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Concurrent NetKAT

Concurrent NetKAT

Modeling and analyzing stateful, concurrent networks

  • Jana Wagemaker  ORCID: orcid.org/0000-0002-8616-39059,
  • Nate Foster  ORCID: orcid.org/0000-0002-6557-684X10,
  • Tobias Kappé  ORCID: orcid.org/0000-0002-6068-880X11,
  • Dexter Kozen  ORCID: orcid.org/0000-0002-8007-472510,
  • Jurriaan Rot9 &
  • …
  • Alexandra Silva  ORCID: orcid.org/0000-0001-5014-978410 
  • Conference paper
  • Open Access
  • First Online: 29 March 2022

  • 2047 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13240)

Abstract

We introduce Concurrent NetKAT (CNetKAT), an extension of NetKAT with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on partially-ordered multisets (pomsets), which are a well-established mathematical structure for defining the denotational semantics of concurrent languages. We provide a sound and complete axiomatization of this model, and we illustrate the use of CNetKAT through examples. More generally, CNetKAT can be understood as an algebraic framework for reasoning about programs with both local state (in packets) and global state (in a global store).

Keywords

  • Concurrent Kleene algebra
  • NetKAT
  • completeness
  • concurrency

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References

  1. Alglave, J., Maranget, L., Sarkar, S., Sewell, P.: Litmus: Running tests against hardware. In: TACAS. pp. 41–44 (2011). https://doi.org/10.1007/978-3-642-19835-9_5

  2. Alpernas, K., Manevich, R., Panda, A., Sagiv, M., Shenker, S., Shoham, S., Velner, Y.: Abstract interpretation of stateful networks. In: Static Analysis. pp. 86–106. Springer International Publishing (2018), https://doi.org/10.1007/978-3-319-99725-4_8

  3. Anderson, C.J., Foster, N., Guha, A., Jeannin, J., Kozen, D., Schlesinger, C., Walker, D.: NetKAT: semantic foundations for networks. In: POPL. pp. 113–126 (2014). https://doi.org/10.1145/2535838.2535862

  4. Bosshart, P., Daly, D., Gibb, G., Izzard, M., McKeown, N., Rexford, J., Schlesinger, C., Talayco, D., Vahdat, A., Varghese, G., Walker, D.: P4: Programming protocol-independent packet processors. SIGCOMM Comput. Commun. Rev. 44(3), 87–95 (jul 2014). https://doi.org/10.1145/2656877.2656890

  5. Brunet, P., Pous, D.: Petri automata. Logical Methods in Computer Science 13 (02 2017). https://doi.org/10.23638/LMCS-13(3:33)2017

  6. Brunet, P., Pous, D., Struth, G.: On decidability of concurrent Kleene algebra. In: CONCUR (2017), https://doi.org/10.4230/LIPIcs.CONCUR.2017.28

  7. Caltais, G., Hojjat, H., Mousavi, M.R., Tunc, H.C.: DyNetKAT: An algebra of dynamic networks (2021), https://arxiv.org/abs/2102.10035

  8. Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall, Ltd., London (1971)

    Google Scholar 

  9. Dang, H.T., Bressana, P., Wang, H., Lee, K.S., Zilberman, N., Weatherspoon, H., Canini, M., Pedone, F., Soulé, R.: P4xos: Consensus as a network service. IEEE/ACM Trans. Netw. 28(4), 1726–1738 (2020). https://doi.org/10.1109/TNET.2020.2992106

  10. Foster, N., Kozen, D., Milano, M., Silva, A., Thompson, L.: A coalgebraic decision procedure for netkat. In: POPL. pp. 343–355 (2015). https://doi.org/10.1145/2676726.2677011

  11. Gischer, J.L.: The equational theory of pomsets. Theor. Comput. Sci. 61, 199–224 (1988). https://doi.org/10.1016/0304-3975(88)90124-7

  12. Grabowski, J.: On partial languages. Fundam. Inform. 4(2),  427 (1981)

    Google Scholar 

  13. Hoare, T., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra. In: CONCUR. pp. 399–414 (2009). https://doi.org/10.1007/978-3-642-04081-8_27

  14. Jipsen, P., Moshier, M.A.: Concurrent Kleene algebra with tests and branching automata. J. Log. Algebr. Meth. Program. 85(4), 637–652 (2016). https://doi.org/10.1016/j.jlamp.2015.12.005

  15. Kappé, T., Brunet, P., Rot, J., Silva, A., Wagemaker, J., Zanasi, F.: Kleene algebra with observations. In: CONCUR. pp. 41:1–41:16 (2019). https://doi.org/10.4230/LIPIcs.CONCUR.2019.41

  16. Kappé, T., Brunet, P., Silva, A., Wagemaker, J., Zanasi, F.: Concurrent Kleene algebra with observations: From hypotheses to completeness. In: FOSSACS. pp. 381–400 (2020). https://doi.org/10.1007/978-3-030-45231-5_20

  17. Kappé, T., Brunet, P., Silva, A., Zanasi, F.: Concurrent Kleene algebra: Free model and completeness. In: ESOP. pp. 856–882 (2018). https://doi.org/10.1007/978-3-319-89884-1_30

  18. Kazemian, P., Varghese, G., McKeown, N.: Header space analysis: Static checking for networks. In: NSDI. pp. 113–126 (2012)

    Google Scholar 

  19. Khurshid, A., Zou, X., Zhou, W., Caesar, M., Godfrey, P.B.: VeriFlow: Verifying network-wide invariants in real time. In: NSDI. pp. 15–29 (2013)

    Google Scholar 

  20. Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput. 110(2), 366–390 (1994). https://doi.org/10.1006/inco.1994.1037

  21. Kozen, D.: Kleene algebra with tests and commutativity conditions. In: TACAS. pp. 14–33 (1996). https://doi.org/10.1007/3-540-61042-1_35

  22. Kozen, D., Tseng, W.D.: The Böhm-Jacopini theorem is false, propositionally. In: MPC. pp. 177–192 (2008). https://doi.org/10.1007/978-3-540-70594-9_11

  23. Krob, D.: A complete system of B-rational identities. In: ICALP. pp. 60–73 (1990). https://doi.org/10.1007/BFb0032022

  24. Lamport, L.: How to make a correct multiprocess program execute correctly on a multiprocessor. IEEE Trans. Computers 46(7), 779–782 (1997). https://doi.org/10.1109/12.599898

  25. Laurence, M.R., Struth, G.: Completeness theorems for bi-Kleene algebras and series-parallel rational pomset languages. In: RAMiCS. pp. 65–82 (2014). https://doi.org/10.1007/978-3-319-06251-8_5

  26. Laurence, M.R., Struth, G.: Completeness theorems for pomset languages and concurrent Kleene algebras (2017), https://arxiv.org/abs/1705.05896

  27. Liu, J., Hallahan, W., Schlesinger, C., Sharif, M., Lee, J., Soulé, R., Wang, H., Caşcaval, C., McKeown, N., Foster, N.: p4v: Practical verification for programmable data planes. In: ACM SIGCOMM. pp. 490–503 (2018). https://doi.org/10.1145/3230543.3230582

  28. Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theoretical Computer Science 237(1), 347–380 (2000). https://doi.org/10.1016/S0304-3975(00)00031-1

  29. Long, X.: Primitives for Match-Action in Theory and Practice. Ph.D. thesis, Cornell University (2021)

    Google Scholar 

  30. Mai, H., Khurshid, A., Agarwal, R., Caesar, M., Godfrey, P.B., King, S.T.: Debugging the data plane with Anteater. In: SIGCOMM. pp. 290–301 (2011). https://doi.org/10.1145/2018436.2018470

  31. McClurg, J., Hojjat, H., Foster, N., Cerný, P.: Event-driven network programming. In: PLDI. pp. 369–385 (2016). https://doi.org/10.1145/2908080.2908097

  32. Panda, A., Lahav, O., Argyraki, K., Sagiv, M., Shenker, S.: Verifying reachability in networks with mutable datapaths. In: NSDI. pp. 699–718. USENIX Association, Boston, MA (Mar 2017)

    Google Scholar 

  33. Reynolds, J.C.: Separation Logic: A Logic for Shared Mutable Data Structures. In: LICS (July 2002). https://doi.org/10.1109/LICS.2002.1029817

  34. Salomaa, A.: Two complete axiom systems for the algebra of regular events. J. ACM 13(1), 158–169 (1966). https://doi.org/10.1145/321312.321326

  35. Schlesinger, C., Greenberg, M., Walker, D.: Concurrent netcore: From policies to pipelines. In: ICFP. p. 11–24 (Aug 2014). https://doi.org/10.1145/2628136.2628157

  36. Smolka, S., Foster, N., Hsu, J., Kappé, T., Kozen, D., Silva, A.: Guarded Kleene algebra with tests: Verification of uninterpreted programs in nearly linear time. In: POPL (2020). https://doi.org/10.1145/3371129

  37. Wagemaker, J., Brunet, P., Docherty, S., Kappé, T., Rot, J., Silva, A.: Partially observable concurrent Kleene algebra. In: CONCUR. pp. 20:1–20:22 (2020). https://doi.org/10.4230/LIPIcs.CONCUR.2020.20

  38. Wagemaker, J., Foster, N., Kappé, T., Kozen, D., Rot, J., Silva, A.: Concurrent NetKAT: modeling and analyzing stateful, concurrent networks (2022), https://arxiv.org/abs/2201.10485, full version of this article

  39. Yang, H., Lam, S.S.: Real-time verification of network properties using atomic predicates. In: IEEE ICNP (2013), https://doi.org/10.1109/ICNP.2013.6733614

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Authors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Jana Wagemaker & Jurriaan Rot

  2. Cornell University, Ithaca, New York, USA

    Nate Foster, Dexter Kozen & Alexandra Silva

  3. ILLC, University of Amsterdam, Amsterdam, The Netherlands

    Tobias Kappé

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  1. Jana Wagemaker
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Corresponding author

Correspondence to Jana Wagemaker .

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Editors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Ilya Sergey

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Wagemaker, J., Foster, N., Kappé, T., Kozen, D., Rot, J., Silva, A. (2022). Concurrent NetKAT. In: Sergey, I. (eds) Programming Languages and Systems. ESOP 2022. Lecture Notes in Computer Science, vol 13240. Springer, Cham. https://doi.org/10.1007/978-3-030-99336-8_21

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  • DOI: https://doi.org/10.1007/978-3-030-99336-8_21

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