A set is an unordered collection of objects or an unordered collection of elements. Sets are always written with curly braces {}, and the elements in the set are written within the curly braces.ExamplesThe set {a, b, c} has elements a, b, and c.The sets {a, b, c} and {b, ... Read More

Let G = (V, T, P, S) be a CFL. If every production in P is of the form as given belowA -> aaWhere A is in V, a is in T, and a is in V*, then G is said to be in Greibach Normal Form (GNF).ExampleS -> aAB ... Read More

A context-free grammar is a quadruple G = (N, T, P, S), Where, N is a finite set of nonterminal symbols, T is a finite set of terminal symbols, N ∩ T = ∅, P is a finite set of productions of the form A → α, Where A ∈ ... Read More

The Chomsky hierarchy is given below −Type 2 − Context Free Grammar (CFG)Type 2 grammars are generated by context free languages.The language that is generated by the grammar is recognized by Push Down Automata.Type 2 must be in Type 1.Left-hand side of production can have only one variable.|alpha| =1There is ... Read More

A Turing machine (TM) can be formally described as seven tuples −(Q, X, ∑, δ, q0, B, F)Where, Q is a finite set of states.X is the tape alphabet.∑ is the input alphabet.δ is a transition function:δ𝛿:QxX->QxXx{left shift, right shift}.q0 is the initial state.B is the blank symbol.F is the ... Read More

Chomsky Hierarchy represents the class of languages that are accepted by the different machines.Chomsky hierarchyHierarchy of grammars according to Chomsky is explained below as per the grammar types −Type 0. Unrestricted grammars   Turing Machine (TM)Type 1. Context-sensitive grammars   Linear Bounded Automaton (LBA)Type 2. Context-free grammars   Pushdown Automaton (PDA)Type 3. Regular ... Read More

Chomsky Hierarchy represents the class of languages that are accepted by the different machines.Chomsky hierarchyHierarchy of grammars according to Chomsky is explained below as per the grammar types −Type 0. Unrestricted grammars   Turing Machine (TM)Type 1. Context-sensitive grammars   Linear Bounded Automaton (LBA)Type 2. Context-free grammars   Pushdown Automaton (PDA)Type 3. Regular ... Read More

Chomsky Hierarchy represents the class of languages that are accepted by the different machines.Chomsky hierarchyHierarchy of grammars according to Chomsky is explained below as per the grammar types −Type 0 − It is an Unrestricted grammarsUnrestricted grammar − an unrestricted grammar is a 4-tuple (T, N, P, S), which consisting ... Read More

The closure properties for context free language (CFG) are as follows −Closed under Union Operationn order to show that context-free language is closed under union operation, consider two starting variables S1 and S2 for the two different languages L1 and L2.Grammar for union operation is as shown below −S ->S1|S2If ... Read More

Pushdown Automata (PDA) are the finite automata (FAs), but with the ability to push and pop symbols to/from a stack.PDA accepts strings if there is a legal path from start state to acceptance state for input. Otherwise, the string is rejected.A PDA can be represented by a 7-tuple(Q, ∑, ℾ, ... Read More