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Synthesis of Parametric Locally Symmetric Protocols from Abstract Temporal Specifications

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2025)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15530))

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Abstract

Scalable distributed systems are typically parametric in design. The key parameter is the number of isomorphic components, K. A second important parameter is the number of neighbors, k, of each component process. In this work, we describe a methodology that uses an automated synthesis procedure to construct parametric system instances where both K and k can vary arbitrarily, extending prior work on synthesis for a fixed k. The methodology relies crucially on locality, symmetry, and abstraction. The first step is to eliminate K by refining a general, system-wide specification to a local temporal specification for a generic process in its parameterized neighborhood. Next, the local process specification is abstracted to remove its dependence on k. These steps are done by hand. The given synthesis procedure then automatically constructs an abstract process from the abstract local specification with a worst-case cost exponential in the length of the abstract local specification. We show that, for any k, the concretized abstract process meets the local specification. We then show that instantiating the abstract process with different k and K forms system instances that satisfy the system-level specification. The worst-case cost of instantiation is linear in K. We use this method to synthesize an atomic snapshots protocol on fully connected networks and a dining philosophers protocol on hypercubes.

R. Trefler and R. Zhang were supported, in part, by an Individual Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Kedar Namjoshi was supported in part by DARPA under contract HR001120C0159. The views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.

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Notes

  1. 1.

    An extended version of this paper is available at https://github.com/rzhang378/LocalSynth.git.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Ruoxi Zhang & Richard Trefler

  2. Nokia Bell Labs, Murray Hill, NJ, USA

    Kedar S. Namjoshi

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  1. Ruoxi Zhang
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  2. Richard Trefler
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  3. Kedar S. Namjoshi
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Correspondence to Ruoxi Zhang .

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Editors and Affiliations

  1. Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Krishna Shankaranarayanan

  2. University of Colorado Boulder, Boulder, CO, USA

    Sriram Sankaranarayanan

  3. University of Colorado Boulder, Boulder, CO, USA

    Ashutosh Trivedi

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Zhang, R., Trefler, R., Namjoshi, K.S. (2025). Synthesis of Parametric Locally Symmetric Protocols from Abstract Temporal Specifications. In: Shankaranarayanan, K., Sankaranarayanan, S., Trivedi, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2025. Lecture Notes in Computer Science, vol 15530. Springer, Cham. https://doi.org/10.1007/978-3-031-82703-7_4

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  • DOI: https://doi.org/10.1007/978-3-031-82703-7_4

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