Abstract
Over infinite structures, there is a strict hierarchy of languages that is obtained by alternating uses of the least-fixed point operator and negation. For finite structures, we show that the hierarchy collapses to its first-level.
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Notes
One way to see this is that the condition is equivalent to there not being a resolution proof of ¬ϕ.
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© 1999 Springer Science+Business Media New York
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Immerman, N. (1999). Complementation and Transitive Closure. In: Descriptive Complexity. Graduate Texts in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0539-5_10
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DOI: https://doi.org/10.1007/978-1-4612-0539-5_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6809-3
Online ISBN: 978-1-4612-0539-5
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