On-the-fly LTLf Synthesis under Partial Observability

2026-04-29

AI Summary

This work addresses the inefficiency of traditional approaches to LTLf synthesis under partial observability, which typically require constructing a belief-state DFA laden with redundant states upfront. To overcome this limitation, the paper proposes an on-the-fly LTLf synthesis method grounded in observable progress, incrementally building the belief-state DFA on demand during synthesis while simultaneously performing game solving—thereby achieving, for the first time, a fully integrated on-the-fly coupling of belief construction and game solving. The approach leverages multi-terminal binary decision diagrams (MTBDDs) for compact DFA representation and incorporates immediate universal quantification over unobservable variables to avoid generating unnecessary states. Experimental results demonstrate that the proposed method significantly outperforms existing techniques, confirming the effectiveness of on-the-fly integration in enhancing synthesis efficiency.

Abstract

LTLf synthesis under partial observability requires reasoning about unobservable environment variables, which is typically handled by constructing a belief-state DFA via subset construction that universally quantifies these variables. Existing approaches perform this construction as a separate step prior to game solving, often generating belief states that are unnecessary in practice. We propose an on-the-fly approach to LTLf synthesis under partial observability based on observable progression. Our method incrementally builds the belief-state DFA by progressing the specification with respect to observable variables only, universally quantifying unobservable variables on the fly. We prove the correctness of the construction and show that it naturally enables on-the-fly game solving, leading to a fully on-the-fly synthesis framework. Our implementation leverages DFAs represented using Multi-Terminal Binary Decision Diagrams: a compact representation that has proven highly effective for LTLf synthesis under full observability. Experimental results demonstrate that our approach significantly outperforms existing methods and further highlight the practical benefits of integrating on-the-fly game solving with belief-state construction.

Problem

• LTLf synthesis
• partial observability
• belief-state DFA
• unobservable variables
• on-the-fly synthesis

Innovation

• on-the-fly synthesis
• partial observability
• LTLf
• belief-state DFA
• observable progression