A Compositional Framework for On-the-Fly LTLf Synthesis

Reactive synthesis from Linear Temporal Logic over finite traces (LTLf) can be reduced to a two-player game over a Deterministic Finite Automaton (DFA) of the LTLf specification. The primary challenge here is DFA construction, which is 2EXPTIME-complete in the worst case. Existing techniques either construct the DFA compositionally before solving the game, leveraging automata minimization to mitigate state-space explosion, or build the DFA incrementally during game solving to avoid full DFA construction. However, neither is dominant. In this paper, we introduce a compositional on-the-fly synthesis framework that integrates the strengths of both approaches, focusing on large conjunctions of smaller LTLf formulas common in practice. This framework applies composition during game solving instead of automata (game arena) construction. While composing all intermediate results may be necessary in the worst case, pruning these results simplifies subsequent compositions and enables early detection of unrealizability. Specifically, the framework allows two composition variants: pruning before composition to take full advantage of minimization or pruning during composition to guide on-the-fly synthesis. Compared to state-of-the-art synthesis solvers, our framework is able to solve a notable number of instances that other solvers cannot handle. A detailed analysis shows that both composition variants have unique merits.

On-the-fly Synthesis for LTL over Finite Traces: An Efficient Approach that Counts

We present an on-the-fly synthesis framework for Linear Temporal Logic over finite traces (LTLf) based on top-down deterministic automata construction. Existing approaches rely on constructing a complete Deterministic Finite Automaton (DFA) corresponding to the LTLf specification, a process with doubly exponential complexity relative to the formula size in the worst case. In this case, the synthesis procedure cannot be conducted until the entire DFA is constructed. This inefficiency is the main bottleneck of existing approaches. To address this challenge, we first present a method for converting LTLf into Transition-based DFA (TDFA) by directly leveraging LTLf semantics, incorporating intermediate results as direct components of the final automaton to enable parallelized synthesis and automata construction. We then explore the relationship between LTLf synthesis and TDFA games and subsequently develop an algorithm for performing LTLf synthesis using on-the-fly TDFA game solving. This algorithm traverses the state space in a global forward manner combined with a local backward method, along with the detection of strongly connected components. Moreover, we introduce two optimization techniques -- model-guided synthesis and state entailment -- to enhance the practical efficiency of our approach. Experimental results demonstrate that our on-the-fly approach achieves the best performance on the tested benchmarks and effectively complements existing tools and approaches.