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Computers Articles
Page 82 of 100
Construct a TM for the language L= {ww : w ∈ {0,1}}
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 MoreConstruct PDA for accepting L = {anb(2n) | n>=1} U {anbn | n>=1}
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 MoreConstruct a DPDA for anb2n n ≥ 1 in TOC
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 MoreConstruct a PDA for language L = {0n 1m2m3n | n>=1, m>=1}
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 MoreExplain the basic properties of the Turing machine?
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 MoreDistinguish between DPDAs and NPDAs in TOC?
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 MoreDesign a push down automaton for L = {wwR | w ∈ {a, b}+}?
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 MoreWhat happens when a String is accepted or rejected by NPDA?
A string is accepted by an Non-deterministic Push down Automata (NPDA), if there is some path (i.e., sequence of instructions) from the start state to a final state that consumes all the letters of the string. Otherwise, the string is rejected by the NPDA.The language of an NPDA is the set of all strings that it accepts.An input string rejected by the NPDA under following conditions −If reading an input string finishes without reaching a final state.If for a current state/symbol on the stack/input symbol there is no transition.If it attempts to pop the empty stack.ExampleBuild an NPDA which recognises ...
Read MoreWhat are the restrictions of regular grammar?
A regular grammar is the one where each production takes one of the following restricted forms −B → ∧, B → w, B → A, B → wA.(Where A, B are non-terminals and w is a non-empty string of terminals.)Restrictions of regular grammarOnly one nonterminal can appear on the right-hand side of a production.Nonterminal must appear on the right end of the right-hand side.Therefore, the productions are as follows −A → aBc and S → TUThese are not part of a regular grammar, but the production A → abcA is.Things like A → aB|cC are allowed because they are actually ...
Read MoreDesign a DFA that accepts at most 3 a"s
Construct deterministic finite automata that accepts at most 3 a’s over an alphabet ∑={a,b}.At most 3 a’s means,The string contains 0 to max 3 a’s and any number of b’s.L= {Є,a,aa,aaa,ab,abb,bab,bbabaa, bbabaabbb,…..}Construct DFALet’s construct DFA step by step −Step 1Valid inputs − aaa, a, aa,ε .Step 2Valid inputs − b, ba, baa, baaa, bb, bba, bbba,…Step 3Valid input − bab, abba, abbbaa, babba,…Step 4Valid inputs − babab, aabb, aaba, bbbaaba, …Step 5Valid inputs − aaabbb, aaabab, baaaba, …Step 6InValid inputs − aaaa, aaabab, baaaba,
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