Nondeterministic tree-walking automata are not closed under complementation
Olga Martynova, Alexander Okhotin
TL;DR
This paper proves that nondeterministic tree-walking automata are not closed under complementation and are more powerful than unambiguous automata, resolving a longstanding open problem in automata theory.
Contribution
It demonstrates the non-closure under complementation of nondeterministic tree-walking automata and establishes their greater expressive power over unambiguous automata.
Findings
Nondeterministic tree-walking automata are not closed under complementation.
They are strictly more powerful than unambiguous tree-walking automata.
The result solves a problem posed by Bojańczyk and Colcombet.
Abstract
It is proved that the family of tree languages recognized by nondeterministic tree-walking automata is not closed under complementation, solving a problem raised by Boja\'nczyk and Colcombet ("Tree-walking automata do not recognize all regular languages", SIAM J. Comp. 38 (2008) 658--701). In addition, it is shown that nondeterministic tree-walking automata are stronger than unambiguous tree-walking automata.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression