On the Expressibility of Languages by Word Equations with a Bounded Number of Variables
نویسنده
چکیده
A language (resp. a relation) is expressible by a word equation e if it is dened as the set of all values of an unknown (resp. a set of unknowns) over all solutions of the equation e. We show rst tools that a language or a relation is not expressible by using a certain number of auxiliary unknowns. As a consequence an in nite hierarchy based on the number of auxiliary unknowns of expressible language is established. Also a number of auxiliary unknowns to encode a boolean formula of word equations into a single equation or inequality is considered. Finally, two new tools to show the nonexpressibility in general are shown, and as a consequence, a gap theorem for expressible languages is obtained. TUCS Research Group Mathematical Structures of Computer Science
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