The Complexity of Synthesis from Probabilistic Components

  • Krishnendu ChatterjeeEmail author
  • Laurent Doyen
  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)


The synthesis problem asks for the automatic construction of a system from its specification. In the traditional setting, the system is “constructed from scratch” rather than composed from reusable components. However, this is rare in practice, and almost every non-trivial software system relies heavily on the use of libraries of reusable components. Recently, Lustig and Vardi introduced dataflow and controlflow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while controlflow synthesis is decidable. The problem of controlflow synthesis from libraries of probabilistic components was considered by Nain, Lustig and Vardi, and was shown to be decidable for qualitative analysis (that asks that the specification be satisfied with probability 1). Our main contribution for controlflow synthesis from probabilistic components is to establish better complexity bounds for the qualitative analysis problem, and to show that the more general quantitative problem is undecidable. For the qualitative analysis, we show that the problem (i) is EXPTIME-complete when the specification is given as a deterministic parity word automaton, improving the previously known 2EXPTIME upper bound; and (ii) belongs to UP \(\cap \) coUP and is parity-games hard, when the specification is given directly as a parity condition on the components, improving the previously known EXPTIME upper bound.


Pure Strategy Index Function Stochastic Game Synthesis Problem Exit State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
    Email author
  • Laurent Doyen
    • 2
  • Moshe Y. Vardi
    • 3
  1. 1.IST AustriaKlosterneuburgAustria
  2. 2.CNRS and LSV, ENS CachanCachanFrance
  3. 3.Rice UniversityHoustonUSA

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