Unrestricted complementation in language equations over a one-letter alphabet
Theoretical Computer Science
Handbook of formal languages, vol. 1
Context-free languages and pushdown automata
Handbook of formal languages, vol. 1
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
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)
Conjunctive Grammars and Systems of Language Equations
Programming and Computing Software
The Boolean Closures of the Deterministic and Nondeterministic Context-Free Languages
Gesellschaft für Informatik e.V., 3. Jahrestagung
Information and Computation
Unresolved systems of language equations: expressive power and decision problems
Theoretical Computer Science
Decision problems for language equations with Boolean operations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Language equations with complementation: Decision problems
Theoretical Computer Science
A simple P-complete problem and its representations by language equations
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
A simple P-complete problem and its language-theoretic representations
Theoretical Computer Science
Language equations with symmetric difference
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Language equations with complementation: Expressive power
Theoretical Computer Science
Language equations with complementation
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Defining contexts in context-free grammars
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Language Equations with Symmetric Difference
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
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A binary language-theoretic operation is proposed, which is dual to the concatenation of languages in the same sense as the universal quantifier in logic is dual to the existential quantifier; the dual of Kleene star is defined accordingly. These operations arise whenever concatenation or star appear in the scope of negation. The basic properties of the new operations are determined in the paper. Their use in regular expressions and in language equations is considered, and it is shown that they often eliminate the need of using negation, at the same time having an important technical advantage of being monotone. A generalization of context-free grammars featuring dual concatenation is introduced and proved to be equivalent to the recently studied Boolean grammars.