2025/11/12 by Weinhuber, Christoph, De Giacomo, Giuseppe, Li, Yong +2
#Artificial Intelligence (cs.AI) #Computer Science and Game Theory (cs.GT) #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #I.2.4 #I.2.8
paper · doi:10.48550/arxiv.2511.09073
We study stochastic planning problems in Markov Decision Processes (MDPs) with goals specified in Linear Temporal Logic (LTL). The state-of-the-art approach transforms LTL formulas into good-for-MDP (GFM) automata, which feature a restricted form of nondeterminism. These automata are then composed with the MDP, allowing the agent to resolve the nondeterminism during policy synthesis. A major factor affecting the scalability of this approach is the size of the generated automata. In this paper, we propose a novel GFM state-space reduction technique that significantly reduces the number of automata states. Our method employs a sophisticated chain of transformations, leveraging recent advances in good-for-games minimisation developed for adversarial settings. In addition to our theoretical contributions, we present empirical results demonstrating the practical effectiveness of our state-reduction technique. Furthermore, we introduce a direct construction method for formulas of the form GFφ, where φ is a co-safety formula. This construction is provably single-exponential in the worst case, in contrast to the general doubly-exponential complexity. Our experiments confirm the scalability advantages of this specialised construction.