Regular expression is the language which is used to describe the language and is accepted by finite automata. Regular expressions are the most effective way to represent any language. Let Σ be an alphabet which denotes the input set.The regular expression over Σ can be defined as follows −Φ is ... Read More

Problem 1Write the regular expression for the language accepting all the strings containing any number of a's and b's.SolutionThe regular expression will be −r.e. = (a + b)*This will give the set as L = {E, a, aa, b, bb, ab, ba, aba, bab, .....}, any combination of a and ... Read More

Moore machine described by 6 tuples(Q, q0, Σ, O, δ, λ) Where, Q: Finite set of statesq0: Initial state of machineΣ: Finite set of input symbolsO: Output alphabetδ: Transition function where Q × Σ → Qλ: Output function where Q → OGiven Σ ={a, b} and Δ ={0, 1}Sequence= ‘abb’Partial Moore ... Read More

ProblemGiven a Deterministic Finite Automata (DFA), try to reduce the DFA by removing unreachable states and removing similar rows.SolutionStep 1Remove the unreachable states from q0From the initial states, we are not able to reach q2 and q4. So, remove these two states as shown below −After removing unreachable states, the ... Read More

The two finite automata (FA) are said to be equivalent if both the automata accept the same set of strings over an input set Σ.When two FA’s are equivalent then, there is some string x over Σ. On acceptance of that string, if one FA reaches to the final state, ... Read More

ProblemConsider a Non-deterministic finite automata (NFA) and convert that NFA into equivalent Deterministic Finite Automata (DFA).SolutionLet’s construct NFA transition table for the given diagram −States\inputsab->q0{q0, q1}q0q1q2q1q2q3q3q3-q2DFA cannot have multiple states. So, consider {q0, q1} as a single state while constructing DFA.Let’s convert the above table into equivalent DFAStates\inputsab->q1[q0, q1]q0[q0, q1][q0q1q2][q0q1]*[q0q1q2][q0q1q2q3][q0q1q3]*[q0q1q2q3][q0q1q2q3][q0q1q2q3]*[q0q1q3][q0q1q2][q0q1q2]In ... Read More

ProblemConstruct a minimum state DFA for the following automata −SolutionWe first construct a transition table for the given finite automata −States\inputs01q0q1q5q1q6q2*q2q0q2q3q2q6q4q7q5q5q2q6q6q6q4q7q6q2Q={q0, q1, q2, q3, q4, q5, q6, q7}Q01={q2} and Q02={q0, q1, q2, q3, q4, q5, q6, q7}S0={{q2} {q0, q1, q2, q3, q4, q5, q6, q7}}Consider the set {q0, q1, q2, ... Read More

A finite state machine (FSM) which 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 ... Read More

In this method, we try to remove all the ε-transitions from the given Non-deterministic finite automata (NFA) −The method is mentioned below stepwise −Step 1 − Find out all the ε-transitions from each state from Q. That will be called as ε-closure(qi) where, qi ∈Q.Step 2 − Then, 𝛿1 transitions ... Read More

The ε closure(P) is a set of states which are reachable from state P on ε-transitions.The epsilon closure is as mentioned below −ε-closure (P) = P, where P ∈ QIf there exists ε-closure (P) = {q} and 𝛿(q, ε) =r then, ε-closure (P) = {q, r}ExampleFind ε-closure for the following ... Read More