Brief Announcement: On Decidability of 2-Process Affine Models

Authors Petr Kuznetsov, Thibault Rieutord

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Author Details

Petr Kuznetsov
  • LTCI, Télécom Paris, Institut Polytechnique Paris, France
Thibault Rieutord
  • CEA LIST, PC 174, Gif-sur-Yvette, France

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Petr Kuznetsov and Thibault Rieutord. Brief Announcement: On Decidability of 2-Process Affine Models. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 54:1-54:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Affine models of computation, defined as subsets of iterated immediate-snapshot runs, capture a wide variety of shared-memory systems: wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The question of whether a given task is solvable in a given affine model is, in general, undecidable. In this paper, we focus on affine models defined for a system of two processes. We show that task computability of 2-process affine models is decidable and presents a complete hierarchy of five equivalence classes of 2-process affine models.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Affine tasks
  • Decidability


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  1. Elizabeth Borowsky and Eli Gafni. A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In PODC, pages 189-198, 1997. Google Scholar
  2. Eli Gafni, Yuan He, Petr Kuznetsov, and Thibault Rieutord. Read-write memory and k-set consensus as an affine task. In OPODIS, pages 6:1-6:17, 2016. Google Scholar
  3. Eli Gafni and Elias Koutsoupias. Three-processor tasks are undecidable. SIAM J. Comput., 28(3):970-983, 1999. Google Scholar
  4. Eli Gafni, Petr Kuznetsov, and Ciprian Manolescu. A generalized asynchronous computability theorem. In PODC, pages 222-231, 2014. Google Scholar
  5. Maurice Herlihy and Sergio Rajsbaum. The decidability of distributed decision tasks (extended abstract). In STOC, pages 589-598, 1997. Google Scholar
  6. Petr Kuznetsov and Thibault Rieutord. On decidability of 2-process affine models, 2020. URL:
  7. Petr Kuznetsov, Thibault Rieutord, and Yuan He. An asynchronous computability theorem for fair adversaries. In PODC, pages 387-396, 2018. Google Scholar
  8. Vikram Saraph, Maurice Herlihy, and Eli Gafni. Asynchronous computability theorems for t-resilient systems. In DISC, pages 428-441, 2016. Google Scholar