Deterministic Push down Automata (DPDA)

“Deterministic Push down Automata” (DPDA):

Formal definition:
A PDA M can be defined as a 7-tuple:
M = (Q,Σ,Γ,q0,Z0,A,δ) where
 Q is a finite set of states
 Σ is a finite set of the input alphabet
 Γ is a finite set of the stack alphabet
 q0 is the start state, an element of Q
 Z0 is the initial stack symbol, an element of Γ
 A is the set of final states, a subset of Q
 δ is a finite transition relation (Q x (Σ U {Λ} x Γ ) ----> the set of finite subsets of (Q x Γ* )

Automata Step by Step

Now we will define “Sequence”

Sequence:
A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and the exact same elements can appear multiple times at different positions in the sequence.

Now we will define “Language”.

Language(or Formal Language):

A Language is a set of strings over a given input alphabet.
As an example of formal language, an alphabet might be {a, b}and a string over that alphabet might be “ababba”

Automata Step by Step

Let’s see the definitions of “String”, “Alphabet”,” Sequence” and “Language”. Remember all above terms are connected. You can’t understand any of them without knowing the definitions of all of them.

String:

In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. These symbols are chosen from a predetermined set.

Example: Empty String (contains no symbols)

Length of Empty String is zero.

Now we will define “Alphabet”.

Alphabet:
An alphabet is a finite set of symbols.
Examples:
Binary Alphabet = {0, 1}
Unary alphabet= {1}
ASCII Alphabet= {…..A, B, C………, a, b, c…………}
Decimal Alphabet= {0, 1, 2…….8, 9}

Automata Step by Step

This post is connected to the previous post. So if you have not read that post, please give few minutes in reading that post.

Parsing:

Parsing (more formally syntax analysis) is the process of analyzing a sequence of tokens to determine its grammatical structure with respect to a given formal grammar. A parser is the component of a compiler that carries out this task.

Parsing transforms input text into a data structure, usually a tree, which is suitable for later processing and which captures the implied hierarchy of the input. Lexical analysis creates tokens from a sequence of input characters and it is these tokens that are processed by a parser to build a data structure such as parse tree or abstract syntax trees.

Can you guess what the next question is? Yes, you are right. Next question is what the Formal Grammar is.