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Synthesis from hyperproperties.

Bernd Finkbeiner1, Christopher Hahn1, Philip Lukert1

  • 1Reactive Systems Group, Saarland University, Saarbrücken, Germany.

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Summary
This summary is machine-generated.

We explored reactive synthesis for hyperproperties using HyperLTL, finding decidability for specific fragments. This research advances synthesis for complex properties like information flow and secrecy.

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Area of Science:

  • Formal methods
  • Computer science
  • Logic

Background:

  • Hyperproperties generalize trace properties to sets of traces, crucial for policies like noninterference.
  • Standard temporal logics (LTL, CTL) cannot express hyperproperties.
  • HyperLTL offers a framework for these complex properties, encompassing realizability extensions.

Purpose of the Study:

  • Investigate the reactive synthesis problem for hyperproperties specified in HyperLTL.
  • Determine the decidability of synthesis for various HyperLTL fragments.
  • Develop procedures for synthesizing systems and generating counterexamples for universal HyperLTL.

Main Methods:

  • Formal analysis of the synthesis problem for HyperLTL.
  • Identification and characterization of decidable fragments of HyperLTL.
  • Development of a semi-decision procedure for universal HyperLTL.

Main Results:

  • The synthesis problem is undecidable for full HyperLTL.
  • Decidability is retained for the , , and fragments of HyperLTL.
  • A semi-decision procedure for universal HyperLTL constructs implementations and counterexamples.

Conclusions:

  • Synthesis for hyperproperties is feasible within specific HyperLTL fragments.
  • The study provides a foundation for synthesizing systems with complex security and information-flow guarantees.
  • Experimental results demonstrate the practical applicability of the developed methods.