Syntactic Complexity of Ideal and Closed Languages
The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the worst-cas...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
15.10.2010
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| Subjects | |
| Online Access | Get full text |
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| Summary: | The state complexity of a regular language is the number of states in the
minimal deterministic automaton accepting the language. The syntactic
complexity of a regular language is the cardinality of its syntactic semigroup.
The syntactic complexity of a subclass of regular languages is the worst-case
syntactic complexity taken as a function of the state complexity $n$ of
languages in that class. We study the syntactic complexity of the class of
regular ideal languages and their complements, the closed languages. We prove
that $n^{n-1}$ is a tight upper bound on the complexity of right ideals and
prefix-closed languages, and that there exist left ideals and suffix-closed
languages of syntactic complexity $n^{n-1}+n-1$, and two-sided ideals and
factor-closed languages of syntactic complexity $n^{n-2}+(n-2)2^{n-2}+1$. |
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| DOI: | 10.48550/arxiv.1010.3263 |