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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 subword we mean subsequence. We study the quotient complexity (usually called state complexity) of operations on prefix-, suffix-, factor-, and subword-closed languages. We find tight upper bounds on the complexity...
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 “quotient complexity” to “state complexity”, and we use quotient formulas to calculate upper bounds on...
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