On Computing the Measures of First-Order Definable Sets of Trees

Marcin Przybyłko

We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.

In Andrea Orlandini and Martin Zimmermann: Proceedings Ninth International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2018), Saarbrücken, Germany, 26-28th September 2018, Electronic Proceedings in Theoretical Computer Science 277, pp. 206–219.
Published: 7th September 2018.

ArXived at: http://dx.doi.org/10.4204/EPTCS.277.15 bibtex PDF
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