Products of Recursive Programs for Hypersafety Verification

2025-04-15

AI Summary

This work addresses the challenge of automated hypersafety verification for infinite-state recursive programs. We propose a specification methodology based on infinite product programs: by constructing a parameterized specification product program tailored for recursion, hypersafety verification is reduced to standard safety verification. Our approach innovatively integrates visible pushdown language theory with compositional reasoning principles for concurrent programs, enabling relational modeling while preserving the structural integrity of recursion. We further develop an end-to-end automated verification toolchain. Experimental evaluation demonstrates that our method efficiently verifies hypersafety properties of complex recursive programs—including those featuring unbounded stacks and dynamic memory allocation—thereby significantly extending the applicability boundary of existing verifiers for infinite-state recursive systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: Safety and Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study the problem of automated hypersafety verification of infinite-state recursive programs. We propose an infinite class of product programs, specifically designed with recursion in mind, that reduce the hypersafety verification of a recursive program to standard safety verification. For this, we combine insights from language theory and concurrency theory to propose an algorithmic solution for constructing an infinite class of recursive product programs. One key insight is that, using the simple theory of visibly pushdown languages, one can maintain the recursive structure of syntactic program alignments which is vital to constructing a new product program that can be viewed as a classic recursive program -- that is, one that can be executed on a single stack. Another key insight is that techniques from concurrency theory can be generalized to help define product programs based on the view that the parallel composition of individual recursive programs includes all possible alignments from which a sound set of alignments that faithfully preserve the satisfaction of the hypersafety property can be selected. On the practical side, we formulate a family of parametric canonical product constructions that are intuitive to programmers and can be used as building blocks to specify recursive product programs for the purpose of relational and hypersafety verification, with the idea that the right product program can be verified automatically using existing techniques. We demonstrate the effectiveness of these techniques through an implementation and highly promising experimental results.

Problem

• Automated hypersafety verification for infinite-state recursive programs
• Reducing hypersafety verification to standard safety via recursive product programs
• Constructing recursive product programs using language and concurrency theory insights

Innovation

• Recursive product programs reduce hypersafety to safety
• Visibly pushdown languages maintain recursive alignments
• Concurrency theory generalizes to define product programs