LTLf Synthesis on Probabilistic Systems
This addresses a gap in automated synthesis for probabilistic systems with finite-trace properties, which is incremental as it builds on existing LTL synthesis methods.
The paper tackles the problem of policy synthesis for Markov Decision Processes (MDPs) with behaviors specified in Linear Temporal Logic over finite traces (LTLf), where no tools previously existed, by presenting two algorithms and showing that the native LTLf approach offers better scalability compared to existing LTL tools.
Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.