Abstract
AbstractIt cannot be decided whether a pushdown automaton accepts using a pushdown height, which does not depend on the input length, i.e., when it accepts using constant height. Furthermore, when a pushdown automaton accepts in constant height, the height can be arbitrarily large with respect to the size of the description of the machine, namely it does not exist any recursive function in the size of the description of the machine bounding the height of the pushdown. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the situation is different. First, acceptance in constant height is decidable. Moreover, in the case of acceptance in constant height, the height is at most exponential with respect to the size of the description of the pushdown automaton. We also prove a matching lower bound. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal.
Funder
Università degli Studi di Milano
Publisher
Springer Science and Business Media LLC
Subject
Computer Networks and Communications,Information Systems,Software
Reference18 articles.
1. Alberts, M.: Space complexity of alternating Turing machines. In: Budach , L. (ed.) Fundamentals of Computation Theory, FCT ’85, Cottbus, GDR, 1985, Lecture Notes in Computer Science, vol. 199, pp. 1–7. Springer (1985). https://doi.org/10.1007/BFb0028785
2. Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple phrase structure grammars. Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 14, 143–172 (1961)
3. Bednárová, Z., Geffert, V.: Two double-exponential gaps for automata with a limited pushdown. Inf. Comput. 253, 381–398 (2017). https://doi.org/10.1016/j.ic.2016.06.005
4. Bednárová, Z., Geffert, V., Mereghetti, C., Palano, B.: Removing nondeterminism in constant height pushdown automata. Inf. Comput. 237, 257–267 (2014). https://doi.org/10.1016/j.ic.2014.03.002
5. Bednárová, Z., Geffert, V., Mereghetti, C., Palano, B.: Boolean language operations on nondeterministic automata with a pushdown of constant height. J. Comput. Syst. Sci. 90, 99–114 (2017). https://doi.org/10.1016/j.jcss.2017.06.007
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