Complexity Analysis for Term Rewriting by Integer Transition Systems

Naaf, Matthias; Frohn, Florian; Brockschmidt, Marc; Fuhs, Carsten; Giesl, Jürgen

doi:10.1007/978-3-319-66167-4_8

Cited by 13 publications

(10 citation statements)

References 32 publications

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“…Note that invariant inference and complexity analysis are closely related: Invariant inference techniques can be used to compute complexity bounds by introducing an additional counter that is incremented in each step and deducing an invariant that bounds its value (see, e.g., [50]). Conversely, complexity analysis techniques can be used to bound the value of any arithmetic expression b (i.e., to compute invariants) by choosing the costs of transitions in a way that reflects changes of the value of b (see, e.g., [48,50]).…”

Section: Related Workmentioning

confidence: 99%

Lower Runtime Bounds for Integer Programs

Frohn

Naaf

Hensel

et al. 2016

Automated Reasoning

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We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples.

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Section: Related Workmentioning

confidence: 99%

Lower Runtime Bounds for Integer Programs

Frohn

Naaf

Hensel

et al. 2016

Automated Reasoning

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“…Similarly AProVE [29] yields the tight bound employing a size abstraction to integer transition systems (ITSs for short), cf. [30]. The resulting ITSs are then solved with CoFloCo [31], which also embodies an amortisation analysis.…”

Section: Experimental Evaluationmentioning

confidence: 99%

Automated amortised resource analysis for term rewrite systems

Moser

Schneckenreither

2020

Science of Computer Programming

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In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated 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 so that rewrite systems may serve as abstractions of first-order, eagerly evaluated functional programs over user-defined inductive data-types. This facilitates integration in a general framework for resource analysis of programs. In particular, we have implemented the method and integrated it into our analysis tool T C T. Furthermore, we have coupled the established analysis with a complexity reflecting transformation from pure OCaml programs. This extends the provided analysis to a fully automated resource analysis of higher-order functional programs.

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“…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. Here the search for an upper bound for innermost runtime complexity is encoded as the search for an upper bound for the runtime of integer transition systems.…”

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

confidence: 99%

“…We conjecture that this is because a number of advanced Table 4. Lower bounds for derivational complexity of full rewriting techniques (e.g., [19,29,30,32]) for analysis of runtime complexity are available only for innermost rewriting. Still, Ex.…”

Section: Implementation and Experimental Evaluationmentioning

confidence: 99%

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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Complexity Analysis for Term Rewriting by Integer Transition Systems

Cited by 13 publications

References 32 publications

Lower Runtime Bounds for Integer Programs

Lower Runtime Bounds for Integer Programs

Automated amortised resource analysis for term rewrite systems

Transforming Derivational Complexity of Term Rewriting to Runtime Complexity

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