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- W1604594841 abstract "AbstractSystems of language equations of the form {ϕ(X 1, ..., X n ) = ∅, ψ(X 1, ..., X n )≠∅} are studied, where ϕ,ψ may contain set-theoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X 1, ..., X n ) ⊂ L 0. 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.KeywordsDecision ProblemRegular SolutionTuring MachineDescription LogicStrict InequalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W1604594841 created "2016-06-24" @default.
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- W1604594841 date "2005-01-01" @default.
- W1604594841 modified "2023-09-25" @default.
- W1604594841 title "Strict Language Inequalities and Their Decision Problems" @default.
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- W1604594841 doi "https://doi.org/10.1007/11549345_61" @default.
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