complexity problems for innermost rewriting and for full rewriting. We have implemented the transformation in the tool AProVE and conducted an extensive experimental evaluation. Our results indicate that bounds for derivational complexity can now be inferred for rewrite systems that have been out of reach for automated analysis thus far.

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Section: Related Worksupporting

confidence: 58%

“…For the inference of the upper bound, first a sufficient criterion [12] is used to show that this TRS belongs to a class of TRSs where runtime complexity and innermost runtime complexity coincide. To analyze innermost runtime complexity, the approach by Naaf et al [30] is applied.…”

Section: (This Is a Priori Not Completely Obvious Since Innermost Rewmentioning

confidence: 99%

Transforming Derivational Complexity of Term Rewriting to Runtime Complexity

Fuhs

2019

Frontiers of Combining Systems

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“…Among other related work, mainly on resource analysis, are [9,4,11,1,10], which use different methods than our approach.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Linear Tree Constraints

Bauer,

Hofmann

2018

Preprint

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Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus, once we have found an algorithm to solve the constraints generated from a program, we can read off the resource consumption from their solutions.These constraints have the form of pointwise linear inequalities between infinite trees labeled with nonnegative rational numbers. We are interested in the question if a system of such constraints is simultaneously satisfiable. Bauer and Hofmann have recently identified a fragment of the tree constraint problem (UTC) that is still sufficient for program analysis and they proved that the list case of UTC is decidable (which was presented at LPAR-21), whereas the case with trees of degree at least two remained open. In this paper, we solve this problem. We give a decision procedure that covers the entire range of constraints needed for resource analysis.

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“…Hofmann and Moser applied amortised analysis to term rewriting [24], Hoffmann refined his work, made it fully automatic and carried over the analysis to concurrent programs and programs in C and OCaml [17,6,7,20,21]. Among other related work, mainly on resource analysis, are [10,5,13,1,11], which use different methods than our approach.…”

Section: Related Workmentioning

confidence: 99%

Decidable Inequalities over Infinite Trees

Bauer¹,

Jost

Hofmann³

EPiC Series in Computing

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Linear tree constraints are given by pointwise linear inequalities between infinite trees labeled with nonnegative rational numbers. Satisfiablity of such constraints is at least as hard as solving the Skolem-Mahler-Lech Problem. We provide an interesting subcase, for which we prove that satisfiablity is decidable. Our decision procedure is based on intricate arguments using automata and combinatorics of words.Our subcase allows to construct an inference mechanism for resource bounds of object oriented Java-like programs: actual resource bounds can be read off from solutions of tree constraints. So far, only the case of degenerated tree constraints (i.e. lists) was known to be decidable which, however, is insufficient to generally solve the given resource analysis problem. The present paper therefore provides a generalisation to trees of higher degree in order to cover the entire range of constraints encountered by resource analysis.

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Analyzing Runtime Complexity via Innermost Runtime Complexity

Cited by 4 publications

References 21 publications

Transforming Derivational Complexity of Term Rewriting to Runtime Complexity

Transforming Derivational Complexity of Term Rewriting to Runtime Complexity

Linear Tree Constraints

Decidable Inequalities over Infinite Trees

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