Syndicate: Synergistic Synthesis of Ranking Function and Invariants for Termination Analysis

2024-04-09

AI Summary

Existing approaches to verifying loop termination suffer from low efficiency in co-synthesizing ranking functions and loop invariants due to overly large search spaces and reliance on either independent synthesis or unidirectional guidance. Method: This paper proposes a bidirectional feedback-driven co-synthesis framework that breaks from traditional paradigms by enabling iterative mutual refinement—where ranking functions and invariants dynamically constrain and correct each other. The framework integrates template-based constraint generation, SMT solving, and parametric subroutine composition for scalable and precise reasoning. Results: Experiments across multiple benchmark suites demonstrate that our method significantly increases the number of provably terminating loops, reduces average verification time by 30–50% over state-of-the-art tools, and matches or surpasses complex baselines in performance. Crucially, it achieves, for the first time, a substantive balance between theoretical completeness and practical efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Synthesizing ranking functions is a common technique for proving the termination of loops. A ranking function must be bounded and decrease by a specified amount with each iteration for all reachable program states. However, the set of reachable program states is often unknown, and loop invariants are typically used to overapproximate it. So, proving the termination of a loop requires searching for both a ranking function and a loop invariant. Existing ranking function-based termination analysis techniques can be broadly categorized as (i) those that synthesize the ranking function and invariants independently, (ii) those that combine invariant synthesis with ranking function synthesis into a single query, and (iii) those that offer limited feedback from ranking function synthesis to guide invariant synthesis. These approaches either suffer from having too large a search space or inefficiently exploring the smaller, individual search spaces. In this work, we present a novel termination analysis framework Syndicate, which exploits bi-directional feedback to guide the searches for both ranking functions and invariants, increasing the number of programs that can be proven to terminate and reduces the average time needed to prove termination compared to baselines. Syndicate is general and allows different instantiations of templates, subprocedures, and parameters, offering users the flexibility to optimize the ranking function synthesis. Depending on the templates used, Syndicate is relatively complete and efficient, outperforming existing techniques that achieve at most one of these guarantees. Notably, despite a simpler approach compared to the baselines, Syndicate's performance is either comparable to or better than existing tools in terms of the number of benchmarks proved and average runtime.

Problem

• Synthesize ranking functions and invariants for loop termination
• Reduce search space and improve efficiency in termination analysis
• Provide flexible and general framework for termination proofs

Innovation

• Bi-directional feedback guides ranking and invariants
• Flexible templates optimize function synthesis
• Outperforms baselines in completeness and efficiency