Improving Automatic Complexity Analysis of Integer Programs

Giesl, Jürgen; Lommen, Nils; Hark, Marcel; Meyer, Fabian

doi:10.1007/978-3-031-08166-8_10

Cited by 4 publications

References 45 publications

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Targeting Completeness: Using Closed Forms for Size Bounds of Integer Programs

Lommen,

Giesl

2023

Lecture Notes in Computer Science

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We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our technique is complete (i.e., it always computes finite size bounds) for a subclass of loops, possibly with non-linear arithmetic. Moreover, we present a novel approach to combine and integrate this complete technique into an incomplete approach to infer size and runtime bounds of general integer programs. We prove completeness of our integration for an important subclass of integer programs. We implemented our new algorithm in the automated complexity analysis tool to evaluate its power, in particular on programs with non-linear arithmetic.

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Targeting Completeness: Using Closed Forms for Size Bounds of Integer Programs

Lommen,

Giesl

2023

Lecture Notes in Computer Science

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Control-Flow Refinement for Complexity Analysis of Probabilistic Programs in KoAT (Short Paper)

Lommen,

Meyer,

Giesl

2024

Lecture Notes in Computer Science

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A Machine Learning-Based Approach for Solving Recurrence Relations and Its use in Cost Analysis of Logic Programs

RUSTENHOLZ,

KLEMEN,

CARREIRA-PERPIÑÁN

et al. 2024

Theory and Practice of Logic Programming

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Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data and presents such information as functions of input data sizes. Most of the analysis tools for logic programs (and many for other languages), as CiaoPP, are based on setting up recurrence relations representing (bounds on) the computational cost of predicates and solving them to find closed-form functions. Such recurrence solving is a bottleneck in current tools: many of the recurrences that arise during the analysis cannot be solved with state-of-the-art solvers, including computer algebra systems (CASs), so that specific methods for different classes of recurrences need to be developed. We address such a challenge by developing a novel, general approach for solving arbitrary, constrained recurrence relations, that uses machine learning (sparse-linear and symbolic) regression techniques to guess a candidate closed-form function, and a combination of an SMT-solver and a CAS to check whether such function is actually a solution of the recurrence. Our prototype implementation and its experimental evaluation within the context of the CiaoPP system show quite promising results. Overall, for the considered benchmark set, our approach outperforms state-of-the-art cost analyzers and recurrence solvers and can find closed-form solutions, in a reasonable time, for recurrences that cannot be solved by them.

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Improving Automatic Complexity Analysis of Integer Programs

Cited by 4 publications

References 45 publications

Targeting Completeness: Using Closed Forms for Size Bounds of Integer Programs

Targeting Completeness: Using Closed Forms for Size Bounds of Integer Programs

Control-Flow Refinement for Complexity Analysis of Probabilistic Programs in KoAT (Short Paper)

A Machine Learning-Based Approach for Solving Recurrence Relations and Its use in Cost Analysis of Logic Programs

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