Synthesis of Distributed Algorithms with Parameterized Threshold Guards

Authors Marijana Lazic, Igor Konnov, Josef Widder, Roderick Bloem



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Marijana Lazic
Igor Konnov
Josef Widder
Roderick Bloem

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Marijana Lazic, Igor Konnov, Josef Widder, and Roderick Bloem. Synthesis of Distributed Algorithms with Parameterized Threshold Guards. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.OPODIS.2017.32

Abstract

Fault-tolerant distributed algorithms are notoriously hard to get right. In this paper we introduce an automated method that helps in that process: the designer provides specifications (the problem to be solved) and a sketch of a distributed algorithm that keeps arithmetic details unspecified. Our tool then automatically fills the missing parts. Fault-tolerant distributed algorithms are typically parameterized, that is, they are designed to work for any number n of processes and any number t of faults, provided some resilience condition holds; e.g., n > 3t. In this paper we automatically synthesize distributed algorithms that work for all parameter values that satisfy the resilience condition. We focus on threshold- guarded distributed algorithms, where actions are taken only if a sufficiently large number of messages is received, e.g., more than t or n/2. Both expressions can be derived by choosing the right values for the coefficients a, b, and c, in the sketch of a threshold a·n+b·t+c. Our method takes as input a sketch of an asynchronous threshold-based fault-tolerant distributed algorithm — where the guards are missing exact coefficients—and then iteratively picks the values for the coefficients. Our approach combines recent progress in parameterized model checking of distributed algo- rithms with counterexample-guided synthesis. Besides theoretical results on termination of the synthesis procedure, we experimentally evaluate our method and show that it can synthesize sev- eral distributed algorithms from the literature, e.g., Byzantine reliable broadcast and Byzantine one-step consensus. In addition, for several new variations of safety and liveness specifications, our tool generates new distributed algorithms.
Keywords
  • fault-tolerant distributed algorithms
  • byzantine faults
  • parameterized model checking
  • program synthesis

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References

  1. Rajeev Alur, Rastislav Bodík, Garvit Juniwal, Milo M. K. Martin, Mukund Raghothaman, Sanjit A. Seshia, Rishabh Singh, Armando Solar-Lezama, Emina Torlak, and Abhishek Udupa. Syntax-guided synthesis. In FMCAD, pages 1-8, 2013. Google Scholar
  2. K. Apt and D. Kozen. Limits for automatic verification of finite-state concurrent systems. IPL, 15:307-309, 1986. Google Scholar
  3. Clark Barrett, Christopher L. Conway, Morgan Deters, Liana Hadarean, Dejan Jovanovic, Tim King, Andrew Reynolds, and Cesare Tinelli. CVC4. In CAV, pages 171-177, 2011. Google Scholar
  4. Benjamin Bisping, Paul-David Brodmann, Tim Jungnickel, Christina Rickmann, Henning Seidler, Anke Stüber, Arno Wilhelm-Weidner, Kirstin Peters, and Uwe Nestmann. A constructive proof for FLP. Archive of Formal Proofs, 2016. Google Scholar
  5. Roderick Bloem, Nicolas Braud-Santoni, and Swen Jacobs. Synthesis of self-stabilising and Byzantine-resilient distributed systems. In CAV, volume 9779 of LNCS, pages 157-176, 2016. Google Scholar
  6. Roderick Bloem, Swen Jacobs, Ayrat Khalimov, Igor Konnov, Sasha Rubin, Helmut Veith, and Josef Widder. Decidability of Parameterized Verification. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2015. Google Scholar
  7. Tushar Deepak Chandra and Sam Toueg. Unreliable failure detectors for reliable distributed systems. J. ACM, 43(2):225-267, 1996. Google Scholar
  8. Bernadette Charron-Bost and André Schiper. The heard-of model: computing in distributed systems with benign faults. Distributed Computing, 22(1):49-71, 2009. Google Scholar
  9. Kaustuv Chaudhuri, Damien Doligez, Leslie Lamport, and Stephan Merz. Verifying safety properties with the TLA+ proof system. In IJCAR, volume 6173 of LNCS, pages 142-148, 2010. Google Scholar
  10. Edmund M. Clarke, Orna Grumberg, and Doron A. Peled. Model Checking. MIT Press, 1999. Google Scholar
  11. Leonardo De Moura and Nikolaj Bjørner. Z3: An efficient SMT solver. In TACAS, volume 1579 of LNCS, pages 337-340. Springer Berlin Heidelberg, 2008. Google Scholar
  12. Danny Dolev, Keijo Heljanko, Matti Järvisalo, Janne H. Korhonen, Christoph Lenzen, Joel Rybicki, Jukka Suomela, and Siert Wieringa. Synchronous counting and computational algorithm design. J. Comput. Syst. Sci., 82(2):310-332, 2016. Google Scholar
  13. Cezara Drăgoi, Thomas A. Henzinger, Helmut Veith, Josef Widder, and Damien Zufferey. A logic-based framework for verifying consensus algorithms. In VMCAI, volume 8318 of LNCS, pages 161-181, 2014. Google Scholar
  14. Fathiyeh Faghih and Borzoo Bonakdarpour. SMT-based synthesis of distributed self-stabilizing systems. TAAS, 10(3):21:1-21:26, 2015. Google Scholar
  15. Fathiyeh Faghih, Borzoo Bonakdarpour, Sébastien Tixeuil, and Sandeep S. Kulkarni. Specification-based synthesis of distributed self-stabilizing protocols. In FORTE, volume 9688 of LNCS, pages 124-141, 2016. Google Scholar
  16. Adrià Gascón and Ashish Tiwari. A synthesized algorithm for interactive consistency. In NFM, volume 8430 of LNCS, pages 270-284. Springer, 2014. Google Scholar
  17. Chris Hawblitzel, Jon Howell, Manos Kapritsos, Jacob R. Lorch, Bryan Parno, Michael L. Roberts, Srinath Setty, and Brian Zill. Ironfleet: Proving safety and liveness of practical distributed systems. Commun. ACM, 60(7):83-92, 2017. Google Scholar
  18. Swen Jacobs and Roderick Bloem. Parameterized synthesis. LMCS, 10(1:12), 2014. Google Scholar
  19. Igor Konnov, Marijana Lazić, Helmut Veith, and Josef Widder. A short counterexample property for safety and liveness verification of fault-tolerant distributed algorithms. In POPL, pages 719-734, 2017. Google Scholar
  20. Igor Konnov, Helmut Veith, and Josef Widder. SMT and POR beat counter abstraction: Parameterized model checking of threshold-based distributed algorithms. In CAV (Part I), volume 9206 of LNCS, pages 85-102, 2015. Google Scholar
  21. Igor Konnov, Josef Widder, Francesco Spegni, and Luca Spalazzi. Accuracy of message counting abstraction in fault-tolerant distributed algorithms. In VMCAI, pages 347-366, 2017. Google Scholar
  22. Leslie Lamport. Specifying systems: The TLA+ language and tools for hardware and software engineers. Addison-Wesley, 2002. Google Scholar
  23. Mohsen Lesani, Christian J. Bell, and Adam Chlipala. Chapar: certified causally consistent distributed key-value stores. In POPL, pages 357-370, 2016. Google Scholar
  24. Nancy Lynch. Distributed Algorithms. Morgan Kaufman, 1996. Google Scholar
  25. Ognjen Maric, Christoph Sprenger, and David A. Basin. Cutoff bounds for consensus algorithms. In CAV, pages 217-237, 2017. Google Scholar
  26. Laure Millet, Maria Potop-Butucaru, Nathalie Sznajder, and Sébastien Tixeuil. On the synthesis of mobile robots algorithms: The case of ring gathering. In SSS, volume 8756 of LNCS, pages 237-251, 2014. Google Scholar
  27. Achour Mostéfaoui, Eric Mourgaya, Philippe Raipin Parvédy, and Michel Raynal. Evaluating the condition-based approach to solve consensus. In DSN, pages 541-550, 2003. Google Scholar
  28. Yee Jiun Song and Robbert van Renesse. Bosco: One-step Byzantine asynchronous consensus. In DISC, volume 5218 of LNCS, pages 438-450, 2008. Google Scholar
  29. T.K. Srikanth and Sam Toueg. Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Dist. Comp., 2:80-94, 1987. Google Scholar
  30. Josef Widder and Ulrich Schmid. Booting clock synchronization in partially synchronous systems with hybrid process and link failures. Dist. Comp., 20(2):115-140, 2007. Google Scholar
  31. James R. Wilcox, Doug Woos, Pavel Panchekha, Zachary Tatlock, Xi Wang, Michael D. Ernst, and Thomas E. Anderson. Verdi: a framework for implementing and formally verifying distributed systems. In PLDI, pages 357-368, 2015. Google Scholar
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