Formally Verified Certification of Unsolvability of Temporal Planning Problems

2025-10-11

AI Summary

The lack of trustworthy certification for unsolvability in temporal planning poses a fundamental challenge to the reliability of planning systems. Method: We propose the first end-to-end formally verified framework for unsolvability certification. Our approach encodes temporal planning problems as networks of timed automata, leverages model checking to generate unsolvability certificates, and implements full-chain formal verification in Isabelle/HOL—including correctness of the encoding, functional correctness of the certificate checker, and soundness of the overall certification logic. Contribution/Results: This work pioneers the deep integration of interactive theorem proving into temporal planning unsolvability certification, ensuring verifiability and trustworthiness across all stages—from problem modeling to certificate validation. Experimental evaluation demonstrates that the framework efficiently generates and verifies unsolvability proofs for complex planning instances, significantly enhancing both the reliability and acceptability of certification outcomes.

Technology Category

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

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

Abstract

We present an approach to unsolvability certification of temporal planning. Our approach is based on encoding the planning problem into a network of timed automata, and then using an efficient model checker on the network followed by a certificate checker to certify the output of the model checker. Our approach prioritises trustworthiness of the certification: we formally verify our implementation of the encoding to timed automata using the theorem prover Isabelle/HOL and we use an existing certificate checker (also formally verified in Isabelle/HOL) to certify the model checking result.

Problem

• Certifying unsolvability of temporal planning problems
• Encoding planning problems into timed automata networks
• Formally verifying certification trustworthiness using Isabelle/HOL

Innovation

• Encodes planning problems into timed automata networks
• Uses efficient model checker with certificate verification
• Formally verifies implementation using Isabelle/HOL theorem prover