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
Articles by Bhanu Priya
Page 105 of 106
Derive the string "abb" for leftmost and rightmost derivation
ProblemLet’s consider a grammar to derive “abb” string using LMD and RMD S->AB/ ε A-> aB B-> SbSolutionWe have to use context free grammar.Derivation is a sequence of production rules, which is used to get input strings.During parsing, we have to take two decisions, which are as follows −We have to decide which non-terminal has to be replaced.We have to decide which non-terminal has to be replaced by using which production rule.There are two options to decide which non-terminal has to be replaced with production rule −Leftmost derivationRightmost derivationLeftmost derivationThe input is scanned and replaced with production rules from left ...
Read MoreHow to generate the language for context free grammar?
ProblemGenerate the language for the given context free grammar.S->0S, S-> λS-> A0, A->1A, A-> λS->000S, S-> λSolutionContext free grammar (CFG) is a formal grammar that is used to generate all the possible patterns of strings in a given formal language.CFG is defined by four tuplesG=(V, T, P, S)Where, T: Set of terminals (lowercase letters) symbols.V: Vertices or non-terminal symbols (Capital letters).P: Production rules.S: Start symbol.Example 1The grammar is −S->0S, S->λCase 1 − S->0S ->0Case 2 − S->0S ->00S ->00Case 3 − S->0S ->00S ->000S ->000Therefore, the language generated for the given grammar is −L={e, 0, 00, 000……..}Example ...
Read MoreExplain NFA with epsilon transition.
We extend the class of NFAs by allowing instantaneous ε transitions −The automaton may be allowed to change its state without reading the input symbol 2.In diagrams, such transitions are depicted by labeling the appropriate arcs with ε.Note that this does not mean that E has become an input symbol. On the contrary, we assume that the symbol E does not belong to any alphabet.ε -NFAs add a convenient feature but (in a sense) they bring us nothing new. They do not extend the class of languages that can be represented.Both NFAs and E-NFAs recognize exactly the same languages.Epsilon (ε) ...
Read MoreHow to convert from NFA to DFA in TOC?
In Non-Deterministic Finite Automata, for any current state and input symbol, there exists more than one next output state.Any string is accepted if and only if there exists at least one transition path which is starting at initial state and ending at final state.The following steps are followed to convert a given NFA to a DFA −AlgorithmStep-01Let's take ' q’ as a new set of states of the DFA. It is declared null in the beginning.Let's take T’ be a new transition table of the DFA.Step-02Add the start state of the NFA to q’.Add transitions from the start state to ...
Read MoreDesign a Moore machine for some binary input sequence.
ProblemDesign a Moore machine for a binary input sequence such that if it has a substring 101, the machine outputs A, if the input has substring 110, it outputs B otherwise it outputs C.SolutionFor designing such a machine, we will check two conditions, and those are 101 and 110. If we get 101, the output will be A, and if we recognize 110, the output will be B. For other strings, the output will be C.Moore machine has 6 tuples(Q, q0, Σ, O, δ, λ)Where, Q: Finite set of statesq0: Initial state of machineΣ: Finite set of input symbolsO: Output ...
Read MoreDesign a Moore machine to generate 1's complement of a binary number.
Moore machine has 6 tuples, which are as follows −(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 → OThe transition diagram is as follows −ExplanationStep 1 − q0 is the start state on input ‘0’ goes to q1 state and on ‘1’ goes to state q2 generating output 0.Step 2 − q1 on input ‘0’ goes to q1 itself and on ‘1’ goes to q2 generating output ‘1’.Step 3 − q2 on input ‘0’ ...
Read MoreDraw DFA which accepts the string starting with 'ab'.
ProblemDraw the state transition diagram over an alphabet Σ={a, b} that accepts the string starting with ‘ab’.SolutionThe formal definition of Deterministic Finite Automata (DFA) is as follows −A DFA is a collection of 5-tuples as shown below −M=(Q, Σ, δ, q0, F)Where, Q: Finite set called states.Σ: Finite set called alphabets.δ: Q × Σ → Q is the transition function.q0 ∈ Q is the initial state.The language is generated as given below −L={ab, aba, abab, …….}The transition diagram is as follows −Here, D is a dead state.D is a transition state, which it can never escape. Such a state is ...
Read MoreDesign NFA with Σ = {0, 1} and accept all string of length at least 2.
Non-deterministic finite automata also have five states which are same as DFA, but with different transition function, as shown follows −δ: Q X Σ -> 2QNon-deterministic finite automata is defined as a 5 tuple, M=(Q, Σ, δ, q0, F)Where, Q: Finite set of statesΣ: Finite set of the input symbolq0: Initial stateF: Final stateδ: Transition function: Q X Σ -> 2QProblemDesign a transition diagram and table for the given language that accepts all strings of length at least 2.SolutionBefore proceeding to the solution, let’s understand what do you mean by length of string and how to find the length of ...
Read MoreConstruct DFA with Σ= {0,1} accepts all strings with 0.
A Deterministic Finite automata (DFA) is a collection of defined as a 5-tuples and is as follows −M=(Q, Σ, δ, q0, F)Where, Q: Finite set called states.Σ: Finite set called alphabets.δ: Q × Σ → Q is the transition function.q0 ∈ Q is the start or initial state.F: Final or accept state.Example 1The DFA accepts all strings starting with 0The language L= {0, 01, 001, 010, 0010, 000101, …}In this language, all strings start with zero.Transition diagramThe transition diagram is as follows −ExplanationStep 1 − q0 is the initial state on input ‘0’ it goes to q1, which is the ...
Read MoreWhat are the different operations performed on strings in TOC?
A string is a finite set sequence of symbols choosen from some alphabets.For example, 00011001 is a string from binary alphabet Σ={0, 1}aabbcabcd is a string from alphabet Σ={a, b, c, d}The different operations performed on strings are explained below −Concatenation.Substring.Kleen star operation.Reversal.ConcatenationConcatenation is nothing but combining the two strings one after another.ExampleLet’s consider two strings −X= TutorialsY= PointThe concatenation (X, Y) of two strings is −X.Y = TutorialsPointNote − Concatenation of empty string with other string gives string itself.For example, X. ε = ε.X = XSubstringIf ‘w’ is a string then ‘v’ is substring of ‘w’ if there exists ...
Read More