Domain mu-calculus

Zhang, Guo-Qiang

doi:10.1051/ita:2003023

Domain mu-calculus

Zhang, Guo-Qiang

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 337-364

Résumé

The basic framework of domain $μ$ -calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the $μ$ -calculus without function space or powerdomain constructions, and studies some open problems related to this $μ$ -calculus such as decidability and expressive power. A class of language equations is introduced for encoding $μ$ -formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain $μ$ -calculus. The existence and uniqueness of solutions to this class of language equations constitute an important component of this approach. Our formulation is based on the recent work of Leiss [23], who established a sophisticated framework for solving language equations using Boolean automata (a.k.a. alternating automata [12, 35]) and a generalized notion of language derivatives. Additionally, the early notion of even-linear grammars is adopted here to treat another fragment of the domain $μ$ -calculus.

MR Zbl

DOI : 10.1051/ita:2003023

Classification : 03B70, 68Q45, 68Q55
Keywords: domain theory, mu-calculus, formal languages, boolean automata

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     author = {Zhang, Guo-Qiang},
     title = {Domain mu-calculus},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {337--364},
     year = {2003},
     publisher = {EDP Sciences},
     volume = {37},
     number = {4},
     doi = {10.1051/ita:2003023},
     mrnumber = {2053031},
     zbl = {1038.03038},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita:2003023/}
}

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Zhang, Guo-Qiang. Domain mu-calculus. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 337-364. doi: 10.1051/ita:2003023

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