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To plot an angle spectrum, we can take the following steps −Set the figure size and adjust the padding between and around the subplots.Get random seed value.Initialize dt for sampling interval and find the sampling frequency.Create random data points for t.To generate noise, get nse, r, cnse and s, using numpy.Create a figure and a set of subplots using subplots() method.Set the title of the plot.Plot the angle spectrum.To display the figure, use show() method.Exampleimport matplotlib.pyplot as plt import numpy as np plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] = True np.random.seed(0) dt = 0.01 # sampling interval Fs ... Read More
To change the datetime tick label frequency for Matplotlib plots, we can create a dataframe and plot them in some date rangeStepsSet the figure size and adjust the padding between and around the subplots.To make potentially heterogeneous tabular data, use Pandas dataframe.Plot the dataframe using plot() method.Set X-axis major locator, i.e., ticks.Set X-axis major formatter, i.e., tick labels.Use autofmt_xdate(). Date ticklabels often overlap, so it is useful to rotate them and right align them.To display the figure, use show() method.Exampleimport pandas as pd import numpy as np import matplotlib.pyplot as plt import matplotlib.dates as mdates plt.rcParams["figure.figsize"] = [7.50, ... Read More
To animate text in a plot, we can take the following stepsSet the figure size and adjust the padding between and around the subplots.Set x and y axis limit.Initialize a variable, string.Use text() method to place text over the plot.Use FuncAnimation() to animate the text. Set text on the text axis.Turn off the axes.To display the figure, use show() method.Examplefrom matplotlib import pyplot as plt, animation plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] = True fig, ax = plt.subplots() ax.set(xlim=(-1, 1), ylim=(-1, 1)) string = 'Hello, how are you doing?' label = ax.text(0, 0, string[0], ha='center', va='center', fontsize=20, color="Red") def animate(i): ... Read More
There are two methods for converting deterministic finite automata (DFA) to Regular expression (RE). These are as follows −Arden’s MethodState Elimination MethodLet us understand these methods in detail.Arden’s TheoremLet P and Q be the two regular expressions.If P does not contain null string, then following equation in R, viz R = Q + RP,Which has a unique solution by R = QP*Here,The finite Automata do not have epsilon movesIt must have only initial state q1It’s states are q1, q2, q3,…….qn. The final state may be some qi where i
Linear Bounded Automaton (LBA) is a restricted form of Turing Machine in which input tape is finite.ExampleProve that LBA ⊂ PSPACEPSPACE is a superset of the set of context-sensitive languages.Now to prove LBA=PSPACE, We use theorem of Space compression with tape reduction which states that, For every k-tape S(n) space-bounded off-line Turing Machine M and constant c>0, there exists a one-tape cS(n) space-bounded off-line turing machine N such that L(M)=L(N).Following identity holds for −DSPACE(S(n))=DSPACE(O(S(n)))and NSPACE(S(n))=NSPACE(O(S(n)))Since LBA is one-tape n space-bounded Turing Machine it follows −LBA=NSPACE(n)---------------------(1)Now by Savitch theorem, if S is fully space constructible and S(n)>log(n) thenNSPACE(S(n)) ⊆DSPACE(S^{2}(n)) -------------(2)Final proofLBA=NSPACE(n)............by(1)⊆DSPACE(n^{2})............by(2)⊂DSPACE(n^{3})............by ... Read More
Push down Automata (PDA) is complement of the PDA that contain Substring bbbStepsMake the PDA for accepting those strings that have conation bbb.Complement it by making non-accepting as accepting and vice versa.Construct PDAYou can construct the PDA as shown below for the (a, b)* languageThe nature of transition format is Input, Top of stack, PUSH/POPExamplea ,a , aa means on i/p a and top of stack is a then push aAt q0 i, e initial if a or b anything came move state to q1Till q1 we get 1 b to make substring b_ _ so now on q1 if ... Read More
Let us begin by understanding the concept of deterministic finite automata (DFA) in the theory of computation (TOC).Deterministic Finite Automaton (DFA)In DFA, for each info image, one can decide the state to which the machine will move. Henceforth, it is called Deterministic Automaton.Formal Definition − A Deterministic Finite automata is a 5-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.Non-deterministic finite automata (NDFA)In NDFA, for a specific info image, ... Read More
A Turing machine (TM) is a 7-tuple (Q, ∑, Γ, δ, q0, qaccept , qreject).Where, Q is a finite set of states.∑ is the input alphabet that does not contain the blank symbol t.Γ is the tape alphabet, where t ∈ Γ and ∑ ⊆ Γ.δ: (Q × Γ) → (Q × Γ × {L, R}) is the transition function.q0 ∈ Q is the start state.qaccept ∈ Q is the accept state.qreject ∈ Q is the reject state, where qreject ≠ qaccept.For accepting even-length palindrome over the alphabet {0, 1}, follow the steps given below −Match the first and last ... Read More
ProblemDesign a TM (Turing Machine) that takes a binary number as an input and replaces the last digit of the string with its Boolean complement.SolutionA Turing machine is a 7-tuple (Q, ∑, Γ, δ, q0, qaccept , qreject)Where, Q is a finite set of states.∑ is the input alphabet that does not contain the blank symbol t.Γ is the tape alphabet, where t ∈ Γ and ∑ ⊆ Γ.δ − (Q × Γ) → (Q × Γ × {L, R}) is the transition function.q0 ∈ Q is the start state.qaccept ∈ Q is the accept state.qreject ∈ Q is the ... Read More
CFL refers to Context Free Language in the theory of computation (TOC). Let us now understand how CFL is closed under Union.CFL is closed under UNIONIf L1 and L2 are CFL’s then L1 U L2 is also CFL.Let L1 and L2 are generated by the Context Free Grammar (CFG).G1=(V1, T1, P1, S1) and G2=(V2, T2, P2, S2) without loss of generality subscript each non terminal of G1 and a1 and each non terminal of G2 with a2 (so that V1∩V2=φ).Subsequent steps are used production entirely from G1 or from G2.Each word generated thus is either a word in L1 or ... Read More