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Technical articles with clear explanations and examples
Characteristics of Network and Electric Circuit
Electric NetworkAn electrical network is an interconnection of electrical components (like sources, resistors, inductors, capacitors, diodes, transistors etc.). An electrical network need not contain a closed path for the flow of electric current. Some examples of the network are shown in the figure given below.Characteristics of Electric NetworkAn electric network possesses the following characteristics −It is an interconnection of electrical components.Electric network need not provide a return path for the current.It may or may not contain active electrical components.It may be consist of, passive elements, active elements or both active and passive elements.Examples of electric network are − Resistive network, ...
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 MoreWhat is a finite state machine in TOC?
A finite state machine has a set of states and two functions called the next-state and output function.The set of states correspond to all the possible combinations of the internal storage. If there are n bits of storage, there are 2n possible states.The next state function is a combinational logic function that, given the inputs and the current state, determines the next state of the system.The diagram given below explains the functioning of a finite state machine in TOC.The output function generates a set of outputs from the current state and the inputs.TypesThe two types of finite state machines are ...
Read MoreExplain the power of an alphabet in TOC.
If Σ is an alphabet, the set of all strings can be expressed as a certain length from that alphabet by using exponential notation. The power of an alphabet is denoted by Σk and is the set of strings of length k.For example, Σ ={0, 1}Σ1= {0, 1} ( 21=2)Σ2= {00, 01, 10, 11} (22=4)Σ3= {000, 001, 010, 011, 100, 101, 110, 111} (23= 8)The set of strings over an alphabet Σ is usually denoted by Σ*(Kleene closure)For instance, Σ*= {0, 1}*={ ε, 0, 1, 00, 01, 10, 11, ………}Therefore, Σ*= Σ0U Σ1U Σ2U Σ3…………. With ε symbolThe set of ...
Read MoreWhat are the fundamental concepts of TOC?
The basic definitions of the fundamental concepts in the Theory of Computation (TOC) along with the relevant examples are explained below −SymbolSymbols simply call it as a character.It is an atomic unit, such as a digit, character, lowercase letter, etc. Sometimes it is also a word. The formal language does not deal with the “meaning” of the symbols.For example, a, b, c, ……………z0, 1, 2, …………..9+, -, *, %, …………special characters.AlphabetThe set of characters is called as the alphabet.An alphabet is a finite, non-empty set of symbols. It is denoted by Σ or E.For example, Σ ={0, 1} set of ...
Read MoreExplain the concept of derivation in TOC
Derivation is a sequence of production rules. It is used to get input strings. During parsing, we have to take two decisions, which are as followsWe have to decide the non-terminal which is to be replaced.We have to decide the production rule by which the non-terminal will be replaced.Two options to decide which non-terminal has to be replaced with the production rule are as follows −Left most derivationRight most derivation.Let us understand these two options in detail.Left Most DerivationIn the leftmost derivation, the input is scanned and then replaced with the production rule from left side to right. So, we ...
Read MoreDerive the string "00101" using LMD and RMD while using CFG
ProblemDerive the string"00101" for left most derivation (LMD) and right most derivation (RMD) using context free grammar (CFG).SolutionThe grammar is as follows −S->A1B A->0A| ε B->0B| 1B| εLeft Most derivation (LMD)In the left most derivation, the given input is scanned and then replaced with the production rule from left side to right. So, we have to read that input string from left to right.The grammar is as follows −S->A1B rule1 A->0A| ε rule 2 B->0B| 1B| ε rule 3Hence, the LMD will be as follows −S->A1B ->0A1B rule2 ->00A1B rule2 ->001B rule2 ->0010B rule3 ->00101B rule3 ->00101 rule3 Derived the ...
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