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12. Formal Language - MATH 224 Discrete Mathematics Syntax...

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8/27/09 11 MATH 224 – Discrete Mathematics Syntax and formal languages Noam Chomsky developed the idea of grammars for formal languages in the mid 1950s In an attempt to formalize grammars for natural languages he came up with the Chomsky hierarchy of languages Though not all that useful for natural languages this proved to be very useful for computer science and the implementation of compilers A grammar is defined as a four-tupple G = (V, T, P, S), where V, T, P are fine sets and S is an element of T
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8/27/09 22 MATH 224 – Discrete Mathematics The Chomsky hierarch The Chomsky hierarchy consists of four language categories based on four grammars and the languages generated by those grammars Type 0 unrestricted grammars generating recursively enumerable languages Type 1 context sensitive grammars and languages (programming languages) Type 2 context free grammars and languages (syntax for programming languages) Type 3 regular languages and grammars – regular expressions (syntax for
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