Work

The complexity of HyperQPTL

Year: 2026

Type: article

Abstract: HyperQPTL and HyperQPTL + are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking. Here, we settle the complexity of satisfiability for HyperQPTL as well as satisfiability, finite-state satisfiability, and model-checking for HyperQPTL + : the former is Σ 1 2 -complete, the latter are all equivalent to truth in third-order arithmetic, i.e., all four are very undecidable.

Source: Information Processing Letters

DOI: 10.1016/j.ipl.2026.106626

Authors: Gaëtan Regaud, Martin Zimmermann

Institutions: École Normale Supérieure de Rennes, Aalborg University

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590

Funders: European Commission, Danmarks Frie Forskningsfond, Erasmus+