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* )

Non Deterministic Finite Automata (NFA)-continued

For every NFA a deterministic finite state machine (DFA) can be found that accepts the same language. Therefore it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine. This can be performed using the power set construction which may lead to an exponential rise in the number of necessary states.

NFA is very important for depth knowledge of Automata. You will see that almost everything in Automata Theory is related to NFA.
See you later..

regular language-formal defnition continued

A regular language is a formal language (i.e., a possibly infinite set of finite sequences of symbols from a finite alphabet) that satisfies the following equivalent properties:
 it can be accepted by a deterministic finite state machine
 it can be accepted by a nondeterministic finite state machine
 it can be accepted by an alternating finite automaton
 it can be described by a regular expression
 it can be generated by a regular grammar
 it can be accepted by a read-only Turing machine
In next post, I will discuss formal definition of deterministic finite state machine (DFA). DFA is my Favorite topic.
I am sure you will also like it when we will discuss it in detail after completing all formal definitions.

Automata Step by Step

I am writing this blog for the people who are strongly interested in Automata and Formal languages or who want to start from basics of Automata.

First of all, we will discuss some very basic definitions of Automata. In Automata theory, all things are related to each other so you will notice that you need definitions of other words for understanding a particular definition. We will also see formal definitions of all terms after understanding their basic definitions. After basic and formal definitions, we will solve a lot of good “Problems of Automata” and see a lot of good examples.

Basic Definitions:

If you are a beginner, you should know what is Automata and Automata theory.

1. Automaton:
In Simple Words, An automaton (plural: automata) is a self-operating machine. The word is sometimes used to describe a robot, more specifically an autonomous robot. Used colloquially, it refers to a mindless follower.

An automaton is a mathematical model for a finite state machine (FSM). An FSM is a machine that, given an input of symbols, 'jumps' through a series of states according to a transition function (which can be expressed as a table). In the common "Mealy" variety of FSMs, this transition function tells the automaton which state to go to next given a current state and a current symbol.

2. Automata theory:

Automata theory is the study of abstract machines and problems they are able to solve. Automata theory is closely related to formal language theory as the automata are often classified by the class of formal languages they are able to recognize.

Now at this point, it is important to know about Finite state machines.

3. Finite state machine (FSM):

A finite state automaton (plural: automata) is a model of behavior composed of a finite number of states, transitions between those states, and actions.

4. States:

A state is a unique configuration of information in a program or machine. It is a concept that occasionally extends into some forms of systems programming such as lexers and parsers.

We will see the definition of parser in the next post. Above 4 definitions are enough for today. Please don’t forget to review them otherwise you will not be able to understand the next post. Read carefully. Have a good day.