Finite LTL synthesis as planning
LTL synthesis is the task of generating a strategy that satisfies a Linear Temporal Logic (LTL) specification interpreted over infinite traces. In this paper we examine the problem of LTLf synthesis, a variant of LTL synthesis where the specification of the behaviour of the strategy we generate is interpreted over finite traces – similar to the assumption we make in many planning problems, and important for the synthesis of business processes and other system interactions of finite duration. Existing approaches to LTLf synthesis transform LTLf into deterministic finite-state automata (DFA) and reduce the synthesis problem to a DFA game. Unfortunately, the DFA transformation is worst-case double-exponential in the size of the formula, presenting a computational bottleneck. In contrast, our approach exploits non-deterministic automata, and we reduce the synthesis problem to a non-deterministic planning problem. We leverage our approach not only for strategy generation but also to generate certificates of unrealizability – the first such method for LTLf. We employ a battery of techniques that exploit the structure of the LTLf specification to improve the efficiency of our transformation to automata. We combine these techniques with lazy determinization of automata and on-the-fly state abstraction. We illustrate the effectiveness of our approach on a set of established LTL synthesis benchmarks adapted to finite LTL.