Non-deterministic finite automata also have five states which are same as DFA, but with different transition function, as shown follows −δ: Q X Σ -> 2QNon-deterministic finite automata is defined as a 5 tuple, M=(Q, Σ, δ, q0, F)Where, Q: Finite set of statesΣ: Finite set of the input symbolq0: Initial stateF: Final stateδ: Transition function: Q X Σ -> 2QProblemDesign a transition diagram and table for the given language that accepts all strings of length at least 2.SolutionBefore proceeding to the solution, let’s understand what do you mean by length of string and how to find the length of ... Read More

NFA stands for non-deterministic finite automata. It is easy to construct an NFA when compared to DFA for a given regular language.The finite automata are called NFA when there exist many paths for specific input from the current state to the next state.Each NFA can be translated into DFA but every NFA is Non DFA.NFA is defined in the same way as DFA but with the following two exceptions, which are as follows −It contains multiple next states.It contains ε transitions.ExampleThe transition diagram is as follows −In the above NFA, it is clear that there exist many paths for specific ... Read More

A Deterministic Finite automata (DFA) is a collection of defined as a 5-tuples and is as follows −M=(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 ∈ Q is the start or initial state.F: Final or accept state.Example 1The DFA accepts all strings starting with 0The language L= {0, 01, 001, 010, 0010, 000101, …}In this language, all strings start with zero.Transition diagramThe transition diagram is as follows −ExplanationStep 1 − q0 is the initial state on input ‘0’ it goes to q1, which is the ... Read More

DFA refers to deterministic finite automata. Deterministic refers to the uniqueness of the computation. The finite automata are deterministic FA, if the machine reads an input string one symbol at a time.In DFA, there is only one path input from the current state to the next state. It does not accept the null move, i.e. it cannot change state without any input. It can contain multiple final states. It is used in Lexical Analysis in compilers.Formal definition of different automata (DFA)A Deterministic Finite automata (DFA) is a collection of defined as a 5-tuples and is as follows −M=(Q, Σ, δ, ... Read More

Finite automata is an abstract computing device. It is a mathematical model of a system with discrete inputs, outputs, states and a set of transitions from state to state that occurs on input symbols from the alphabet Σ.Formal definition of Finite AutomataFinite automata is defined as 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 ∈ Q is the start or initial state.F: Final or accept state.TypesThe different types of Finite Automata are as follows −Finite Automata without outputDeterministic Finite Automata (DFA).Non-Deterministic Finite Automata (NFA ... Read More

Finite automata is an abstract computing device. It is a mathematical model of a system with discrete inputs, outputs, states and a set of transitions from state to state that occurs on input symbols from the alphabet Σ.Finite Automata RepresentationThe finite automata can be represented in three ways, as given below −Graphical (Transition diagram)Tabular (Transition table)Mathematical (Transition function)Formal definition of Finite AutomataFinite automata is defined as 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 ∈ Q is the start or initial state.F: Final or ... Read More

A language is a set of strings from some alphabet (finite or infinite). In other words, any subset L of E* is a language in TOC.Some special languages are as follows −{} The empty set/language, containing no string.{s} A language containing one string, the empty string.ExamplesE = {0, 1}L = {x | x is in E* and x contains an even number of 0’s}E = {0, 1, 2, ., 9, .}L = {x | x is in E* and x forms a finite length real number}= {0, 1.5, 9.326, .}E = {a, b, c, ., z, A, B, ., Z}L ... Read More

A string is a finite set sequence of symbols choosen from some alphabets.For example, 00011001 is a string from binary alphabet Σ={0, 1}aabbcabcd is a string from alphabet Σ={a, b, c, d}The different operations performed on strings are explained below −Concatenation.Substring.Kleen star operation.Reversal.ConcatenationConcatenation is nothing but combining the two strings one after another.ExampleLet’s consider two strings −X= TutorialsY= PointThe concatenation (X, Y) of two strings is −X.Y = TutorialsPointNote − Concatenation of empty string with other string gives string itself.For example, X. ε = ε.X = XSubstringIf ‘w’ is a string then ‘v’ is substring of ‘w’ if there exists ... Read More

A finite state machine has a set of states and two functions called the next-state and output function.The set of states correspond to all the possible combinations of the internal storage. If there are n bits of storage, there are 2n possible states.The next state function is a combinational logic function that, given the inputs and the current state, determines the next state of the system.The diagram given below explains the functioning of a finite state machine in TOC.The output function generates a set of outputs from the current state and the inputs.TypesThe two types of finite state machines are ... Read More

If Σ is an alphabet, the set of all strings can be expressed as a certain length from that alphabet by using exponential notation. The power of an alphabet is denoted by Σk and is the set of strings of length k.For example, Σ ={0, 1}Σ1= {0, 1} ( 21=2)Σ2= {00, 01, 10, 11} (22=4)Σ3= {000, 001, 010, 011, 100, 101, 110, 111} (23= 8)The set of strings over an alphabet Σ is usually denoted by Σ*(Kleene closure)For instance, Σ*= {0, 1}*={ ε, 0, 1, 00, 01, 10, 11, ………}Therefore, Σ*= Σ0U Σ1U Σ2U Σ3…………. With ε symbolThe set of ... Read More