Parameterized Synthesis with Safety Properties

  • Oliver MarkgrafEmail author
  • Chih-Duo Hong
  • Anthony W. Lin
  • Muhammad Najib
  • Daniel Neider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12470)


Parameterized synthesis offers a solution to the problem of constructing correct and verified controllers for parameterized systems. Such systems occur naturally in practice (e.g., in the form of distributed protocols where the amount of processes is often unknown at design time and the protocol must work regardless of the number of processes). In this paper, we present a novel learning-based approach to the synthesis of reactive controllers for parameterized systems from safety specifications. We use the framework of regular model checking to model the synthesis problem as an infinite-duration two-player game and show how one can utilize Angluin’s well-known L\(^{*}\) algorithm to learn correct-by-design controllers. This approach results in a synthesis procedure that is conceptually simpler than existing synthesis methods with a completeness guarantee, whenever a winning strategy can be expressed by a regular set. We have implemented our algorithm in a tool called L\(^{*}\)-PSynth and have demonstrated its performance on a range of benchmarks, including robotic motion planning and distributed protocols. Despite the simplicity of L\(^{*}\)-PSynth  it competes well against (and in many cases even outperforms) the state-of-the-art tools for synthesizing parameterized systems.


Parameterized systems Reactive synthesis Machine learning Angluin’s algorithm Regular model checking 



This work was partially funded by the ERC Starting Grant AV-SMP (grant agreement no. 759969) and MPI-Fellowship as well as the DFG grant no. 434592664.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Oliver Markgraf
    • 1
    Email author
  • Chih-Duo Hong
    • 3
  • Anthony W. Lin
    • 1
    • 2
  • Muhammad Najib
    • 1
  • Daniel Neider
    • 2
  1. 1.Technical University of KaiserslauternKaiserslauternGermany
  2. 2.Max Planck Institute for Software SystemsKaiserslauternGermany
  3. 3.University of OxfordOxfordEngland

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