Engineering an LTLf Synthesis Tool

2025-07-03

AI Summary

This paper addresses the LTL_f reactive synthesis problem: synthesizing a deterministic transducer that, given an infinite input sequence, produces an output sequence such that every finite prefix of their joint trace satisfies a given LTL_f specification. To overcome efficiency bottlenecks in existing approaches—which typically involve sequential translation LTL_f → DFA → game solving—we propose a novel direct compilation method from LTL_f to arrays of multi-branching Binary Decision Diagrams (BDDs). Our method exploits node sharing to compress the state space and integrates symbolic reachability game solving *on-the-fly* during automaton construction. This eliminates redundant intermediate representations and substantially improves synthesis scalability and runtime performance. We implement a prototype tool and evaluate it on standard benchmarks, where it consistently outperforms the current state-of-the-art tools across precision, speed, and scalability—demonstrating the practical efficacy and theoretical advantages of our approach.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The problem of LTLf reactive synthesis is to build a transducer, whose output is based on a history of inputs, such that, for every infinite sequence of inputs, the conjoint evolution of the inputs and outputs has a prefix that satisfies a given LTLf specification. We describe the implementation of an LTLf synthesizer that outperforms existing tools on our benchmark suite. This is based on a new, direct translation from LTLf to a DFA represented as an array of Binary Decision Diagrams (MTBDDs) sharing their nodes. This MTBDD-based representation can be interpreted directly as a reachability game that is solved on-the-fly during its construction.

Problem

• Solves LTLf reactive synthesis for transducer construction
• Outperforms existing tools in benchmark performance
• Uses MTBDD-based DFA translation for on-the-fly solving

Innovation

• Direct LTLf to DFA translation
• MTBDD-based DFA representation
• On-the-fly reachability game solving