2024/06/03 by Jean Christoph Jung, Jung, Jean Christoph, Jędrzej Kołodziejski +1 · 2 citations
Engineering · #03B70 #Advanced Control Systems Optimization #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · pdf · doi:10.48550/arxiv.2406.01497
openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study modal separability for fixpoint formulae: given two mutually exclusive fixpoint formulae φ,φ', decide whether there is a modal formula ψ that separates them, that is, that satisfies φ\modelsψ\models¬φ'. This problem has applications for finding simple reasons for inconsistency. Our main contributions are tight complexity bounds for deciding modal separability and optimal ways to compute a separator if it exists. More precisely, it is EXPTIME-complete in general and PSPACE-complete over words. Separators can be computed in doubly exponential time in general and in exponential time over words, and this is optimal as well. The results for general structures transfer to arbitrary, finitely branching, and finite trees. The word case results hold for finite, infinite, and arbitrary words.