Abstract
We show that it is decidable in time complexity \(2^{2^{2^{O{(n)}}}}\) whether the language accepted by an n-state non-deterministic automaton is of star height one, which is the first ever complexity result for the star height one problem. To achieve this, we introduce distance desert automata as a joint generalization of distance automata and desert automata, and show the decidability of its limitedness problem by solving the underlying Burnside problem.
Supported by the grant KI 822/1–1 of the German Research Community (DFG). On leave from Institute of Algebra, Dresden University of Technology, Germany.
See www.math.tu-dresden.de/~kirsten for a complete version [6].
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Kirsten, D. (2004). Distance Desert Automata and the Star Height One Problem . In: Walukiewicz, I. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2004. Lecture Notes in Computer Science, vol 2987. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24727-2_19
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DOI: https://doi.org/10.1007/978-3-540-24727-2_19
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