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Articles by Bhanu Priya
Page 102 of 106
Prove that the Hamiltonian Path is NP-Complete in TOC
A Hamilton cycle is a round trip path along n edges of graph G which visits every vertex once and returns to its starting vertexExampleGiven below is an example of the Hamilton cycle path −Hamilton cycle path: 1, 2, 8, 7, 6, 5, 4, 3, 1TSP is NP-CompleteThe travelling salesman problem (TSP) is having a salesman and a set of cities. The salesman needs to visit each one of the cities starting from a certain one and returning to the same city i.e. back to starting position. The challenge of this problem is that the travelling salesman wants to minimise ...
Read MoreWhat is NP-completeness in TOC?
The Non-deterministic Polynomial (NP) problems were a little harder to understand. In terms of solving a NP problem, the run-time is not polynomial. It would be something like O(n!) or something larger.However, this class of problems are given a specific solution, and checking the solution would have a polynomial run-time.For example, the Sudoku game.NP-Hard ProblemsA problem is said to be NP-Hard when an algorithm for solving NP Hard can be translated to solve any NP problem. Then we can say, this problem is at least as hard as any NP problem, but it could be much harder or more complex.NP-Complete ...
Read MoreWhy the NP-complete problems are significant?
The Non-deterministic Polynomial (NP) problems were a little harder to understand. In terms of solving a NP problem, the run-time cannot be polynomial. It would be something like O(n!) or something larger.However, this class of problems are given a specific solution, and checking the solution would have a polynomial run-time.For example, the Sudoku game.NP-Hard ProblemsA problem is said to be NP-Hard, when an algorithm for solving the NP Hard can be translated to solve any NP problem. Then we can say, this problem is at least as hard as any NP problem, but it could be much harder or more ...
Read MoreExplain the Decidable and undecidable problems
Before we understand about the decidable and undecidable problems in the theory of computation (TOC), we must learn about the decidable and undecidable language. Hence, let us first see what do you mean by decidable language.Decidable LanguageA language L is called decidable if there is a decider M such that L( M) = L.Given a decider M, you can learn whether or not a string w ∈ L(M).Run M on w.Although it might take a long time, M will accept or reject w.The set R is the set of all decidable languages.L ∈ R if L is decidable.Undecidable LanguageA decision ...
Read MoreExplain how to convert CFG to CNF
CFG stands for context free grammar and CNF stands for Chomsky’s Normal Form in the theory of computation.Context Free Grammar (CFG)A context free grammar (CFG) is a forma grammar which is used to generate all possible patterns of strings in a given formal language.It is defined as four tuples −G=(V, T, P, S)Where, G is a grammar, which consists of a set of production rules. It is used to generate the strings of a language.T is the final set of terminal symbols. It is denoted by lower case letters.V is the final set of non-terminal symbols. It is denoted by ...
Read MoreWhat are the regular expressions to finite automata?
For each of the following languages, draw the finite automata (FA) accepting it.{a, b}*{a}The language states that the automata accept the strings containing any number of a's and b's and finally ending in a.The finite state automaton for the language is as follows −{a, b}*{b, aa}{a, b*}The language states that the automata accept the strings starting and ending with any number of a's and b's and containing any of the substrings b and aa.The finite state automaton for the language is a follows −{bbb, baa}*{a}The language states that the automata accept the strings containing any number of bbb's and baa's ...
Read MoreEliminate epsilon, unit and useless symbols and rewrite into CNF
ProblemEliminate epsilon, unit and the useless symbols for the given grammar and rewrite it into CNF.S->0E0|1FF| εE->GF->S|EG->S| εSolutionIn the given grammar, we will first remove the null production. There are two null productions in the grammar, as given below −S ==> εG ==> εSo, remove null production and rewrite all the other rules containing G by epsilon there, along with old productions. We do not remove S ==> epsilon as it is the start symbol.Remove G ==> epsilon, we get the following −S ==> 0E0 | 1FF | εE ==> G | εF ==> S | EG ==> SNow remove ...
Read MoreConvert the given Context free grammar to CNF
ProblemConvert the given grammar into Chomsky's Normal Form (CNF)S->AAA|BA->aA|BB-> εSolutionFollow the steps given below to convert CFG to CNF −Step 1 − Eliminate epsilon productionsTo eliminate epsilon productions, the variable which is producing epsilon must be replaced on the RHS of all other productions for the epsilon production to be removed.Replacing B with ε in all other productions gives the following production set −S-> AAA | ε | BA->aA | ε | BReplacing A with \epsilon in all other productions gives the following −S ->AAA | AA | A | B | ε [replacing 1, 2, and 3 A's with ε ...
Read MoreExplain the Star Height of Regular Expression and Regular Language
The star height of Regular expression (RE) is nothing but the depth of Kleene stars in the theory of computation (TOC).For example, a+b the star height is 0(a+b)* the star height is 1(a*+b*)* the star height is 2 …….Star height is used to indicate the structural complexity of regular languages and expressions.The regular expressions may have different star height that depends on structural complexity or nesting.The star height of a regular language is a unique number and that is equal to the least star height of any regular expression which represents that language.The star height of regular expressions is a ...
Read MoreHow to convert FA to Left Linear Grammar in TOC?
A grammar with at most one variable at the right side of production is called linear grammar.Following is an example of the linear grammar −S→aSb/εHere, if you observe, we can write the same production by dividing …..S→AbA→aAbA→εLeft Linear GrammarA grammar is left linear grammar where all non-terminals in the right hand sides are at the left end.For example, A→Sa/εSteps for conversionThe steps for the conversion of finite automata (FA) to the left linear grammar are as follows −Step 1 − Take reverse of the finite automataStep 2 − write right linear grammarStep 3 − Then take reverse of the right ...
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