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We study the state complexity of regular operations in the class of ideal languages. A language L ⊆ Σ * is a right (left) ideal if it satisfies L = LΣ * (L = Σ * L). It is a two-sided ideal if L = Σ * LΣ * , and an all-sided ideal if L = Σ * L, the shuffle of Σ * with L. We prefer the term " quotient complexity " instead of " state complexity " , and we use(More)
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u = v. Suffix-, factor-, and subword-free languages are defined similarly, where " subword " means " subsequence ". A language is bifix-free if it is both prefix-and suffix-free. We study the quotient complexity , more commonly known as state complexity, of(More)
A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in an analogous way, where by factor we mean contiguous subsequence, and by subword we mean scattered subsequence. We study the state complexity (which we prefer to call quotient complexity) of operations(More)