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Articles by Bhanu Priya
Page 78 of 106
What is Instantaneous Description and Turnstile Notation?
The instantaneous description (ID) of a push down automata (PDA) is represented by a triple (q, w, s)Where, q is the state.w is unconsumed input.s is the stack contents.ID is an informal notation of how a PDA compares an input string and makes a decision that string is accepted or rejected.Turnstile NotationIt is used for connecting pairs of ID's that represent one or more moves of a PDA.The process of transition is denoted by the turnstile symbol "⊢"⊢ it represents one move.⊢ sign describes a sequence of moves.Example(P, b, T) ⊢ (q, w, a)While taking a transition from P to ...
Read MoreExplain the elimination of epsilon productions in CFG
All grammars are not always optimized, which means the grammar may consist of some extra symbols (non-terminals) which increase the length of grammar.So, we have to reduce the grammar by removing the useless symbols.PropertiesThe properties to reduce grammar are explained below −Each non-terminal and terminal of G appears in the derivation of some word in L.There should not be any production as X->Y where X and Y are non-terminals.If epsilon is not in language L then there need not be in the production X-> ε.The diagram given below depicts the use of reduce grammar−The productions of type S-> ε are ...
Read MoreConstruct a Turing machine for adding 2 to the binary natural number?
A Turing machine (TM) can be formally described as seven tuples −(Q, X, ∑, δ, q0, B, F)Where, Q is a finite set of states.X is the tape alphabet.∑ is the input alphabet.δ is a transition function:δ:QxX->QxXx{left shift, right shift}.q0 is the initial state.B is the blank symbol.F is the final state.Input − n a natural numberOutput − n + 2Let’s represent natural numbers in unary form (e.g. 3 = 111, 5 = 11111) and 0 will be represented by the empty symbol.AlgorithmMove the tape head to the left of the first 1 (if it exists).Change that empty cell to ...
Read MoreHow to use Turing machines to recognize languages in TOC?
A Turing machine (TM) can be formally described as seven tuples −(Q, X, ∑, δ, q0, B, F)Where, Q is a finite set of states.X is the tape alphabet.∑ is the input alphabet.δ is a transition function: 𝛿:QxX->QxXx{left shift, right shift}.q0 is the initial state.B is the blank symbol.F is the final state.A Turing machine T recognises a string x (over ∑) if and only when T starts in the initial position and x is written on the tape, T halts in a final state.T is said to recognize a language A, if x is recognised by T and if ...
Read MoreDraw a Turing machine to find 2’s complement of a binary number
2’s complement of binary numbers can be done by using two approaches.Adding 1’s complement+1Traverse bits from left to right, find the 1st 1 bit then reverse all the bits after the 1 bit.ExampleLet the input be 1110010Thus, after performing 2’s complement, the output will be as follows −Output − 0001110Coming to the Turing machine to find 2’s complement, If input is as follows −B010000100The output is as follows −B101111100ExplanationStep 1 − Here, we need to start from the rightmost ends.Step 2 − We will move the R/W head all the way to the right, skipping all the 0s and 1s.Step ...
Read MoreDraw a Turing machine to find 1’s complement of a binary number
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 MoreConstruct 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 ...
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