formal definition of Push down Automata.

In this post we will concentrate on formal definition of Push down Automata. It is also called “Non deterministic Push down Automata” (NPDA). But remember that NPDA is different from “Deterministic Push down Automata” (DPDA)
“Non deterministic Push down Automata” (NPDA)
Formal definition:
A NPDA W can be defined as a 7-tuple:
W = (Q,Σ,Φ,σ,s,Ω,F) where
• Q is a finite set of states
• Σ is a finite set of the input alphabet
• Φ is a finite set of the stack alphabet
• σ (or sometimes δ) is a finite transition relation
(Q x (Σ U {ε} x Ø) ----> P (Q x Ø)
• s is an element of Q the start state
• Ω is the initial stack symbol
• F is subset of Q, consisting of the final states.

Automata Step by Step

Now we will discuss regular languages in this post.

Regular language:
A regular language is the set of strings generated by a regular grammar. Regular grammars are also known as Type-3 grammars in the Chomsky hierarchy.
A regular grammar can be represented by a deterministic or non-deterministic finite automaton. Such automata can serve to either generate or accept sentences in a particular regular language. Note that since the set of regular languages is a subset of context-free languages, any deterministic or non-deterministic finite automaton can be simulated by a pushdown automaton.
Now you will be curious to know about the terms “deterministic finite automaton”, “non-deterministic finite automaton”, “pushdown automaton” and “context-free languages”.
In next Post, we will discuss only “deterministic finite automaton” and “nondeterministic finite state machine”.

Automata Step by Step

Now we also need definition of “regular grammar”

Regular Grammars:

Regular grammars describe exactly all regular languages and are in that sense equivalent to finite state automata and regular expressions. Moreover, the right regular grammars by themselves are also equivalent to the regular languages, as are the left regular grammars.

Every regular grammar is a context-free grammar. Every context-free grammar can be easily rewritten into a form in which only a combination of left regular and right regular rules is used. Therefore, such grammars can express all context-free languages. Regular grammars, which use either left-regular or right-regular rules but not both, can only express a smaller set of languages, called the regular languages. In that sense they are equivalent with finite state automata and regular expressions.

What is a regular language? It is important to understand “regular language” for better understanding of above definitions. We will discuss it in our next post..