The state complexities of some basic operations on regular languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
On the state complexity of reversals of regular languages
Theoretical Computer Science
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
State complexity of combined operations
Theoretical Computer Science
The State Complexity of Two Combined Operations: Star of Catenation and Star of Reversal
Fundamenta Informaticae
Finite automata and their decision problems
IBM Journal of Research and Development
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Syntactic complexity of ideal and closed languages
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Note on reversal of binary regular languages
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
State complexity of union and intersection of star on k regular languages
Theoretical Computer Science
State complexity of combined operations with two basic operations
Theoretical Computer Science
Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages
Theoretical Computer Science
On the State Complexity of Star of Union and Star of Intersection
Fundamenta Informaticae
Syntactic complexities of some classes of star-free languages
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Quotient complexities of atoms of regular languages
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
State complexity of union and intersection of square and reversal on k regular languages
Theoretical Computer Science
State Complexity of Combined Operations with Union, Intersection, Star and Reversal
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
Universal witnesses for state complexity of basic operations combined with reversal
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
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Regular languages that are most complex under common complexity measures are studied. In particular, certain ternary languages Un(a,b,c), n ≥ 3, over the alphabet {a,b,c} are examined. It is proved that the state complexity bounds that hold for arbitrary regular languages are also met by the languages Un(a,b,c) for union, intersection, difference, symmetric difference, product (concatenation) and star. Maximal bounds are also met by Un(a,b,c) for the number of atoms, the quotient complexity of atoms, the size of the syntactic semigroup, reversal, and 22 combined operations, 5 of which require slightly modified versions. The language Un(a,b,c,d) is an extension of Un(a,b,c), obtained by adding an identity input to the minimal DFA of Un(a,b,c). The witness Un(a,b,c,d) and its modified versions work for 14 more combined operations. Thus Un(a,b,c) and Un(a,b,c,d) appear to be universal witnesses for alphabets of size 3 and 4, respectively.