Languages and Grammars play an important role in theory of computation. In this chapter, we presented an overview on languages and grammars where we covered the basics of languages and more specifically formal languages.
Grammar is a formal system that defines a set of rules for generating valid strings within a language. It serves as a blueprint for constructing syntactically correct sentences or meaningful sequences in a formal language.
We study a sequence of restrictions that limit grammars first to Turing machines, then to two types of systems from which a phrase structure description of a generated language can be drawn, and finally to finite state Markov sources (finite automata).
Grammars and Growth For the following exercises, let ∈ f (n) be the number of words w L with |w| < n. To answer the questions, either construct a grammar witnessing that such an L exists or prove that it cannot exist.
The theory of formal languages finds its applicability extensively in the fields of Computer Science. Noam Chomsky gave a mathematical model of grammar in 1956 which is effective for writing computer languages.
We’ll study different “machine models” (finite automata, pushdown automata). . . . . . with a view toward characterizing what they can compute. Why Study This Topic? To understand the limits of computation. Some things require more resources to compute, and others cannot be computed at all.
A grammar is a set of production rules that generate a language, while a language is a collection of strings that conform to these rules. Understanding their relationship is crucial for designing programming languages, parsers, and automata.
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these notes in a course. There are 61 exercises.
When I took Theory of Computation, the main points of interest were three kinds of automata: finite, pushdown, and Turing, one type of expression: regular expressions which are equivalent to finite automata, and one type of grammar: context-free grammars which are equivalent to pushdown automata.
