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.
KW - CTL
KW - model checking
KW - synthesis
KW - multi-weighted logic
UR - https://www.sciencedirect.com/science/article/pii/S2352220818300336?via%3Dihub
U2 - 10.1016/j.jlamp.2019.02.001
DO - 10.1016/j.jlamp.2019.02.001
M3 - Journal article
SN - 2352-2208
VL - 105
SP - 28
EP - 46
JO - Journal of Logic and Algebraic Programming
JF - Journal of Logic and Algebraic Programming
IS - 1
ER -