On the Undecidability of Asynchronous Session Subtyping

  • Julien Lange
  • Nobuko Yoshida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)


Asynchronous session subtyping has been studied extensively in [9, 10, 28, 29, 30, 31] and applied in [23, 32, 33, 35]. An open question was whether this subtyping relation is decidable. This paper settles the question in the negative. To prove this result, we first introduce a new sub-class of two-party communicating finite-state machines (CFSMs), called asynchronous duplex (ADs), which we show to be Turing complete. Secondly, we give a compatibility relation over CFSMs, which is sound and complete wrt. safety for ADs, and is equivalent to the asynchronous subtyping. Then we show that the halting problem reduces to checking whether two CFSMs are in the relation. In addition, we show the compatibility relation to be decidable for three sub-classes of ADs.



We thank A. Scalas, B. Toninho and G. Zavattaro for their comments on earlier versions of this paper, in particular G. Zavattaro for identifying the need for additional blank insertion cycles (in Fig. 3). This work is partially supported by EPSRC EP/K034413/1, EP/K011715/1, EP/L00058X/1, EP/N027833/1 and EP/N028201/1; and by EU FP7 612985 (UPSCALE).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK

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