[Paper Review] Forward LTLf Synthesis: DPLL At Work

Marco Favorito|arXiv (Cornell University)|Feb 27, 2023

Natural Language Processing Techniques4 citations

TL;DR

This paper introduces a novel forward synthesis approach for Linear Temporal Logic over finite traces (LTLf) using a DPLL-inspired search framework that avoids exhaustive enumeration and costly compilations. The method employs syntactic equivalence checks for state formulas and integrates Binary Decision Diagrams (BDDs) as a fallback, achieving state-of-the-art performance—its implementation, Nike, won the 2023 SYNTCOMP LTLf Realizability Track.

ABSTRACT

This paper proposes a new AND-OR graph search framework for synthesis of Linear Temporal Logic on finite traces (\LTLf), that overcomes some limitations of previous approaches. Within such framework, we devise a procedure inspired by the Davis-Putnam-Logemann-Loveland (DPLL) algorithm to generate the next available agent-environment moves in a truly depth-first fashion, possibly avoiding exhaustive enumeration or costly compilations. We also propose a novel equivalence check for search nodes based on syntactic equivalence of state formulas. Since the resulting procedure is not guaranteed to terminate, we identify a stopping condition to abort execution and restart the search with state-equivalence checking based on Binary Decision Diagrams (BDD), which we show to be correct. The experimental results show that in many cases the proposed techniques outperform other state-of-the-art approaches. Our implementation Nike competed in the LTLf Realizability Track in the 2023 edition of SYNTCOMP, and won the competition.

Motivation & Objective

• Address the scalability bottleneck of traditional LTLf synthesis, which relies on doubly exponential deterministic finite automaton (DFA) construction.
• Overcome limitations of prior forward search methods that either enumerate all agent-environment moves or incur high compilation costs via knowledge compilation.
• Develop a search framework that scales with computational power by focusing on exploration rather than pre-processing overhead.
• Introduce a lightweight syntactic equivalence check for state formulas to reduce redundancy without sacrificing correctness.
• Ensure correctness and termination by integrating BDD-based equivalence checking as a fallback when the DPLL-inspired procedure fails to terminate.

Proposed method

• Propose a new AND-OR graph search framework for LTLf synthesis based on two primitive operations: state-equivalence checking and search node expansion.
• Design a DPLL-inspired procedure for generating agent-environment moves in a depth-first, on-the-fly manner, avoiding full enumeration of variable assignments.
• Introduce a novel syntactic equivalence check for state formulas to detect and merge equivalent search nodes efficiently.
• Use Binary Decision Diagrams (BDDs) as a correctness-preserving fallback when the DPLL-based search does not terminate.
• Implement the framework in the tool Nike, which supports multiple search strategies (e.g., true/false/random first) and multithreaded execution.
• Integrate the framework with a game-theoretic view of LTLf synthesis, treating the DFA of the specification as a game arena where the agent must enforce acceptance.

Experimental results

Research questions

• RQ1 Can a forward search approach for LTLf synthesis avoid the doubly exponential DFA construction bottleneck while scaling efficiently with computational resources?
• RQ2 Can a DPLL-inspired procedure for move generation in LTLf synthesis reduce the search space without relying on expensive knowledge compilation?
• RQ3 Does a syntactic equivalence check for state formulas provide sufficient pruning to improve performance without sacrificing correctness?
• RQ4 Can a hybrid strategy combining lightweight syntactic checks with BDD-based equivalence detection ensure correctness and termination in practice?
• RQ5 Does the proposed framework outperform existing state-of-the-art tools in real-world LTLf synthesis benchmarks?

Key findings

• Nike, the implementation of the proposed framework, won the LTLf Realizability Track at the 2023 SYNTCOMP competition.
• On the Nim 02 benchmark, Nike Hash True First solved 10 out of 10 instances with an average time of 114.93ms, outperforming Lydia (22.99ms) and Lisa Explicit (0.33ms), though it was slower than Lisa Symbolic (0.33ms) in some cases.
• For the Single Counter benchmark, Nike Bdd True First solved counter_05 in 3.75s, while Lisa Symbolic took 13.7s, showing competitive performance on complex instances.
• In the Nim 03 benchmark, Nike Hash True First solved counter_01 in 14.59ms, outperforming Lydia (270.72ms) and Lisa Explicit (0.26ms), demonstrating efficiency on medium-sized problems.
• On the more complex Nim 05 benchmark, Nike's BDD-based variants solved counter_01 in 220.65s, while Lisa Symbolic and Lisa Explicit failed to solve it within time limits, indicating robustness on hard instances.
• The DPLL-inspired move generation avoided full enumeration and reduced compilation overhead, enabling faster exploration of the search space compared to SDD-based approaches in many cases.