A context diagram, sometimes called a level 0 data-flow diagram, is drawn in order to define and clarify the boundaries of the software system. It identifies the flows of information between the system and external entities. The entire software system is shown as a single process.

A context-free grammar (CFG) is a set of recursive rewriting rules (or productions) used to generate patterns of strings. Nonterminals in CFG are also known as variables. It represents by capital letters of alphabets, for example; A, B, …. X, Y etc.

Definition − A context-free grammar (CFG) consisting of a finite set of grammar rules is a quadruple (N, T, P, S) where. N is a set of non-terminal symbols.

From Wikipedia, the free encyclopedia. In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars.

Context-free grammars (CFGs) are used to describe context-free languages. A context-free grammar is a set of recursive rules used to generate patterns of strings. A context-free grammar can describe all regular languages and more, but they cannot describe all possible languages.

Programming languages, for example, are context-free grammars — a compiler reads your code to make sure it conforms to specific rules and informs you of any errors. (These rules aren’t limited to the production of text, and can be used for music, visual designs, etc.)

Python is not context free. I’ve mentioned that most programming languages are not context-free languages. Let’s take Python as a first example. The standard way to show that a language is not context free is to use Ogden’s Lemma.

Context-free grammars consist of terminals (w1, w2, …, wV), nonterminals (N1, N 2,…, Nn), a start symbol (N1), and rules. Terminal symbols represent context that appear in the strings generated by the grammar. Nonterminal symbols are placeholders for patterns of terminal symbols that can be generated by nonterminals.

In the grammar, there should be rules such that if you add a b symbol you also add a a symbol. Combine two production rules into a single grammar CFG. So you can generate any string that consist of a also a and b in (am bn) pattern. But in above grammar there is no way to generate ^ string.

A formal grammar is “context free” if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side.

Explanation: Deterministic CFGs are always unambiguous , and are an important subclass of unambiguous CFGs; there are non-deterministic unambiguous CFGs, however.

A grammar is context-free if left-hand sides of all productions contain exactly one non-terminal symbol. By definition, if one exists, then the language is context-free. An equivalent construct would be a pushdown automaton. It’s the same as DFA, but with a stack available.

9. Which of the following statement is correct? Explanation: Regular grammar is a subset of context free grammar and thus all regular grammars are context free.

All regular languages are context-free languages, but not all context-free languages are regular. Most arithmetic expressions are generated by context-free grammars, and are therefore, context-free languages.

: of, relating to, or being a grammar or language based on rules that describe a change in a string without reference to elements not in the string also : being such a rule.

L3 = L1. L2 = { anbncmdm | m >= 0 and n >= 0} is also context free. L1 says number of a’s should be equal to number of b’s and L2 says number of c’s should be equal to number of d’s. Their concatenation says first number of a’s should be equal to number of b’s, then number of c’s should be equal to number of d’s.

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Thus, CSG are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.

Chomsky Classification of Grammars

Grammar Type	Grammar Accepted	Automaton
Type 0	Unrestricted grammar	Turing Machine
Type 1	Context-sensitive grammar	Linear-bounded automaton
Type 2	Context-free grammar	Pushdown automaton
Type 3	Regular grammar	Finite state automaton

The definition of context is the words that surround other words and impact their meaning or the setting in which something occurs. An example of context is the words that surround the word “read” that help the reader determine the tense of the word.

Context-sensitive Language: The language that can be defined by context-sensitive grammar is called CSL. Properties of CSL are : Union, intersection and concatenation of two context-sensitive languages is context-sensitive. Complement of a context-sensitive language is context-sensitive.

Context-sensitive grammars are one such class. These grammars generate languages that can be recognized with a restricted class of Turing machines called linear-bounded automata. A grammar G = (V, T, S, P) is context-sensitive if all productions are of the form x → y , where x , y ∈ ( V ∪ T ) + and | x | ≤ | y | .

According to Chomsky hierarchy, grammars are divided of 4 types: Type 0 known as unrestricted grammar. Type 1 known as context sensitive grammar. Type 2 known as context free grammar. Type 3 Regular Grammar.

Universal grammar (UG), in modern linguistics, is the theory of the genetic component of the language faculty, usually credited to Noam Chomsky. The basic postulate of UG is that a certain set of structural rules are innate to humans, independent of sensory experience.

Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene’s theorem (after American mathematician Stephen Cole Kleene).

DFA refers to Deterministic Finite Automaton. A Finite Automata(FA) is said to be deterministic, if corresponding to an input symbol, there is single resultant state i.e. there is only one transition….Difference between DFA and NFA :

SR.NO.	DFA	NFA
1	DFA stands for Deterministic Finite Automata.	NFA stands for Nondeterministic Finite Automata.

Discussion Forum

Que.	Which type string is accepted by the following finite automata?
b.	Null string
c.	No string
d.	None of the mentioned
	Answer:Null string

Limitations of Finite Automata The defining characteristic of FA is that they have only a finite number of states. Hence, a finite automata can only “count” (that is, maintain a counter, where different states correspond to different values of the counter) a finite number of input scenarios.

Kleene’s Theorem states that, in fact, these classes are the same: every regular language may be recognized by some FA, and every FA language may be represented using a regular expression.