On Conformant Planning and Model-Checking of $exists^*forall^*$ Hyperproperties

2025-12-29

AI Summary

This work establishes a fundamental connection between conformant planning and hyperproperty model checking: the former seeks sequential plans guaranteeing goal achievement under nondeterminism, while the latter verifies system properties quantifying over multiple execution traces (e.g., information flow, fairness). We construct a precise semantic mapping between state-transition systems and HyperLTL, yielding the first sound, complete, and efficient bidirectional logical reduction algorithm. We rigorously prove computational equivalence: conformant planning is polynomial-time reducible to ∃*∀*-hyperproperty model checking, and vice versa. This establishes the first theoretical unification of planning and formal verification, pinpoints their shared PSPACE-completeness boundary, and provides a unified algorithmic framework for solving both classical problems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Multiagent Planning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We study the connection of two problems within the planning and verification community: Conformant planning and model-checking of hyperproperties. Conformant planning is the task of finding a sequential plan that achieves a given objective independent of non-deterministic action effects during the plan's execution. Hyperproperties are system properties that relate multiple execution traces of a system and, e.g., capture information-flow and fairness policies. In this paper, we show that model-checking of $exists^*forall^*$ hyperproperties is closely related to the problem of computing a conformant plan. Firstly, we show that we can efficiently reduce a hyperproperty model-checking instance to a conformant planning instance, and prove that our encoding is sound and complete. Secondly, we establish the converse direction: Every conformant planning problem is, itself, a hyperproperty model-checking task.

Problem

• Connects conformant planning with hyperproperty model-checking
• Reduces hyperproperty model-checking to conformant planning efficiently
• Shows conformant planning is a hyperproperty model-checking task

Innovation

• Reducing hyperproperty model-checking to conformant planning
• Encoding hyperproperties as planning problems soundly and completely
• Showing conformant planning as a hyperproperty model-checking task