Model Checking and Synthesis for Branching Multi-Weighted Logics

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We investigate the open synthesis problem in a quantitative game theoretic setting where the system model is annotated with multiple nonnegative weights representing quantitative resources such as energy, discrete time or cost. We consider system specifications expressed in the branching time logic CTL extended with bounds on resources. As our first contribution, we show that the model checking problem for the full logic is undecidable with already three weights. By restricting the bounds to constant upper or lower-bounds on the individual weights, we demonstrate that the problem becomes decidable and that the model checking problem is PSPACE-complete. As a second contribution, we show that by imposing upper-bounds on the temporal operators and assuming that the cost converges over infinite runs, the synthesis problem is also decidable. Finally, we provide an on-the-fly algorithm for the synthesis problem on an unrestricted model for a reachability fragment of the logic and we prove EXPTIME-completeness of the synthesis problem.
Original languageEnglish
JournalJournal of Logical and Algebraic Methods in Programming
Volume105
Issue number1
Pages (from-to)28-46
Number of pages18
ISSN2352-2208
DOIs
Publication statusPublished - 2019

Fingerprint

Model checking
Model Checking
Branching
Synthesis
Logic
Costs
Upper bound
Resources
Specifications
Reachability
Completeness
Fragment
Discrete-time
Non-negative
Game
Specification
Lower bound
Converge
Operator
Energy

Keywords

  • CTL
  • model checking
  • synthesis
  • multi-weighted logic

Cite this

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title = "Model Checking and Synthesis for Branching Multi-Weighted Logics",
abstract = "We investigate the open synthesis problem in a quantitative game theoretic setting where the system model is annotated with multiple nonnegative weights representing quantitative resources such as energy, discrete time or cost. We consider system specifications expressed in the branching time logic CTL extended with bounds on resources. As our first contribution, we show that the model checking problem for the full logic is undecidable with already three weights. By restricting the bounds to constant upper or lower-bounds on the individual weights, we demonstrate that the problem becomes decidable and that the model checking problem is PSPACE-complete. As a second contribution, we show that by imposing upper-bounds on the temporal operators and assuming that the cost converges over infinite runs, the synthesis problem is also decidable. Finally, we provide an on-the-fly algorithm for the synthesis problem on an unrestricted model for a reachability fragment of the logic and we prove EXPTIME-completeness of the synthesis problem.",
keywords = "CTL, model checking, synthesis, multi-weighted logic",
author = "J.S. Jensen and Isabella Kaufmann and Larsen, {Kim Guldstrand} and S.M. Nielsen and Jiri Srba",
year = "2019",
doi = "10.1016/j.jlamp.2019.02.001",
language = "English",
volume = "105",
pages = "28--46",
journal = "Journal of Logical and Algebraic Methods in Programming",
issn = "2352-2208",
publisher = "Elsevier",
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}

Model Checking and Synthesis for Branching Multi-Weighted Logics. / Jensen, J.S.; Kaufmann, Isabella; Larsen, Kim Guldstrand; Nielsen, S.M.; Srba, Jiri.

In: Journal of Logical and Algebraic Methods in Programming, Vol. 105, No. 1, 2019, p. 28-46.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Model Checking and Synthesis for Branching Multi-Weighted Logics

AU - Jensen, J.S.

AU - Kaufmann, Isabella

AU - Larsen, Kim Guldstrand

AU - Nielsen, S.M.

AU - Srba, Jiri

PY - 2019

Y1 - 2019

N2 - We investigate the open synthesis problem in a quantitative game theoretic setting where the system model is annotated with multiple nonnegative weights representing quantitative resources such as energy, discrete time or cost. We consider system specifications expressed in the branching time logic CTL extended with bounds on resources. As our first contribution, we show that the model checking problem for the full logic is undecidable with already three weights. By restricting the bounds to constant upper or lower-bounds on the individual weights, we demonstrate that the problem becomes decidable and that the model checking problem is PSPACE-complete. As a second contribution, we show that by imposing upper-bounds on the temporal operators and assuming that the cost converges over infinite runs, the synthesis problem is also decidable. Finally, we provide an on-the-fly algorithm for the synthesis problem on an unrestricted model for a reachability fragment of the logic and we prove EXPTIME-completeness of the synthesis problem.

AB - We investigate the open synthesis problem in a quantitative game theoretic setting where the system model is annotated with multiple nonnegative weights representing quantitative resources such as energy, discrete time or cost. We consider system specifications expressed in the branching time logic CTL extended with bounds on resources. As our first contribution, we show that the model checking problem for the full logic is undecidable with already three weights. By restricting the bounds to constant upper or lower-bounds on the individual weights, we demonstrate that the problem becomes decidable and that the model checking problem is PSPACE-complete. As a second contribution, we show that by imposing upper-bounds on the temporal operators and assuming that the cost converges over infinite runs, the synthesis problem is also decidable. Finally, we provide an on-the-fly algorithm for the synthesis problem on an unrestricted model for a reachability fragment of the logic and we prove EXPTIME-completeness of the synthesis problem.

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KW - model checking

KW - synthesis

KW - multi-weighted logic

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