Fast Obligation Translation and Synthesis

2026-05-12

AI Summary

This work addresses the efficient translation and synthesis of the obligation fragment of Linear Temporal Logic (LTL) into deterministic weak ω-automata (DWA). It proposes a direct construction and on-the-fly synthesis method based on multi-terminal binary decision diagrams (MTBDDs). The approach yields, for the first time, a compact MTBDD representation of minimal DWAs for the obligation fragment and enables synthesis computations to be performed directly on this representation. Implemented within the Spot framework, the method demonstrates significant improvements in both automaton translation and synthesis speed, achieving a compelling balance between theoretical elegance and practical efficiency.

Abstract

Syntactic obligations are a fragment of LTL formulas that translate to deterministic weak $ω$-automata (DWA). We show that syntactic obligations can be very efficiently converted to minimal DWA represented using multi-terminal binary decision diagrams (MTBDDs), and that synthesis of such specifications can be solved directly on the MTBDD representation on the fly. Our implementation in Spot shows substantial runtime improvements in translation and synthesis.

Problem

• syntactic obligations
• LTL
• deterministic weak ω-automata
• MTBDDs
• synthesis

Innovation

• syntactic obligations
• deterministic weak ω-automata
• MTBDD
• on-the-fly synthesis
• LTL translation