相关论文: Generating and Solving Symbolic Parity Games
Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic specifications with data. Solving a PBES is…
Solving parity games, which are equivalent to modal $\mu$-calculus model checking, is a central algorithmic problem in formal methods. Besides the standard computation model with the explicit representation of games, another important…
The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every…
Model checking is a technique to automatically assess whether a model of the behaviour of a system meets its requirements. Evidence explaining why the behaviour does (not) meet its requirements is essential for the user to understand the…
The probabilistic modal {\mu}-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS's). Two equivalent semantics have been studied for this logic, both assigning to each state a…
We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the…
Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or…
We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the…
$\omega$-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…
A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, as they are widely…
It is known that the model checking problem for the modal mu-calculus reduces to the problem of solving a parity game and vice-versa. The latter is realised by the Walukiewicz formulas which are satisfied by a node in a parity game iff…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
Solving Partial Differential Equations (PDEs) is fundamental to numerous scientific and engineering disciplines. A common challenge arises from solving the PDE families, which are characterized by sharing an identical mathematical structure…
Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…
It is well-known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires…
We define memory-efficient certificates for $\mu$-calculus model checking problems based on the well-known correspondence of the $\mu$-calculus model checking with winning certain parity games. Winning strategies can independently checked,…