Computer Science Articles - Page 46 of 62

Mealy MachineIn a Mealy machine the output symbol depends upon the present input symbol and present state of the machine.In the Mealy machine, the output is represented with each input symbol and each state is separated by /.The Mealy machine can be described by six tuples (Q, q0, Σ, O, δ, λ')Where, Q: Finite set of states.q0: Initial state of machine.Σ: Finite set of input alphabet.O: Output alphabet.δ: Transition function where Q × Σ → Q.λ': Output function where Q × Σ → O.In the Mealy machine, the output is represented with each input symbol and each state is separated ... Read More

The cross product method process in the deterministic finite automata (DFA) is explained below −Let a's DFA diagram has m number of states and b's DFA diagram has n number of states the cross product m x n will have mxn states.Languages represented by even number of ‘a’ and even number of ‘b’ are given below −L1 = {ε, baa, aa, aba, aab, aaaa, ... }L2 = {ε bb, abb, bab, bba, ...}After cross product we will find the DFA as mentioned below −As, L = {ab, aab, abb, aaab, ...}ExampleLet’s taken two DFAsEven number of a'sEven number of b'sThe ... Read More

The union process in the deterministic finite automata (DFA) is explained below −If L1 and If L2 are two regular languages, their union L1 U L2 will also be regular.For example, L1 = {an | n > O} and L2 = {bn | n > O}L3 = L1 U L2 = {an U bn | n > O} is also regular.ProblemDesign a DFA over an alphabet {a, b} where the start and end are of different symbols.SolutionThere are two different types of languages are formed for a given condition −L1={ab, aab, abab, abb, …….}L1={ab, aab, abab, abb, …….}Here, L1= starts ... Read More

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.ProblemDesign a finite automaton where the second symbol from the right hand side is ‘a’.SolutionThe language for a given string over an alphabet {a, b} is −L={aa, abaa, abbab, aaabab, ………}ExampleInput − aabaOutput − Not acceptedBecause the second letter from right hand side is not aInput − aabbabOutput − AcceptedIt is complicated to directly construct ... Read More

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 a DFA machine accepting odd numbers of 1’s and even number of 0’s.SolutionDesign two separate machines for the two conditions over an alphabet Σ={0, 1}:DFA accepts only an odd number of 1’s.DFA accepts only even number of 0’s.Here, s1 = starts2=odd 1 or start 11s3= starts 11 accepted and stay theres4 = accept even ... Read More

Non-deterministic finite automata (NFA) also have five states which are same as DFA, but with different transition function, as shown follows −δ: Q X Σ → 2QWhere, 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 NFA over an alphabet Σ={0, 1}.SolutionDesign two separate machines for the two conditions, as given below −NFA accepting only odd number of 1’sNFA accepting only even number of 0’sNFA accepting only odd number of 1’s over an alphabet Σ= ... 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.ProblemConstruct a DFA machine accepting odd numbers of 0’s or even numbers of 1’s.SolutionDesign two separate machines for the two conditions over an alphabet Σ={0, 1} −DFA accepting only odd number of 0’sDFA accepting only even number of 1’sDFA accepting only odd number of 1’s over an alphabet Σ={0, 1}    The language L= ... Read More

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