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Parameterized complexity of n-dense modal logics

Year: 2026
Type: preprint
Abstract: Exact tight bounds of the complexity of the satisfiability problem for dense modal logics is a difficult question, likely somewhere between $\PSPACE$ and $\EXPSPACE$ depending of the logic under question. For a class of them, called here $n$-dense logics (characterized by axioms $\Box^n p\rightarrow \Box p$), we refine the known results -- membership in $\NEXPTIME$ -- in the light of parameterized complexity, as introduced in \cite{Downey}, and prove that they belong to the parameterized class para-$\PSPACE$: there exists a poly-space algorithm once the modal depth of the input is considered as a parameter. This is done by generalizing the novel analysis tool introduced in \cite{BalGasq25}, and therein called windows, to \emph{recursive windows}.
DOI: 10.48550/arxiv.2604.16488
Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Université Toulouse-I-Capitole, Institut de Recherche en Informatique de Toulouse, Université Toulouse - Jean Jaurès, Institut Polytechnique de Bordeaux, Université de Toulouse
Open Access status: green
OpenAlex ID: W7155047657
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