Regular vs Context Free Grammars

Question

I\'m studying for my computing languages test, and there\'s one idea I\'m having problems wrapping my head around.

I understood that regular grammars<

Answer 1

a regular grammer is never ambiguous because it is either left linear or right linear so we cant make two decision tree for regular grammer so it is always unambiguous.but othert than regular grammar all are may or may not be regular

Answer 2

Regular Expressions

• Basis of lexical analysis
• Represent regular languages

Context Free Grammars

• Basis of parsing
• Represent language constructs

Answer 3

I think what you want to think about are the various pumping lemmata. A regular language can be recognized by a finite automaton. A context-free language requires a stack, and a context sensitive language requires two stacks (which is equivalent to saying it requires a full Turing machine.)

So, if we think about the pumping lemma for regular languages, what it says, essentially, is that any regular language can be broken down into three pieces, x, y, and z, where all instances of the language are in xy*z (where * is Kleene repetition, ie, 0 or more copies of y.) You basically have one "nonterminal" that can be expanded.

Now, what about context-free languages? There's an analogous pumping lemma for context-free languages that breaks the strings in the language into five parts, uvxyz, and where all instances of the language are in uvⁱxyⁱz, for i ≥ 0. Now, you have two "nonterminals" that can be replicated, or pumped, as long as you have the same number.

Answer 4

Regular grammar is either right or left linear, whereas context free grammar is basically any combination of terminals and non-terminals. Hence you can see that regular grammar is a subset of context-free grammar.

So for a palindrome for instance, is of the form,

S->ABA
A->something
B->something

You can clearly see that palindromes cannot be expressed in regular grammar since it needs to be either right or left linear and as such cannot have a non-terminal on both side.

Since regular grammars are non-ambiguous, there is only one production rule for a given non-terminal, whereas there can be more than one in the case of a context-free grammar.

Answer 5

A grammar is context-free if all production rules have the form: A (that is, the left side of a rule can only be a single variable; the right side is unrestricted and can be any sequence of terminals and variables). We can define a grammar as a 4-tuple where V is a finite set (variables), _ is a finite set (terminals), S is the start variable, and R is a finite set of rules, each of which is a mapping V
regular grammar is either right or left linear, whereas context free grammar is basically any combination of terminals and non-terminals. hence we can say that regular grammar is a subset of context-free grammar. After these properties we can say that Context Free Languages set also contains Regular Languages set

Answer 6

Basically regular grammar is a subset of context free grammar,but we can not say Every Context free grammar is a regular grammar. Mainly context free grammar is ambiguous and regular grammar may be ambiguous.