منابع مشابه
Quotient Complexity of Regular Languages
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of ...
متن کاملQuotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languages
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 prefixand suffix-free. We study the quotient complexity, more commonly known as state complexity, of operations in the classes of bifix-, factor-, and su...
متن کاملQuotient Complexity of Ideal Languages
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 derivatives to calculate upper bounds on quotient co...
متن کاملQuotient Complexities of Atoms of Regular Languages
An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexi...
متن کاملQuotient Complexity of Star-Free Languages
The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of star-free languages is the smallest class containing the finite la...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2009
ISSN: 2075-2180
DOI: 10.4204/eptcs.3.2