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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| Published in | RAIRO. Informatique théorique et applications Vol. 33; no. 4-5; pp. 341 - 356 |
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| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Paris
EDP Sciences
01.07.1999
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0988-3754 1290-385X |
| DOI | 10.1051/ita:1999122 |
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| Abstract | 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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| AbstractList | An elementary proof of the fixpoint alternation hierarchy in arithmetic is provided. This proof allows to simplify the proof of the modal mu-calculus alternation hierarchy. It is shown that the alternation hierarchy on the binary tree is strict, resolving a problem on Niwinski. 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. |
| Author | Bradfield, J. C. |
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| Cites_doi | 10.1007/3-540-60246-1_160 10.1016/S0304-3975(97)00039-X 10.1016/S0304-3975(97)00217-X 10.1109/SFCS.1991.185392 10.1007/3-540-61440-0_119 10.2307/2275338 10.1051/ita:1999121 10.1007/3-540-16761-7_96 10.1016/0304-3975(82)90125-6 10.1007/978-1-4684-6819-9 10.1093/oso/9780198532132.001.0001 |
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| Keywords | Fixed point alternation hierarchy Fix point Binary tree Duality Modal logic Hennessy Milner logic Fixed point operator Mu calculus |
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| References | R2 R3 Niwinski (R15) 1997; 189 R5 R6 R7 R8 Stirling (R16) 1991; 2 Bradfield (R4) 1997; 195 Lenzi (R12) 1996; 1099 R10 Niwinski (R14) 1986; 226 Kozen (R11) 1983; 27 Walukiewicz (R17) 1996; 1046 Janin (R9) 1995; 969 Lubarsky (R13) 1993; 58 R1 |
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| Snippet | 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... An elementary proof of the fixpoint alternation hierarchy in arithmetic is provided. This proof allows to simplify the proof of the modal mu-calculus... |
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| SubjectTerms | 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 |
| Title | Fixpoint alternation: arithmetic, transition systems, and the binary tree |
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