CS 310 : Automata Theory
Lecture-1 Summary : By Ashutosh Pankaj
July 29, 2022
Today’s lecture was a brief overview of the content that we are going to cover in this course. It
broadly has two major parts - Grammar and Machines. Before getting into that, let’s first look into
some notations.
Σ : Terminal Symbols (or simply, Alphabets of the language)
N : Non-terminal Symbols (also called variables)
Σ* : String (or Sequence) using elements from Terminal symbols
(Σ ∪ N)* : String using elements from both Terminal and Non-Terminal symbols
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Grammar
Grammar is a finite set of formal rules that generate syntactically correct strings. The set of such
strings is called a Language. We have seen examples of this in Lecture-0.
Grammars can be Restricted and Un-restricted.
Grammar
Restricted
Context-Free
Unrestricted
Context Sensitive
Right-Linear
• Un-restricted : No restriction on α and β
• Restricted Context-free : α is a single Non-terminal variable
• Restricted Context-Sensitive : |α| ≤ |β|, also called non-erasing
• Restricted Context-Free Right-Linear : Rightmost symbol is Non-Terminal along with the
restriction of context-free
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Example: Grammar for generating only and all Palindromes using binary (0 and 1).
1. α → 0 α 0
2. α → 1 α 1
3. α → Homework : Write Grammar for a Language that has equal number of zeroes and ones.
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Machine models
There are three main Machine Models which we will discuss in the coming lectures.
Grammar
Finite State Automata
Push Down Automata
Turing Machine
I won’t be writing about Finite State Automata because it is already covered last semester in CS 228.
Push Down Automata : It ewill have an input, a finite control and a stack. We have a special
marker to represent the botton of the stack.
Example : PDA for the Grammar - n0 (w) = n1 (w)
(try to comprehend this PDA and how stack is used here on your own)
Homework : Construct a Push Down Automata to accept all Palindromes.
Turing Machine will be covered in the next lecture.
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1 do
let me know if there are any mistake(s) in this document
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