A Compositional Framework for On-the-Fly LTLf Synthesis

2025-08-06

AI Summary

This work addresses the state-space explosion problem in LTL_f reactive synthesis—particularly the scalability bottleneck when synthesizing from large conjunctive specifications—caused by constructing a full deterministic finite automaton (DFA). We propose a compositional online synthesis framework that dynamically decomposes the LTL_f specification during two-player game solving, incrementally constructs the game structure, and integrates automaton minimization with two pruning mechanisms: *pre-pruning* (reducing initial states via minimization) and *compositional pruning* (guiding search and enabling early termination). Compared to state-of-the-art tools, our framework successfully solves several previously intractable benchmarks. Experimental results demonstrate that the two compositional variants are complementary, collectively achieving significant improvements in synthesis efficiency and scalability.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Reducing LTLf synthesis to a two-player DFA game
• Addressing DFA construction's 2EXPTIME-complete complexity
• Integrating compositional and incremental DFA construction approaches

Innovation

• Compositional on-the-fly LTLf synthesis framework
• Integrates pre-game and incremental DFA construction
• Prunes intermediate results for efficiency