Cantor meets Scott: Semantic Foundations for Probabilistic Networks

[ paper ] [ doi ]

POPL 2017

Steffen Smolka, Praveen Kumar, Nate Foster, Dexter Kozen, and Alexandra Silva.


ProbNetKAT is a probabilistic extension of NetKAT with a denotational semantics based on Markov kernels. The language is expressive enough to generate continuous distributions, which raises the question of how to compute effectively in the language. This paper gives an new characterization of ProbNetKAT’s semantics using domain theory, which provides the foundation needed to build a practical implementation. We show how to use the semantics to approximate the behavior of arbitrary ProbNetKAT programs using distributions with finite support. We develop a prototype implementation and show how to use it to solve a variety of problems including characterizing the expected congestion induced by different routing schemes and reasoning probabilistically about reachability in a network.


  author = {Smolka, Steffen and Kumar, Praveen and Foster, Nate and
      Kozen, Dexter and Silva, Alexandra},
  title = {Cantor Meets Scott: Semantic Foundations for Probabilistic Networks},
  year = {2017},
  publisher = {Association for Computing Machinery (ACM)},
  booktitle = {Proceedings of the 44th ACM SIGPLAN Symposium on Principles
      of Programming Languages (POPL)},
  pages = {557–571},
  location = {Paris, France},
  series = {POPL 2017}
[ paper ] [ doi ]