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Articles by Bhanu Priya
Page 86 of 106
How to identify if a language is regular or not in TOC?
To identify whether a language is regular or not, is based on Pigeon Hole Principle. This is generally called as the Pumping Lemma.Pumping lemma for Regular languagesIt gives a method for pumping (generating) many substrings from a given string.In other words, we say it provides means to break a given long input string into several substrings.It gives the necessary condition(s) to prove a set of strings is not regular.But the pumping lemma is a contradiction test. This means if any language does not satisfy pumping lemma, then we can say that it is not regular. However, if it satisfies the ...
Read MoreExplain Pumping lemma for context free language
Pumping lemma for context free language (CFL) is used to prove that a language is not a Context free languageAssume L is context free languageThen there is a pumping length n such that any string w εL of length>=n can be written as follows −|w|>=nWe can break w into 5 strings, w=uvxyz, such as the ones given below|vxy| >=n|vy| # εFor all k>=0, the string uvkxyyz∈LThe steps to prove that the language is not a context free by using pumping lemma are explained below −Assume that L is context free.The pumping length is n.All strings longer than n can be ...
Read MoreWhat is the Instantaneous description of PDA?
The Instantaneous description is called as an informal notation, and explains how a Push down automata (PDA) computes the given input string and makes a decision that the given string is accepted or rejected.The PDA involves both state and content of the stack.Stack is often one of the important parts of PDA at any time.So, we make a convenient notation for describing the successive configurations of PDA for string processing.The factors of PDA notation by triple (q, w, γ) wereq is the current state.w is the remaining input alphabet.γ is the current contents of the PDA stack.Generally, the leftmost symbol ...
Read MoreConstruct a pair of languages by using CFG
ProblemConsider the following context-free grammars (CFG) and find the pairs of languages which can be generated by Gl and G2 respectively.SolutionConsider the following CFG −G1 : S->aS|B , B->b l bBG2: S->aA | bB , A->aA| B | ε , B->bB | εNow, we can generate the language as follows. First consider G1 as shown belowConsider G1: S->aS|B B->b|bB Using S->B ->b b can be generated Using S->B ->bB ->bb bb can be generated Using S->aS ->aB ...
Read MoreExplain the relationship between grammar and language in TOC
In order to understand the relationship between the grammar and language in the theory of computation (TOC), let us understand what is language generated by grammar in TOC.Language generated by grammarThe grammar is S-> aSb| E.In this grammar, by using S-> E, we can generate E.Therefore, E is part of L(G).Similarly, by using S=>aSb=>ab, ab is generated.Similarly, aabb can also be generated.Therefore, the result is as follows −L(G) = {anbn, n>0}In language L(G) which is discussed above, the condition n =0 is taken to accept the epsilon.Consider the grammar given belowS -> aSa | bSb | a |bNow, let us ...
Read MoreConstruct a Finite Automata for the regular expression ((a+b)(a+b))*.
The language for the given regular expression (RE) is as follows −L={ ε,aa,ab,ba,aaaa,………}ExampleLet the regular expression be ((a+b)(a+b))*(a+b).Construct the Finite automata for the given regular expression.First, generate the language for the given Regular Expression −L={a,d,aaa,bbb,abb,bab,bba,………..}This is the language of odd length stringsThe Finite Automata is as follows −
Read MoreConvert RE 1(0+1)*0 into equivalent DFA.
To convert the regular expression to Finite Automata (FA) we can use the Subset method.Subset method is used to obtain FA from the given regular expression (RE).Step 1 − Construct a Transition diagram for a given RE using Non-deterministic finite automata (NFA) with ε moves.Step 2 − Convert NFA with ε to NFA without ε.Step 3 − Convert the NFA to equivalent DFA.We will divide the given expression into three parts as follows −“1” ,”(0+1)*, and “0”NFA with Epsilon transition is as follows −Now, we will remove the epsilon transition.After removing, the transition diagram is given below −
Read MoreConstruct NFA with Epsilon moves for regular expression a+ba*.
The regular expression R= a+ba* divided into r1 and r2r1= a and r2= ba*Let us draw Non-deterministic finite automata (NFA) for r1 as given below −Now, we will go for r2 = ba *Divide r2 into r3 and r4, where, r3=b and r4=a*The NFA for r3 is as follows −The NFA for r4 is as follows −q5 on epsilon movies goes to q6 and q8, q6 on ‘a’ goes to q7 whereas, q7 on epsilon moves goes to q6 as well as q7.r2= r3.r4Now, concatenate r3 and r4 as shown below −q3 on input ‘b’ goes to q4, q4 on ...
Read MoreWhat is Inductive Hypothesis in TOC?
Induction is a powerful tool in mathematics. It is a way of proving propositions that hold for all natural numbers.Hypothesis − The formal proof can be using deductive proof and inductive proof. The deductive proof consists of sequence of statements given with logical reasoning in order to prove the first or initial statement. The initial statement is called Hypothesis.Suppose there exists a k > 0 such that for any regular expression r where 0 < OP(r) < k, there exists an NFA- s such that L(M) = L(r). Furthermore, suppose that M has exactly one final state.Inductive StepLet r be ...
Read MoreExplain the meanings of some of the regular expressions.
Regular expression is the language which is used to describe the language and is accepted by finite automata. Regular expressions are the most effective way to represent any language. Let Σ be an alphabet which denotes the input set.The regular expression over Σ can be defined as follows −Φ is a regular expression which denotes the empty set.ε is a regular expression and denotes the set { ε} and it is called a null string.For each ‘a’ in Σ ‘a’ is a regular expression and denotes the set {a}.If r and s regular expressions denoting the language.L1 and l2 respectively ...
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