Unrestricted complementation in language equations over a one-letter alphabet
Theoretical Computer Science
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
On the number of nonterminals in linear conjunctive grammars
Theoretical Computer Science
Language equations with complementation: Decision problems
Theoretical Computer Science
The Power of Commuting with Finite Sets of Words
Theory of Computing Systems
On the Computational Completeness of Equations over Sets of Natural Numbers
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
SIAM Journal on Computing
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
Theory of Computing Systems - Special Issue: Symposium on Computer Science, Guest Editors: Sergei Artemov, Volker Diekert and Dima Grigoriev
Fast on-line integer multiplication
Journal of Computer and System Sciences
Decision problems for language equations
Journal of Computer and System Sciences
What do we know about language equations?
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Language equations with complementation: Expressive power
Theoretical Computer Science
On the number of nonterminal symbols in unambiguous conjunctive grammars
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Parsing Boolean grammars over a one-letter alphabet using online convolution
Theoretical Computer Science
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Equations of the form X=@f(X) are considered, where the unknown X is a set of natural numbers. The expression @f(X) may contain the operations of set addition, defined as S+T={m+n|m@?S,n@?T}, union, intersection, as well as ultimately periodic constants. An equation with a non-periodic solution of exponential growth rate is constructed. At the same time it is demonstrated that no sets with super-exponential growth rate can be represented. It is also shown that restricted classes of these equations cannot represent sets with super-linearly growing complements nor sets that are additive bases of order 2. The results have direct implications on the power of unary conjunctive grammars with one nonterminal symbol.