Intersection and union of regular languages and state complexity
Information Processing Letters
The state complexities of some basic operations on regular languages
Theoretical Computer Science
Tight lower bound for the state complexity of shuffle of regular languages
Journal of Automata, Languages and Combinatorics
On the state complexity of reversals of regular languages
Theoretical Computer Science
State complexity of some operations on binary regular languages
Theoretical Computer Science - Descriptional complexity of formal systems
State complexity of combined operations
Theoretical Computer Science
The size of Higman-Haines sets
Theoretical Computer Science
More on the Size of Higman-Haines Sets: Effective Constructions
Fundamenta Informaticae - Machines, Computations and Universality, Part I
The state complexity of L2 and Lk
Information Processing Letters
On inverse operations and their descriptional complexity
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Quotient Complexity of Closed Languages
Theory of Computing Systems
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It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least 2$^{n/2-2}$ states (the known upper bound is 2$^n$), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least 2$^{sqrt{2n+30}-6}$ states. A similar state complexity function for scattered superstrings is determined to be exactly 2$^{n-2}$ + 1 for an alphabet of at least n − 2 letters, and strictly less for any smaller alphabet. For a 3-letter alphabet, the state complexity of scattered superstrings is at least 1/5 4sqrt{n/2}n-3/4.