MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata

ion in general is based on a partition P = {B1,B2, . . . ,Bn} of the state space. The original or concrete states are lumped together into abstract states, defined by the blocks Bi ∈P . For PA, both gameand menu-based abstraction use these blocks Bi as player 1 states (i. e. V1 = P). In game-based abstraction [18] for PA player 2 states in V2 represent sets of concrete states that have the same branching structure. In menu-based abstraction [26] the states of player 2 represent the set of enabled actions within a block Bi. Abstraction refinement for both approaches is based on values and schedulers which are computed for certain properties. MA are an extension of PA, they additionally contain Markov transitions. In our work we aspire to transfer the results of [18] and [26] from PA to MA. Menu-based abstraction [26] is usually more compact than game-based abstraction [18], since in general there are more different states within a block than different enabled actions. However, the game-based abstraction is more suitable for Markovian states as Markov transitions are not labelled with actions. Therefore we decided to combine both techniques, which is described in the following section. 52 MeGARA: Menu-based Game Abstraction and Abstraction Refinement for Markov Automata