Algorithmic Complexity of Well-Quasi-Orders

Abstract : This document is dedicated to the algorithmic complexity of well-quasi-orders, with a particular focus on their applications in verification, where they allow to tackle systems featuring an infinite state-space, representing for instance integer counters, the number of active threads in concurrent settings, real-time clocks, call stacks, cryptographic nonces, or the contents of communication channels. The document presents a comprehensive framework for studying such complexities, encompassing the definition of complexity classes suitable for problems with non-elementary complexity and proof techniques for both upper and lower bounds, along with several examples where the framework has been applied successfully. In particular, as a striking illustration of these applications, it includes the proof of the first known complexity upper bound for reachability in vector addition systems and Petri nets.
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Contributor : Sylvain Schmitz <>
Submitted on : Wednesday, December 13, 2017 - 7:33:38 PM
Last modification on : Thursday, October 25, 2018 - 11:12:18 AM

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Sylvain Schmitz. Algorithmic Complexity of Well-Quasi-Orders. Logic in Computer Science [cs.LO]. École normale supérieure Paris-Saclay, 2017. ⟨tel-01663266⟩

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