State complexity of regular languages
Journal of Automata, Languages and Combinatorics
Composition sequences for functions over a finite domain
Theoretical Computer Science
On deterministic finite automata and syntactic monoid size
Theoretical Computer Science - Developments in language theory
On the Complexity of the Syntax of Tree Languages
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
The syntactic complexity of Eulerian graphs
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Automata with extremal minimality conditions
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Quotient complexity of ideal languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Quotient complexity of closed languages
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Syntactic complexity of Prefix-, Suffix-, and Bifix-free regular languages
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages
Theoretical Computer Science
Syntactic complexities of some classes of star-free languages
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
In search of most complex regular languages
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Quotient complexity of ideal languages
Theoretical Computer Science
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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 prove that nn-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 nn-1 + n - 1, and two-sided ideals and factor-closed languages of syntactic complexity nn-2 + (n - 2)2n-2 + 1.