Solvable Tuple Patterns and Their Applications to Program Verification

2025-08-27

AI Summary

Automated verification of programs manipulating recursive data structures—such as linked lists—remains challenging due to the difficulty of inferring expressive, inductive invariants. Method: This paper introduces Solvable Tuple Patterns (STPs), a formal invariant pattern designed over the theory of sequences to compactly express inductive relations among list-like structures. STPs enable efficient inference from few positive examples only—without requiring negative samples—and enjoy good decidability. We integrate STPs into a Constrained Horn Clause (CHC) verification framework, leveraging SMT solvers to discharge induction checks. Contribution/Results: STPs eliminate reliance on manually crafted templates or large training datasets, establishing a new paradigm for recursive program verification. Our CHC solver, built upon this approach, achieved first place in the ADT-LIN track of CHC-COMP 2025, significantly advancing both verification efficiency and automation.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce the notion of solvable tuple patterns (STPs) to express invariants between list-like recursive data structures. A distinguishing feature of STPs is that they can be efficiently inferred from only a small number of positive samples; no negative samples are required. An SMT solver that supports the sequence theory can be used to check that an inferred STP is indeed an inductive invariant. After presenting basic properties of STPs and an STP inference algorithm, we show how to incorporate the STP inference into a CHC (Constrained Horn Clauses) solver supporting list-like data structures, which serves as a uniform backend for automated program verification tools. A CHC solver incorporating the STP inference has won the ADT-LIN category of CHC-COMP 2025 by a big margin.

Problem

• Automated verification of recursive data structure programs remains challenging
• Introducing solvable tuple patterns to express structural invariants efficiently
• Enhancing CHC solvers for automated program verification with STP inference

Innovation

• Solvable tuple patterns for recursive data invariants
• Efficient inference from positive samples only
• SMT solver integration for inductive invariant verification