Introduction to Formal Languages

  • Yu. I. Manin
Part of the Graduate Texts in Mathematics book series (GTM, volume 53)


1.1. Let A be any abstract set. We call A an alphabet. Finite sequences of elements of A are called expressions in A. Finite sequences of expressions are called texts.

We shall speak of a language with alphabet A if certain expressions and texts are distinguished (as being “correctly composed,” “meaningful,” etc.). Thus, in the Latin alphabet A we may distinguish English word forms and grammatically correct English sentences. The resulting set of expressions and texts is a working approximation to the intuitive notion of the “English language.”

The language Algol 60 consists of distinguished expressions and texts in the alphabet {Latin letters} ∪ {digits} ∪ {logical signs} ∪ {separators}. Programs are among the most important distinguished texts.

In natural languages the set of distinguished expressions and texts usually has unsteady boundaries. The more formal the language, the more rigid these boundaries are.


Formal Language Atomic Formula Riemann Hypothesis Homological Algebra Unordered Pair 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Max-Planck Institut für MathematikBonnGermany

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