Alternating runtime and size complexity analysis of integer programs

We present a modular approach to automatic complexity analysis. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer size bounds on program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. Extensive experiments with the implementation of our method demonstrate its performance and power in comparison with other tools

Analyzing program termination and complexity automatically with AProVE

In this system description, we present the tool AProVE for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and rewrite systems. In addition to classical term rewrite systems (TRSs), AProVE also supports rewrite systems containing built-in integers (int-TRSs). To analyze programs in high-level languages, AProVE automatically converts them to (int-)TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting rewrite systems. The generated proofs can be exported to check their correctness using automatic certifiers. To use AProVE in software construction, we present a corresponding plug-in for the popular Eclipse software development environment

Analysing the Complexity of Functional Programs: Higher-Order Meets First-Order

International audienceWe show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of first-order term rewrite systems. This is done while carefully analysing complexity preservation and reflection of the employed transformations such that the complexity of the obtained term rewrite system reflects on the complexity of the initial program. Further, we describe suitable strategies for the application of the studied transformations and provide ample experimental data for assessing the viability of our method

Transforming derivational complexity of term rewriting to runtime complexity

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 off-the-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

Amortised Resource Analysis and Typed Polynomial Interpretations

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COMPUTERIZED PATTERN CLASSIFICATION OF STRONGLY OVERLAPPED PEAKS IN STATIONARY ELECTRODE POLAROGRAPHY

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Automated Complexity Analysis Based on Context-Sensitive Rewriting

In this paper we present a simple technique for analysing the runtime complexity of rewrite systems. In complexity analysis many techniques are based on reduction orders. We show how the monotonicity condition for orders can be weakened by using the notion of context-sensitive rewriting. The presented technique is very easy to implement, even in a modular setting, and has been integrated in the Tyrolean Complexity Tool. We provide ample experimental data for assessing the viability of our method.Joint International Conference, RTA-TLCA 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 14-17, 201