Fixpoint alternation: arithmetic, transition systems, and the binary tree

We provide an elementary proof of the fixpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy. We further show that the alternation hierarchy on the binary tree is strict, resolving a problem of Niwiński.

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Bibliographic Details
Published inRAIRO. Informatique théorique et applications Vol. 33; no. 4-5; pp. 341 - 356
Main Author Bradfield, J. C.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Paris EDP Sciences 01.07.1999
Subjects
03D55
03D70
03D80
68Q60
alternation
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Fixpoints
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
modal logic
mu-calculus
Recursion theory
Sciences and techniques of general use
Software
Software engineering
Fixed point alternation hierarchy
Fix point
Binary tree
Duality
Modal logic
Hennessy Milner logic
Fixed point operator
Mu calculus
Online AccessGet full text
ISSN0988-3754
1290-385X
DOI10.1051/ita:1999122

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Summary:We provide an elementary proof of the fixpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy. We further show that the alternation hierarchy on the binary tree is strict, resolving a problem of Niwiński.
Bibliography:ark:/67375/80W-RHS3NH6G-K
PII:S0988375499001228
publisher-ID:ita9929
istex:4B28CF6B09783EE393F362AF96CA8F5BD08539D9
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0988-3754
1290-385X
DOI:10.1051/ita:1999122