Abstract
We present a framework to verify both, functional correctness and worst-case complexity of practically efficient algorithms. We implemented a stepwise refinement approach, using the novel concept of resource currencies to naturally structure the resource analysis along the refinement chain, and allow a fine-grained analysis of operation counts. Our framework targets the LLVM intermediate representation. We extend its semantics from earlier work with a cost model. As case study, we verify the correctness and \(O(n\log n)\) worst-case complexity of an implementation of the introsort algorithm, whose performance is on par with the state-of-the-art implementation found in the GNU C++ Library.
Keywords
- Algorithm Analysis
- Program Verification
- Refinement
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References
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Haslbeck, M.P.L., Lammich, P. (2021). For a Few Dollars More. In: Yoshida, N. (eds) Programming Languages and Systems. ESOP 2021. Lecture Notes in Computer Science(), vol 12648. Springer, Cham. https://doi.org/10.1007/978-3-030-72019-3_11
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DOI: https://doi.org/10.1007/978-3-030-72019-3_11
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