A Weakest Precondition Calculus for Programs and Linear Temporal Specifications

2026-02-11

AI Summary

Existing automated verification tools struggle to effectively support the verification of linear temporal properties for structured, data-intensive programs. This work proposes the first weakest-precondition calculus tailored for linear temporal logic, integrating symbolic execution with automated theorem proving to automatically translate program annotations into decidable verification conditions, thereby enabling fully automatic verification without manual intervention. The calculus unifies program semantics with temporal specifications, establishing an end-to-end automated verification workflow. Its effectiveness is demonstrated across multiple representative case studies, offering a scalable and fully automated solution for verifying temporal properties of structured programs.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools, e.g., Why3, Dafny, and Viper, is that this process does not involve user interaction, expecting all guiding hints like invariants to be given upfront. For sequential correctness, this paradigm is well established, thanks to approaches like weakest precondition generation and symbolic execution. However, to capture temporal properties, the specification language of choice for a broader system perspective, additional concerns and challenges are introduced into the translation and proof. Approaches based on symbolic model-checking can verify such properties on system models, e.g., using automata constructions. However, ascribing temporal properties to structured and data-intensive programs is more difficult. Several program calculi have been proposed in the literature, each of which on their own falls short in some regard of supporting an auto-active workflow. However, all essential ideas, while perhaps some are not widely acknowledged, are in fact found in the literature. In this paper, we demonstrate how to assemble these ideas into a weakest-precondition calculus for linear temporal properties and demonstrate it with examples.

Problem

• weakest precondition
• linear temporal logic
• program verification
• auto-active verification
• temporal specifications

Innovation

• weakest precondition
• linear temporal logic
• auto-active verification
• program calculus
• temporal specifications