Article Categories
- All Categories
-
Data Structure
-
Networking
-
RDBMS
-
Operating System
-
Java
-
MS Excel
-
iOS
-
HTML
-
CSS
-
Android
-
Python
-
C Programming
-
C++
-
C#
-
MongoDB
-
MySQL
-
Javascript
-
PHP
-
Economics & Finance
Computer Science Articles
Page 41 of 53
Explain the balancing parenthesis of PDA
Pushdown Automata (PDA) are the finite automata (FAs), but with the ability to push and pop symbols to/from a stack.PDA accepts strings if there is a legal path from start state to acceptance state for input. Otherwise, the string is rejected.A PDA can be represented by a 7-tuple(Q, ∑, ℾ, q0, ha, ∆, δ)WhereThe PDA is to finite subsets of Q ☓ (ℾ ∪ {∆})*.Parentheses are balanced ifWhile reading string, number of opening parentheses >= number of closing parentheses.When string is read, number of opening parentheses = number of closing parentheses.Examples(())() − Balanced((()() − Not balanced)()(() − Not balancedThe context ...
Read MoreDesign a PDA which recognizes the language
ProblemGenerate the push down automata (PDA) that recognizes the language E={aibj| i is not equal to j and I is not equal to 2j}.SolutionConsider the two languages as given below −L1={aibj|i,j>=0 and i>2j}L2={aibj|i,j>=0 and iaA A->aaAb|aA|epsilonIn L2, the number of a's are less than double the number of b'sSo the CFG for L2 becomes as follows − S2->Bb|aBb B->Bb|aBb|aaBb|epsilon S->S1|S2L1: {aibj:i>2j}L2:{aibj: i
Read MoreState the worst case number of states in DFA and NFA for a language?
A Deterministic Finite automata (DFA) is a five tuplesM=(Q, ∑, δ, q0, F)Where, Q − Finite set called states.∑ − Finite set called alphabets.δ − Q × ∑ → Q is the transition function.q0 ∈ Q is the start or initial state.F − Final or accept state.Let’s see the worst case number of states in DFA for the language A∩B and A*Let A and B be the two states, |A| = number of states = nA|B| = number of states = nBDFA = |A∩B| =nA.nB|A ∪ B| =nA.nB|A*|=3/4 2nA|AB| = nA (2nB-2nB-1)NFAThe non-deterministic finite automata (NFA) also have five states ...
Read MoreDesign an unambiguous CFG in CNF that generates E?
ProblemDefine the language, E={aibj|i not equal to j and i not equal to 2j} and design an unambiguous context free grammar (CFG) in Chomsky normal form (CNF) that generates E.SolutionThe unambiguous CFG for the given language is as follows −S->AC|CBA->aA|aB->Bb|bC->aCb|aaCb|epsilonNow, convert this CFG into CNF. You can follow the below mentioned steps for the successful conversion.Step 1First add a new start symbol S0 S0->S S->AC|CB A->aA|a B->Bb|b C->aCb|aaCb|epsilonStep 2Next eliminate the epsilon symbol in the production other than the start symbol. C->epsilon is a null productionAfter eliminating null production, the new productions are as follows − S0->S S->AC|CB A->aA|a B->Bb|b ...
Read MoreExplain if the CFG is recognized by Non-deterministic push down automata
Context Free Grammars (CFG) are definitely recognized by Non-deterministic push down automata (NPDA), but Programming languages are translated to binary (Machine Code) via Deterministic PDA.This is because it has the following below mentioned impacts −If Programming languages were supposed to be translated via NPDA then for one given program instance we will have multiple versions of binary(Machine code) generated for the same program, which ideally shouldn't be the scenario.For a given program only 1 version of binary code should be generated and that should remain consistent across all OS Platforms.Outputs will vary significantly: If we have multiple object files, then ...
Read MoreWhat 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 More