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]
Context-free languages—or rather its subset of deterministic context-free languages—are the theoretical basis for the phrase structure of most programming languages, though their syntax also includes context-sensitive name resolution due to declarations and scope.
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.
All regular languages are linear; conversely, an example of a linear, non-regular language is { a n b n}. as explained above.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.
Unambiguous context-free grammars can be nondeterministic. For example, the language of even-length palindromes on the alphabet of 0 and 1 has the unambiguous context-free grammar S → 0S0 | 1S1 | ε. An arbitrary string of this language cannot be parsed without reading all its symbols first, which means that a pushdown automaton has to try ...
To convert a grammar to Chomsky normal form, a sequence of simple transformations is applied in a certain order; this is described in most textbooks on automata theory. [4]: 87–94 [5] [6] [7] The presentation here follows Hopcroft, Ullman (1979), but is adapted to use the transformation names from Lange, Leiß (2009).
The representation of a grammar is a set of syntax diagrams. Each diagram defines a "nonterminal" stage in a process. There is a main diagram which defines the language in the following way: to belong to the language, a word must describe a path in the main diagram. Each diagram has an entry point and an end point.