Affiliation:
1. Technische Universität München, Munich, Germany
2. University of Twente, Enschede, Netherlands
Abstract
We present a framework to verify both, functional correctness and (amortized) 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 studies, we verify the amortized constant time push operation on dynamic arrays and the
O
(
n
log
n
) introsort algorithm, and refine them down to efficient LLVM implementations. Our sorting algorithm performs on par with the state-of-the-art implementation found in the GNU C++ Library, and provably satisfies the complexity required by the C++ standard.
Funder
DFG Koselleck
Verifizierte Algorithmenanalyse
Verifizierte Model Checker
Publisher
Association for Computing Machinery (ACM)
Cited by
2 articles.
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