Abstract
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is k-ambiguous for some k ∈ N. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. The degree of ambiguity of a regular language is defined in a natural way. A language is k-ambiguous (respectively, boundedly, finitely, countably ambiguous) if it is accepted by a k-ambiguous (respectively, boundedly, finitely, countably ambiguous) automaton. Over finite words every regular language is accepted by a deterministic automaton. Over finite trees every regular language is accepted by an unambiguous automaton. Over ω-words every regular language is accepted by an unambiguous Büchi automaton and by a deterministic parity automaton. Over infinite trees Carayol et al. showed that there are ambiguous languages. We show that over infinite trees there is a hierarchy of degrees of ambiguity: For every k > 1 there are k-ambiguous languages that are not k − 1 ambiguous; and there are finitely (respectively countably, uncountably) ambiguous languages that are not boundedly (respectively finitely, countably) ambiguous.
Original language | English |
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Pages (from-to) | 18:1-18:28 |
Journal | Logical Methods in Computer Science |
Volume | 17 |
Issue number | 3 |
DOIs | |
State | Published - 2021 |
Keywords
- automata ambiguity
- parity tree automata
- regular tree languages
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- General Computer Science