Formal Definition of Regular Grammar:

Regular Grammar and Regular Expressions are different.

We have discussed Regular expressions. Let’s see Regular Grammar.

Formal Definition of Regular Grammar:

In Computer Science, a right regular grammar is a formal grammar (N, Σ, P, S) such that all the production rules in P are of one of the following forms:
1. A → a - where A is a non-terminal in N and a is a terminal in Σ
2. A → aB - where A and B are in N and a is in Σ
3. A → ε - where A is in N and ε denotes the empty string, i.e. the string of length 0.

Formal Definition of Non-Deterministic Finite State Machine (NFA)

A nondeterministic finite state automaton (NFA) is a 5-tuple, (S, Σ, T, s0, A), consisting of
 a finite set of states (S)
 a finite set of input symbols (Σ)
 a transition function (T : S × (Σ ∪{ε}) → P(S)).
 an initial (or start) state s0 such that s0 ∈ S
 a set of states A distinguished as accepting (or final) states (A ⊆ S)
where P(S) is the power set of S, ε is the empty string, and Σ is the input symbol alphabet.

Given an NFA M.
Given a string w.
There is any number of computation paths of M with input w.
M accepts w if some computation path ends in a final state.

Formal Definition of Deterministic Finite State Machine (DFA):

Formal Definition of Deterministic Finite State Machine (DFA):

A DFA is a 5-tuple, (S, Σ, T, s, A), consisting of

 a finite set of states (S)
 a finite set called the alphabet (Σ)
 a transition function (T : S × Σ → S)
 a start state (s ∈ S)
 a set of accept states (A ⊆ S)

Given an DFA M.
Given a string w.
There is at most one computation path of M with input w.
M accepts w if that computation path ends in a final state.

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.