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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.
Formal equivalence is often more goal than reality, if only because one language may contain a word for a concept which has no direct equivalent in another language. In such cases, a more dynamic translation may be used or a neologism may be created in the target language to represent the concept (sometimes by borrowing a word from the source ...
A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
Strings, also known as "words" or "sentences", over an alphabet are defined as a sequence of the symbols from the alphabet set. [4] For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like ...
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).
Formal languages are used as tools in multiple disciplines. However, formal language theory rarely concerns itself with particular languages (except as examples), but is mainly concerned with the study of various types of formalisms to describe languages. For instance, a language can be given as those strings generated by some formal grammar;
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Translation of an English sentence to first-order logic. Logic translation is the process of representing a text in the formal language of a logical system.If the original text is formulated in ordinary language then the term natural language formalization is often used.