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TSO-to-TSO Linearizability Is Undecidable

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Automated Technology for Verification and Analysis (ATVA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9364))

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Abstract

TSO-to-TSO linearizability is a variant of linearizability for concurrent libraries on the Total Store Order (TSO) memory model. It is proved in this paper that TSO-to-TSO linearizability for a bounded number of processes is undecidable. We first show that the trace inclusion problem of a classic-lossy single-channel system, which is known undecidable, can be reduced to the history inclusion problem of specific libraries on the TSO memory model. Based on the equivalence between history inclusion and extended history inclusion for these libraries, we then prove that the extended history inclusion problem of libraries is undecidable on the TSO memory model. By means of extended history inclusion as an equivalent characterization of TSO-to-TSO linearizability, we finally prove that TSO-to-TSO linearizability is undecidable for a bounded number of processes.

This work is partially supported by the National Natural Science Foundation of China under Grants No.60721061, No.60833001, No.61272135, No.61700073, No.61100069, No.61472405, and No.61161130530.

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Notes

  1. 1.

    “t" represents TSO memory model. “e" represents that the operational semantics in this paper extends standard TSO operational semantics [14] similarly as [7].

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Chao Wang, Yi Lv & Peng Wu

  2. University of Chinese Academy of Sciences, Beijing, China

    Chao Wang

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  1. Chao Wang
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  2. Yi Lv
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Correspondence to Chao Wang .

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  1. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  2. East China Normal University, Shanghai, China

    Geguang Pu

  3. Chinese Academy of Sciences, Beijing, China

    Lijun Zhang

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Wang, C., Lv, Y., Wu, P. (2015). TSO-to-TSO Linearizability Is Undecidable. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_24

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  • DOI: https://doi.org/10.1007/978-3-319-24953-7_24

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