Abstract
This paper presents a theory of skiplists with a decidable satisfiability problem, and shows its applications to the verification of concurrent skiplist implementations. A skiplist is a data structure used to implement sets by maintaining several ordered singly-linked lists in memory, with a performance comparable to balanced binary trees. We define a theory capable of expressing the memory layout of a skiplist and show a decision procedure for the satisfiability problem of this theory. We illustrate the application of our decision procedure to the temporal verification of an implementation of concurrent lock-coupling skiplists. Concurrent lock-coupling skiplists are a particular version of skiplists where every node contains a lock at each possible level, reducing granularity of mutual exclusion sections.
The first contribution of this paper is the theory TSL K. TSL K is a decidable theory capable of reasoning about list reachability, locks, ordered lists, and sublists of ordered lists. The second contribution is a proof that TSL K enjoys a finite model property and thus it is decidable. Finally, we show how to reduce the satisfiability problem of quantifier-free TSL K formulas to a combination of theories for which a many-sorted version of Nelson-Oppen can be applied.
This work was funded in part by the EU project FET IST-231620 HATS, MICINN project TIN-2008-05624 DOVES, CAM project S2009TIC-1465 PROMETIDOS, and by the COST Action IC0901 Rich ModelToolkit-An Infrastructure for Reliable Computer Systems.
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Sánchez, A., Sánchez, C. (2011). A Theory of Skiplists with Applications to the Verification of Concurrent Datatypes. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds) NASA Formal Methods. NFM 2011. Lecture Notes in Computer Science, vol 6617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20398-5_25
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