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1’s complement means transforming the 0 bit to 1 and the 1 bit to 0.Let the input be −B00101110BThe output is as follows −B11010001BConceptThe concept is explained below −Step 1 − Start scanning the input from left to right.Step 2 − If the R/W is at 1, then make it 0 and move right.Step 3 − If the R/W is at 0, then make it 1 and move right.Step 4 − Repeat the steps given above and we will reach B (blank).Step 5 − Then move the R/W head all the way to the left without changing anything until it ... Read More
ProblemThe language L = {ww | w ε {0, 1}} having the string of 0’s and 1’s which is followed by itselfL={00, 11, 1100, 0011, …..}SolutionThe logic for solving the problem is as follows −Find the midpoint of the string.Then match the symbols.ExplanationStep 1 − First, we need to find the midpoint of the string.Step 2 − We will make the first 0 to X or 1 to Y and then move R/W head to the right until the last character is found.Step 3 − Then make this 0 to X or 1 to Y.Step 4 − Now, we will ... Read More
A push down automata (PDA) can be formally described as seven tuples(Q, Σ, S, δ, q0, I, F)Where, Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is a set of accepting statesProblemConstruct PDA for L = {anb(2n) | n>=1} ∪ {anbn | n>=1}SolutionLetL = {anb(2n) | n>=1}{anbn | n>=1}Construct PDA for L= L1 U L2So, the strings which are generated by the given language L1 are as follows−L1={abb, aabbbb, aaabbbbbb, ….} andL2= {ab, aabb, aaabbb, ….}L= L1 ... Read More
A deterministic finite automata (DFA) can remember a finite amount of information but A push down automata (PDA) can remember an infinite amount of information.Basically a PDA is as follows −“Finite state machine+ a stack”PDA has three components, which is as follows −An Input tapeA control unitA Stack with infinite sizeA PDA can be formally described as seven tuples (Q, Σ, S, δ, q0, I, F)Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is a set of ... Read More
A push down automata (PDA) can be formally described as seven tuples(Q, Σ, S, δ, q0, I, F)Where, Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is a set of accepting states(F belongs to Q)ProblemConstruct PDA for 0n1m2(n+m) where n, m>=1.SolutionSo, the strings which are generated by the given language are as follows −L={0122, 001222, 000112222, ….}That is to add the number of 0's and 1's, and that will equal the number of 2's.So for every 0's ... Read More
A push down automata (PDA) can be formally described as seven tuples(Q, Σ, S, δ, q0, I, F)Where, Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is a set of accepting states(F belongs to Q)ProblemConstruct PDA for 0n1m2m3n where n, m≥1.SolutionSo, the strings which are generated by the given language are −L={0123, 011223, 001233….}The number of 1’s and 3’s are same and number of 2’s and 1’s are sameConstruction of PDA for given problemThe PDA is as ... Read More
A push down automata (PDA) can be formally described as seven tuples(Q, Σ, S, δ, q0, I, F)Where, Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is a set of accepting statesProblemConstruct PDA for a(n+m)bmcn n, m≥1.SolutionSo, the strings which are generated by the given language are −L={aabc, aaaabccc, aaaaabbccc, ….}That is to add the number of b's and c's, and that will equal the number of a's.For every b's and c's we will pop a's from ... Read More
Turing machines are more powerful than both finite automata (FA) and pushdown automata (PDA). They are as powerful as any computer we have ever built.The main improvements from PDAs in Turing machine are explained below −Infinite “all” accessible memory (in the form of a tape) – option to read and write to it.A read/write head can move to the left and to the right on the input tape (or don’t change a position).The TM works on an infinite tape divided into cells (infinite in both directions), each of which contains either a symbol from an alphabet or the blank symbol. ... Read More
Similar to the finite automata (FA), push-down automata (PDA) can be either deterministic or non-deterministic.A deterministic push down automata (DPDA) never has a choice of the next step −It has the possible output for every combination of state, input character and stack character, as compared to the deterministic finite automata (DFA).We need to be careful about every combination of state and stack character. Only one of the transactions is allowed either for the empty symbol ∧ or for an input symbol. Or there can be no transaction at all.ExampleA non-deterministic push-down automaton (NPDA) can contain the following instructions, but a ... Read More
A pushdown automaton is used to implement a context-free grammar in the same way that we use a technique to design DFA for a regular grammar. A DFA work on a finite amount of information, where as a PDA works on an infinite amount of information.Generally, a pushdown automaton is −"Finite state machine" + "a stack"A pushdown automaton consist of three components −an input tape, a control unit, anda stack with infinite size.Now consider a problem that how to design push down automata for a given language −ProblemDesign a push down automaton which recognizes even length palindromes for L = ... Read More