1 research outputs found
Energy mu-Calculus: Symbolic Fixed-Point Algorithms for omega-Regular Energy Games
-regular energy games, which are weighted two-player turn-based games
with the quantitative objective to keep the energy levels non-negative, have
been used in the context of verification and synthesis. The logic of modal
-calculus, when applied over game graphs with -regular winning
conditions, allows defining symbolic algorithms in the form of fixed-point
formulas for computing the sets of winning states.
In this paper, we introduce energy -calculus, a multi-valued extension
of the -calculus that serves as a symbolic framework for solving
-regular energy games. Energy -calculus enables the seamless reuse
of existing, well-known symbolic -calculus algorithms for -regular
games, to solve their corresponding energy augmented variants. We define the
syntax and semantics of energy -calculus over symbolic representations of
the game graphs, and show how to use it to solve the decision and the minimum
credit problems for -regular energy games, for both bounded and
unbounded energy level accumulations.Comment: Submitted to LMC