A Deterministic Finite automaton (DFA) is a 5-tuplesM=(Q, Σ, δ, q0, F)Where, Q : Finite set called states.Σ : Finite set called alphabets.δ : Q × Σ → Q is the transition function.q0 ϵ Q is the start or initial state.F : Final or accept state.ProblemConstruct DFA of a string with at least two 0’s and at least two 1’s.SolutionThe language generated based on the given condition over the alphabet Σ ={0, 1) is −L={0011, 001011, 0001010, 0011001, 010101, ……}The given language accepts at least two zero’s means it can accept two or more than two zero’s and at least ... Read More

A Deterministic Finite automaton (DFA) is a five tuplesM=(Q, Σ, δ, q0, F)Where, Q : Finite set called states.Σ : Finite set called alphabets.δ : Q × Σ → Q is the transition function.q0 ϵ Q is the start or initial state.F : Final or accept state.Accept Strings which are not ending with "THE"Observe whether the given string is ending with “the” or not.The different notations of “the” which are avoided in the end of the string are as follows −     "tHE", "thE", "THE", "ThE", "THe", "The", "tHe" and "the"These all strings are not accepted from alphabet (A-Z)Let the ... Read More

The finite automata (FA) is represented as follows in the theory of computation (TOC) −Components of FAThe different components of finite automata are as follows −Input tapeThe input tape has a left end and extends to the right end.It is divided into blocks and each block containing a single symbol from the input alphabet Σ.The end block of the tape contains the end markers ₵ at the left end and the end marker $ at the right end.The absence of end markers indicates that the tape is of infinite length.The left-to-right sequence of symbols between the two end markers in ... Read More

ProblemShift the input string right by one place and design a Turing Machine (TM) that can perform right shift over ∑ = {0, 1}.SolutionRefer an algorithm given below to design a TM −Step 1 − Move right side to the last character from the initial character.Step 2 − If the character is „0‟, replace it with „B‟ and move one step right to replace the immediate „B‟ to „0‟.Step 3 − If the character is „1‟, replace it with „B‟ and move one step right to replace the immediate „B‟ to „1‟.Step 4 − After processing as above, move left one ... Read More

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 More

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 More

Construct deterministic finite automata (DFA) for the language L = { w : w has odd number of 0’s and w has odd number of 1’s}, over the alphabet Σ = {0, 1}.Example0111, 010101, 01110011 is an accepted string, because those strings have an odd number of 0’s and an odd number of 1’s.For the given language we will need four states to draw the main DFA which will read odd no. of 0s and 1s. We can also draw it by merging the two DFAs in which one will accept only an odd number of 0s and one accepts ... Read More

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 representation{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 and NFA with epsilon both are almost the same; the only difference is their transition function.NFA transition function is as follows −δ − Q X Σ→ 2QNFA with ε- transition functions is as follows −δ: Q × (Σ∪ε)→2QConstruct NFA ... Read More

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 More

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 representation{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 five 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 More