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Computer Science Articles
Page 47 of 53
Design a TM that increments a binary number by 1
Turing’s machine is more powerful than both finite automata and pushdown automata. These machines are as powerful as any computer we have ever built.Formal Definition of Turing MachineA Turing machine can be formally described as seven tuples(Q, X, Σ, δ, q0, B, F)Where, Q is a finite set of states.X is the tape alphabetΣ is the input alphabetδ is a transition function: δ:QxX→QxXx{left shift, right shift}q0 is the initial stateB is the blank symbolF is the final state.A Turing Machine (TM) is a mathematical model which consists of an infinite length tape divided into cells on which input is given. ...
Read MoreDesign Turing Machine to reverse string consisting of a's and b's
Our aim is to design a Turing machine (TM) to reverse a string consisting of a’s and b’s over an alphabet {a, b}.ExampleInput − aabbabOutput − babbaaAlgorithmStep 1: Move to the last symbol, replace x for a or x for b and move right to convert the corresponding B to „a‟ or „b‟ accordingly. Step 2: Move left until the symbol left to x is reached. Step 3: Perform step 1 and step 2 until „B‟ is reached while traversing left. Step 4: Replace every x to B to make the cells empty since the reverse ...
Read MoreConstruct a Turing Machine for L = {a^n b^n | n>=1}
The Turing machine (TM) is more powerful than both finite automata (FA) and pushdown automata (PDA). They are as powerful as any computer we have ever built.Formal Definition of Turing MachineA Turing machine can be formally described as seven tuples(Q, X, Σ, δ, q0, B, F)Where, Q is a finite set of statesX is the tape alphabetΣ is the input alphabetδ is a transition function: δ:QxX→QxXx{left shift, right shift}q0 is the initial stateB is the blank symbolF is the final state.A Turing Machine (TM) is a mathematical model which consists of an infinite length tape divided into cells on which ...
Read MoreConstruct ∈-NFA of Regular Language L = (0+1)*(00+ 11)
The ε transitions in Non-deterministic finite automata (NFA) are used to move from one state to another without having any symbol from input set Σε-NFA is defined in five tuple{Q, q0, Σ, δ, F}Where, δ − Q × (Σ∪ε)→2QQ − Finite set of statesΣ − Finite set of the input symbolq0 − Initial stateF − Final stateδ − Transition functionNFA without ε transitionNFA is defined in 5 tuple representation{Q, q0, Σ, δ, F}Where, δ − Q X Σ→ 2QQ − Finite set of statesΣ, − Finite set of the input symbolq0 − Initial stateF − Final stateδ − Transition functionNFA ...
Read MoreC Program to construct a DFA which accepts L = {aN | N ≥ 1}
Let us take a string S of size N, we have to design a Deterministic Finite Automata (DFA) for accepting the language L = {aN | N ≥ 1}.The string accepting the language L is {a, aa, aaa, aaaaaaa…, }.Now the user has to enter a string, if that string is present in the given language, then print “entered string is Accepted”. Otherwise, print “entered string is not Accepted”.DFA transition diagram for the given language is −ExampleFollowing is the C program to construct DFA which accepts the language L = {aN | N ≥ 1} −#include int main() { char S[30]; ...
Read MoreC Program to construct DFA for Regular Expression (a+aa*b)*
Design a Deterministic Finite Automata (DFA) for accepting the language L = (a+aa*b)* If the given string is accepted by DFA, then print “string is accepted”. Otherwise, print “string is rejected”.Example 1Input: Enter Input String aaaba Output: String Accepted.Explanation − The given string is of the form (a+aa*b)* as the first character is a and it is followed by a or ab.Example 2Input: Enter Input String baabaab Output: String not Accepted.The DFA for the given regular expression (a+aa*b) is −Explanation −If the first character is always a, then traverse the remaining string and check ...
Read MoreHow to convert right linear grammar to left linear grammar?
For every finite automata (FA) there exists a regular grammar and for every regular grammar there is a left linear and right linear regular grammar.Example 1Consider a regular grammar − a(a+b)* A → aB B → aB|bB|eFor the given regular expression, the above grammar is right linear grammar.Now, convert the above right linear grammar to left linear grammar.The rule to follow for conversion is, Finite Automata → Right linearThe reverse of right linear →left linear grammar.So, A → BaB → Ba|Bb|eFinally for every right linear there is aExampleConsider a language {bnabma| n>=2, m>=2}The right linear grammar for the given language ...
Read MoreExplain about left linear regular grammar in TOC
Regular grammar describes a regular language. It consists of four components, which are as follows −G = (N, E, P, S)Where, N − finite set of non-terminal symbols, E − a finite set of terminal symbols, P − a set of production rules, each of one is in the formsS → aBS → aS → ∈, S ∈ N is the start symbol.The above grammar can be of two forms −Right Linear Regular GrammarLeft Linear Regular GrammarLinear GrammarWhen the right side of the Grammar part has only one terminal then it's linear else nonv linear.Left linear grammarIn a left-regular grammar ...
Read MoreExplain about right linear regular grammars in TOC
Regular grammar describes a regular language. It consists of four components, which are as follows −G = (N, E, P, S)Where, N − finite set of non-terminal symbols, E − a finite set of terminal symbols, P − a set of production rules, each of one is in the formsS → aBS → aS → ∈, S ∈ N is the start symbol.The above grammar can be of two forms −Right Linear Regular GrammarLeft Linear Regular GrammarLinear GrammarWhen the right side of the Grammar part has only one terminal then it's linear else non linear.Let’s discuss about right linear grammar ...
Read MoreProve that the vertex cover is NP complete in TOC
It is the subset(minimum size) of vertices of a graph G such that every edge in G incident to at least one vertex in G.Vertex Cover (VC) ProblemTo prove VC is NP-complete we have to prove the following −VC is Non-deterministic Polynomial (NP).A NPC problem can be reduced into VC.To prove VC is NP, find a verifier which is a subset of vertices which is VC and that can be verified in polynomial time. For a graph of n vertices it can be proved in O(n2). Thus, VC is NP.Now consider the “clique” problem which is NPC and reduce it ...
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