Operations on Subregular Languages and Nondeterministic State Complexity
We study the nondeterministic state complexity of basic regular operations on subregular language families. In particular, we focus on the classes of combinational, finitely generated left ideal, group, star, comet, two-sided comet, ordered, and power-separating languages, and consider the operation...
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| Published in | Descriptional Complexity of Formal Systems Vol. 13439; pp. 112 - 126 |
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| Main Authors | , , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2022
Springer International Publishing |
| Series | Lecture Notes in Computer Science |
| Online Access | Get full text |
| ISBN | 9783031132568 3031132564 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-031-13257-5_9 |
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| Summary: | We study the nondeterministic state complexity of basic regular operations on subregular language families. In particular, we focus on the classes of combinational, finitely generated left ideal, group, star, comet, two-sided comet, ordered, and power-separating languages, and consider the operations of intersection, union, concatenation, power, Kleene star, reversal, and complementation. We get the exact complexity in all cases, except for complementation of group languages where we only have an exponential lower bound. The complexity of all operations on combinational languages is given by a constant function, except for the k-th power where it is k+1 $$k+1$$ . For all considered operations, the known upper bounds for left ideals are met by finitely generated left ideal languages. The nondeterministic state complexity of the k-th power, star, and reversal on star languages is n. In all the remaining cases, the nondeterministic state complexity of all considered operations is the same as in the regular case, although sometimes we need to use a larger alphabet to describe the corresponding witnesses. |
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| Bibliography: | Original Abstract: We study the nondeterministic state complexity of basic regular operations on subregular language families. In particular, we focus on the classes of combinational, finitely generated left ideal, group, star, comet, two-sided comet, ordered, and power-separating languages, and consider the operations of intersection, union, concatenation, power, Kleene star, reversal, and complementation. We get the exact complexity in all cases, except for complementation of group languages where we only have an exponential lower bound. The complexity of all operations on combinational languages is given by a constant function, except for the k-th power where it is k+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k+1$$\end{document}. For all considered operations, the known upper bounds for left ideals are met by finitely generated left ideal languages. The nondeterministic state complexity of the k-th power, star, and reversal on star languages is n. In all the remaining cases, the nondeterministic state complexity of all considered operations is the same as in the regular case, although sometimes we need to use a larger alphabet to describe the corresponding witnesses. Research supported by VEGA grant 2/0132/19 and grant APVV-15-0091. |
| ISBN: | 9783031132568 3031132564 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-031-13257-5_9 |