Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals
نویسندگان
چکیده
We solve two open problems concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with n left quotients (that is, with state complexity n) is at most n n−1 + n − 1, and that of a two-sided ideal or a factor-closed language is at most n n−2 + (n − 2)2 n−2 + 1. Since these bounds are known to be reachable, this settles the problems.
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