Search results
Results from the WOW.Com Content Network
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.
The language is context-free; however, it can be proved that it is not regular. If the productions S → a, S → b, are added, a context-free grammar for the set of all palindromes over the alphabet { a, b} is obtained. [8]
Every regular language is context-free, every context-free language is context-sensitive, every context-sensitive language is recursive and every recursive language is recursively enumerable. These are all proper inclusions, meaning that there exist recursively enumerable languages that are not context-sensitive, context-sensitive languages ...
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language.
For a context-free grammar in Greibach normal form, defining (1,γ) ∈ δ(1,a,A) for each grammar rule A → aγ also yields an equivalent nondeterministic pushdown automaton. [4] The converse, finding a grammar for a given PDA, is not that easy. The trick is to code two states of the PDA into the nonterminals of the grammar. Theorem.
All linear languages are context-free; conversely, an example of a context-free, non-linear language is the Dyck language of well-balanced bracket pairs. Hence, the regular languages are a proper subset of the linear languages, which in turn are a proper subset of the context-free languages.
In formal language theory, a context-free grammar, G, is said to be in Chomsky normal form (first described by Noam Chomsky) [1] if all of its production rules are of the form: [2] [3] A → BC, or A → a, or S → ε,
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 ...