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Termination Analysis for the \(\pi \)-Calculus by Reduction to Sequential Program Termination

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Programming Languages and Systems (APLAS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 13008))

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Abstract

We propose an automated method for proving termination of \(\pi \)-calculus processes, based on a reduction to termination of sequential programs: we translate a \(\pi \)-calculus process to a sequential program, so that the termination of the latter implies that of the former. We can then use an off-the-shelf termination verification tool to check termination of the sequential program. Our approach has been partially inspired by Deng and Sangiorgi’s termination analysis for the \(\pi \)-calculus, and checks that there is no infinite chain of communications on replicated input channels, by converting such a chain of communications to a chain of recursive function calls in the target sequential program. We have implemented an automated tool based on the proposed method and confirmed its effectiveness.

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Notes

  1. 1.

    The actual translation given later is a little more complex.

  2. 2.

    Thus, the simple type system with “regions” introduced in the previous section is used here as a simple may-alias analysis. If \(x\) and \(y\) may be bound to the same channel during reductions, the type system assigns the same region to \(x\) and \(y\), hence \(x\) and \(y\) are mapped to the same function name \(f_{\rho _{x}}\) by our transformation.

  3. 3.

    The program written here has been simplified for the sake of readability. For instance, we removed some redundant \( (\,)\), trivial function definitions, and unused non-deterministic integers. The other examples that will appear in this paper are also simplified in the same way.

  4. 4.

    The rule for replicated inputs is also modified in a similar manner.

  5. 5.

    Unfortunately, there are no standard benchmark set for the termination analysis for the \(\pi \)-calculus.

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Acknowledgments

We would like to thank anonymous referees for useful comments. This work was supported by JSPS KAKENHI Grant Number JP20H05703.

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Tsubasa Shoshi, Takuma Ishikawa, Naoki Kobayashi, Ken Sakayori & Ryosuke Sato

  2. Chiba University, Chiba, Japan

    Takeshi Tsukada

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  1. Tsubasa Shoshi
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  2. Takuma Ishikawa
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  3. Naoki Kobayashi
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Correspondence to Tsubasa Shoshi .

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  1. Korea University, Seoul, Korea (Republic of)

    Hakjoo Oh

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Shoshi, T., Ishikawa, T., Kobayashi, N., Sakayori, K., Sato, R., Tsukada, T. (2021). Termination Analysis for the \(\pi \)-Calculus by Reduction to Sequential Program Termination. In: Oh, H. (eds) Programming Languages and Systems. APLAS 2021. Lecture Notes in Computer Science(), vol 13008. Springer, Cham. https://doi.org/10.1007/978-3-030-89051-3_15

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  • DOI: https://doi.org/10.1007/978-3-030-89051-3_15

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