On the Model Checking of the Graded $$\mu $$ -calculus on Trees

The $$\mu $$ -calculus is an expressive propositional modal logic augmented with least and greatest fixed-points, and encompasses many temporal, program, dynamic and description logics. The model checking problem for the $$\mu $$ -calculus is known to be in NP $$\cap $$ Co-NP. In this paper, we stud...

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Bibliographic Details
Published inAdvances in Artificial Intelligence and Soft Computing pp. 178 - 189
Main Authors Bárcenas, Everardo, Benítez-Guerrero, Edgard, Lavalle, Jesús
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing 2015
SeriesLecture Notes in Computer Science
Subjects
Accessible Node
Description Logic
Input Tree
Linear Temporal Logic
Model Check
Online AccessGet full text
ISBN9783319270593
3319270591
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-27060-9_14

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Summary:The $$\mu $$ -calculus is an expressive propositional modal logic augmented with least and greatest fixed-points, and encompasses many temporal, program, dynamic and description logics. The model checking problem for the $$\mu $$ -calculus is known to be in NP $$\cap $$ Co-NP. In this paper, we study the model checking problem for the $$\mu $$ -calculus extended with graded modalities. These constructors allow to express numerical constraints on the occurrence of accessible nodes (worlds) satisfying a certain formula. It is known that the model checking problem for the graded $$\mu $$ -calculus with finite models is in EXPTIME. In the current work, we introduce a linear-time model checking algorithm for the graded $$\mu $$ -calculus when models are finite unranked trees.
Bibliography:Original Title: On the Model Checking of the Graded \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus on Trees
Original Abstract: The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus is an expressive propositional modal logic augmented with least and greatest fixed-points, and encompasses many temporal, program, dynamic and description logics. The model checking problem for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus is known to be in NP \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cap $$\end{document} Co-NP. In this paper, we study the model checking problem for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus extended with graded modalities. These constructors allow to express numerical constraints on the occurrence of accessible nodes (worlds) satisfying a certain formula. It is known that the model checking problem for the graded \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus with finite models is in EXPTIME. In the current work, we introduce a linear-time model checking algorithm for the graded \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus when models are finite unranked trees.
ISBN:9783319270593
3319270591
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-27060-9_14