Verifying asymptotic time complexity of imperative programs in Isabelle/HOL.
Paper at: https://arxiv.org/abs/1802.01336
The paper corresponds to the initial commit 8d336cd, which uses the version of auto2 (https://github.com/bzhan/auto2) at commit 167808b and Isabelle2017.
The current commit corresponds to commit b4b629e in auto2 and Isabelle2018.
We present a framework in Isabelle for verifying asymptotic time complexity of imperative programs. We build upon an extension of Imperative HOL and its separation logic to include running time. In addition to the basic arguments, our framework is able to handle advanced techniques for time complexity analysis, such as the use of the Akra-Bazzi theorem and amortized analysis. Various automation is built and incorporated into the auto2 prover to reason about separation logic with time credits, and to derive asymptotic behavior of functions. As case studies, we verify the asymptotic time complexity (in addition to functional correctness) of imperative algorithms and data structures such as median of medians selection, Karatsuba's algorithm, and splay trees.
Copyright (c) 2018, Bohua Zhan and Maximilian P. L. Haslbeck All rights reserved.
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