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If L is a linear language and M is a regular language, then the intersection is again a linear language; in other words, the linear languages are closed under intersection with regular sets. Linear languages are closed under homomorphism and inverse homomorphism. [3] As a corollary, linear languages form a full trio. Full trios in general are ...
Deterministic context-free languages can be recognized by a deterministic Turing machine in polynomial time and O(log 2 n) space; as a corollary, DCFL is a subset of the complexity class SC. [3] The set of deterministic context-free languages is closed under the following operations: [4] complement; inverse homomorphism; right quotient with a ...
Context-sensitive languages are closed under complement. This 1988 result is known as the Immerman–Szelepcsényi theorem . [ 19 ] Moreover, they are closed under union , intersection , concatenation , substitution , [ note 4 ] inverse homomorphism , and Kleene plus .
Context-free languages are closed under the various operations, that is, if the languages K and L are context-free, so is the result of the following operations: union K ∪ L; concatenation K ∘ L; Kleene star L * [11] substitution (in particular homomorphism) [12] inverse homomorphism [13] intersection with a regular language [14]
A superset of this language, called the Bach language, [3] is defined as the set of all strings where "a", "b" and "c" (or any other set of three symbols) occurs equally often (aabccb, baabcaccb, etc.) and is also context-sensitive. [4] [5] L can be shown to be a context-sensitive language by constructing a linear bounded automaton which accepts L.
In particular, context-free language cannot be closed under difference, since complement can be expressed by difference: ¯ =. [ 12 ] However, if L is a context-free language and D is a regular language then both their intersection L ∩ D {\displaystyle L\cap D} and their difference L ∖ D {\displaystyle L\setminus D} are context-free languages.
Due to longstanding pushback and controversial health studies surrounding the ingredient, many processed food manufacturers have already shifted away from using Red Dye No. 3, opting instead for ...
A trio is a family of languages closed under homomorphisms that do not introduce the empty word, inverse homomorphisms, and intersections with a regular language. A full trio, also called a cone, is a trio closed under arbitrary homomorphism. A (full) semi-AFL is a (full) trio closed under union.