Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
Unification of concept terms in description logics
Journal of Symbolic Computation
Theory of Automata
Conjunctive Grammars and Systems of Language Equations
Programming and Computing Software
Unification in a Description Logic with Transitive Closure of Roles
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Information and Computation
Decision problems for language equations with Boolean operations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The power of commuting with finite sets of words
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On computational universality in language equations
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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
What do we know about language equations?
DLT'07 Proceedings of the 11th international conference on Developments in language theory
On language equations XXK = XXL and XM = N over a unary alphabet
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Least and greatest solutions of equations over sets of integers
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Univariate Equations Over Sets of Natural Numbers
Fundamenta Informaticae
Language equations with symmetric difference
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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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Systems of language equations of the form {ϕ(X1, ..., Xn) = ∅, ψ(X1, ..., Xn)≠∅} are studied, where ϕ,ψ may contain set-theoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1, ..., Xn) ⊂ L0. It is proved that the problem whether such an inequality has a solution is Σ2-complete, the problem whether it has a unique solution is in (Σ3 ∩ Π3) ∖ (Σ2 ∪ Π2), the existence of a regular solution is a Σ1-complete problem, while testing whether there are finitely many solutions is Σ3-complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached.