Every commutative quasirational language is regular
We prove that for each positive integer the finite commutative language possesses a test set of size at most Moreover, it is shown that each test set for has at least elements. The result is then generalized to commutative languages containing a word such that (i) and (ii) each symbol occurs at least twice in if it occurs at least twice in some word of : each such possesses a test set of size , where . The considerations rest on the analysis of some basic types of word equations....
We prove that for each positive integer the finite commutative language = ( ...) possesses a test set of size at most Moreover, it is shown that each test set for has at least -1 elements. The result is then generalized to commutative languages containing a word such that (i) alph() = alph}(); and (ii) each symbol ∈ alph}() occurs at least twice in if it occurs at least twice in some word of : each such possesses a test set...
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