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Unformatted text preview: 8/27/09 11 8/27/09 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 8/27/09 22 8/27/09 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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This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Fall '08 term at Southern Illinois University Edwardsville.
- Fall '08