The μ-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

@inproceedings{Gutierrez2012TheA,
  title={The μ-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity},
  author={J. Gutierrez and F. Klaedtke and M. Lange},
  booktitle={GandALF},
  year={2012}
}
  • J. Gutierrez, F. Klaedtke, M. Lange
  • Published in GandALF 2012
  • Mathematics, Computer Science
  • It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited… CONTINUE READING
    On guarded transformation in the modal μ-calculus
    • 15
    Guarded Transformation for the Modal mu-Calculus
    • 8
    • PDF
    The μ-calculus alternation hierarchy collapses over structures with restricted connectivity
    • 3
    Alternation Is Strict For Higher-Order Modal Fixpoint Logic
    • F. Bruse
    • Computer Science, Mathematics
    • 2016
    • 3
    • PDF
    The Arity Hierarchy in the Polyadic μ-Calculus
    • M. Lange
    • Computer Science, Mathematics
    • 2015
    • 2
    • PDF
    Dependent Inductive and Coinductive Types are Fibrational Dialgebras
    • 1
    • PDF
    On the Static Analysis for SPARQL Queries Using Modal Logic
    • 1
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 57 REFERENCES
    Tree automata, mu-calculus and determinacy
    • 775
    • PDF
    Adding nesting structure to words
    • 355
    • PDF
    Results on the Propositional µ-Calculus
    • 695
    On the Expressive Completeness of the Propositional mu-Calculus with Respect to Monadic Second Order Logic
    • 299
    Alternating tree automata, parity games, and modal {$\mu$}-calculus
    • 142
    • PDF
    Rudiments of μ-calculus
    • 201
    Weak alternating automata are not that weak
    • 159
    • Highly Influential
    • PDF
    Fixed points vs. infinite generation
    • 97
    • PDF
    Weak alternating automata and tree automata emptiness
    • 123
    • Highly Influential
    • PDF
    Completeness of Kozen's Axiomatisation of the Propositional µ-Calculus
    • 199
    • PDF