Context Free Grammar and Push Down Automata - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit III: Context Free Grammar and Push Down Automata

The leftmost derivation is a derivation in which the leftmost non-terminal is replaced first from the sentential form. The rightmost derivation is a derivation in which rightmost non-terminal is replaced first from the sentential form.

Context Free Grammar and Push Down Automata - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit III: Context Free Grammar and Push Down Automata

Derivation trees is a graphical representation for the derivation of the given production rules for a given CFG.

Context Free Grammar and Push Down Automata - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit III: Context Free Grammar and Push Down Automata

The production rules are used to derive certain strings. We will now formally define the language generated by grammar G = (V, T, P, S). The generation of language using specific rules is called derivation.

Context Free Grammar and Push Down Automata - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit III: Context Free Grammar and Push Down Automata

The context free grammar can be formally defined as a set denoted by G = (V, T, P, S) where V and T are set of non-terminals and terminals respectively.

Context Free Grammar and Push Down Automata - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit III: Context Free Grammar and Push Down Automata

The Chomsky's Hierarchy represents the class of languages that are accepted by different machine.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

No, any language accepted by DFA, NFA, ε-NFA is called a regular language. For any finite automaton we can construct an equivalent regular expression and the language represented by regular expressions is a regular language.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

If certain languages are regular and language L is formed from them by certain operations (such as union or concatenation) then L is also regular.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

Pumping lemma is a basic and important theorem used for checking whether given string is accepted by regular expression or not.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

The two regular expressions P and Q are equivalent (denoted as P = Q) if and only if P represents the same set of strings as Q does.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

The Arden's theorem is useful for checking the equivalence of two regular expression as well as in conversion of DFA to r.e.

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

In any type of regular expression there are only three cases possible.1. Union 2. Concatenation 3. Closure

Regular Expressions and Languages - Theory of Computation

**Subject and UNIT: ** Theory of Computation: Unit II: Regular Expressions and Languages

There is a close relationship between a finite automata and the regular expression