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Bhanu Priya has Published 1581 Articles
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Bhanu Priya
1K+ Views
ProblemExplain the pumping lemma for context free language by showing that the language of strings in the form xnynzn is not a context free language.SolutionPumping lemma (Context free grammar)We can prove that a particular language is not context free grammar using pumping lemma.Let’s take the concept of proof by contradictionHere ... Read More
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Bhanu Priya
2K+ Views
A context-free grammar (CFG) consisting of a finite set of grammar rules is a quadruple (V, T, P, S)Where, V is a variable (non terminals).T is a set of terminals.P is a set of rules, P: V→ (V ∪ T)*, i.e., the left-hand sides of the production rule. P does ... Read More
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Bhanu Priya
12K+ Views
When we talk about Turing machines (TM) it could accept the input, reject it or keep computing which is called loop.Now a language is recognizable if and only if a Turing machine accepts the string, when the provided input lies in the language.Also, a language can be recognizable if the ... Read More
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Bhanu Priya
656 Views
ProblemProve each of the following equalities of regular expressions.a. ab*a(a + bb*a)*b = a(b + aa*b)*aa*b.b. b + ab* + aa*b + aa*ab* = a*(b + ab*).SolutionProblem 1Prove that ab*a(a + bb*a)*b = a(b + aa*b)*aa*b.Let’s take LHS , = ab*a(a + bb*a)*b Use property of (a+b)* = a*(ba*)* ... Read More
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Bhanu Priya
577 Views
Consider a Language L, over an alphabet T is known as recursive enumerable if there exists a turing machine (TM) which generates a sequence of numbers T* which have precisely the members of L.Whereas L is said to be recursive if there exists a Turing Machine enlisting all members of ... Read More
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Bhanu Priya
470 Views
If L is a CFL, then L*is a CFL. Here CFL refers to Context Free Language.StepsLet CFG for L has nonterminal S, A, B, C, . . ..Change the nonterminal from S to S1.We create a new CFG for L* as follows −Include all the nonterminal S1, A, B, C, ... Read More
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Bhanu Priya
724 Views
Here CFL refers to Context Free Language. Now, let us understand closure under concatenation.Closure under ConcatenationsIf L1 and L2 are CFLs, then L1L2 is a CFL.Follow the steps given below −L1 CFL implies that L1 has CFG1 that generates it.Assume that the nonterminals in CFG1 are S, A, B, C, ... Read More
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Bhanu Priya
560 Views
If L1 and L2 are CFLs, then their union L1 + L2 is a CFL.Here CFL refers to Context Free Language.L1 CFL implies that L1 has a CFG, let it is CFG1, that generates it.Assume that the nonterminals in CFG1 are S, A, B, C, . . ..Change the nonterminal ... Read More
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Bhanu Priya
2K+ Views
Let us begin by understanding about the subset in the theory of computation (TOC).SubsetIf A and B are sets, then A ⊂ B (A is a subset of B) if w ∈ A which implies that w ∈ B; that is every element of A is also an element of ... Read More
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Bhanu Priya
4K+ Views
A string over an alphabet is a finite sequence of letters from the alphabet.Examplestoc, money, c, and adedwxq are strings over the alphabet ∑ = {a, b, c, . . . , z}.84029 is a string over the alphabet ∑ = {0, 1, 2, . . . , 9}.Empty StringThe ... Read More