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To clear a Matplotlib textbox that was previously drawn, we can take the following steps −Set the figure size and adjust the padding between and around the subplots.Create x and y data points using numpy.Plot x and y using plot() method.Place characters token on the plot.To clear the text, use text.remove(), where text is a returned artist.To display the figure, use show() method.Exampleimport numpy as np from matplotlib import pyplot as plt plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] = True fig, ax = plt.subplots() x = np.linspace(-10, 10, 100) y = np.sin(x) ax.plot(x, y) text = fig.text(0.5, 0.96, ... Read More
ProblemConstruct DFA which accepts a string that contains second symbol is zero and fourth symbol is 1 over an alphabet ∑={0,1}.SolutionInput − 00110Output is accepted; because in the given string the second symbol is ‘0’ and the fourth symbol is ‘1’.Input − 11001Output − string is not accepted, because the second symbol is not ‘0’.Design DFA step by step as given below −Step 1 -Valid inputs − 0001Step 2 -Valid input − 1001Step 3 -Valid inputs − 0011, 1011Step 4 -Valid inputs − 00010, 10010, 00110, 00011, 10011, 00111, …Step 5 -Invalid inputs − 0101, 0100, 0010, 1100, 0000, 1000, …Step 6 -Valid inputs − 01010, 01000, 11111, 0100000, …
According to the theorem, If L and M are two regular languages, then L ∩ M is also regular language.ExampleConstruct A∩B where A and B is given as follows −The language A ={10, 100, 00, 001, 1010, …..}The language B ={01, 1010, 10, 101, …..}AA = (QA, Σ, δA, qa, FA) AB = (QB, Σ, δB, qB, FB) A∩B=(QA x QB ,Σ, δ(qA x qB ,FA x F B )Where, δ(( p, q), a) =δL (p, a), δM (q, a))Here, QA x QB = {p, q} x {r, s} ={(p, r), (p, s), (q, r), (q, s)} Z = ... Read More
ProblemConstruct a deterministic finite automata (DFA) that accepts a language L which has the number of zero’s is of multiple of 3 over an alphabet ∑=”{0,1}.SolutionIf input is: 000 Output is: string is acceptedBecause here the number of zero’s is multiple of 3.Designing DFAIn order to construct the DFA, follow the below mentioned steps −Step 1 -Valid inputs: 000, 000000, 09 , 012 , …Step 2 -Valid inputs: 1, 1000, 100000, …Step 3 -Valid inputs: 10100, 11000, 101100, …Step 4 -101010, 1101010, 1101110110, …Invalid inputs − 0,00,10000,01011, …
ProblemGiven language to construct the deterministic finite automata (DFA) is, the strings start with ‘a’ but not contain substring ‘aab’ over alphabet ∑={a,b}.SolutionIf the input is: “baabba”The output is: string is not acceptedBecause the string does not start with ‘a’, and generating a substring ‘abb’,DFA transition diagramThe DFA transition diagram for the string beginning with ‘a’ but not having the substring as ‘aab’ is as follows −Transition tableThe transition table is as follows −STATEINPUT (a)INPUT (b)→ 01*4 (dead state)1*2*3*2*2*4 (dead state)3*1*3*4 (dead state)4 (dead state)4 (dead State)
Vertex cover is a subset of vertices that covers all the edges in a graph. It is used to determine whether a given graph has a 3SAT to vertex cover.Clique is called a subset of vertices that are all directly connected. It determines whether a clique of size k exists in a graph.To prove − Vertex cover can be reduced to clique.ProofGiven a graph G=(V, E) and integer k.Get its complement graph G'=(V, E').Solve CLIQUE(G', |V|-k).If there is a solution, return yes. Otherwise, it returns as no.To prove this reduction, we need to show the following −If there is a ... Read More
To assign specific colors to specific cells in a Matplotlib table, we can take the following steps −Set the figure size and adjust the padding between and around the subplots.Make a tuple for columns attribute.Make a list of lists, i.e., list of records.Make a list of lists, i.e., color of each cell.Create a figure and a set of subplots.Add a table to an axes ax.Turn off the axes.To display the figure, use show() method.Exampleimport matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] = True columns = ('name', 'age', 'marks', 'salary') cell_text = [["John", "23", "98", "234"], ["James", ... Read More
To plot with different scales in matplotlib, we can take the following steps −StepsSet the figure size and adjust the padding between and around the subplots.Create t, data1 and data2 data points using numpyCreate a figure and a set of subplots, ax1.Initialize a color variable.Set x and y labels of axis 1.Plot t and data1 using plot() method.Set label colors using tick_params() method.Create a twin Axes sharing the X-axis, ax2.Perform steps 4, 6, 7 with a different dataset on axis 2.To display the figure, use show() method.Exampleimport numpy as np import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] ... Read More
To plot stacked bar chart in Matplotlib, we can use barh() methodsStepsSet the figure size and adjust the padding between and around the subplots.Create a list of years, issues_addressed and issues_pending, in accordance with years.Plot horizontal bars with years and issues_addressed data.To make stacked horizontal bars, use barh() method with years, issues_pending and issues_addressed dataPlace the legend on the plot.To display the figure, use show() method.Examplefrom matplotlib import pyplot as plt plt.rcParams["figure.figsize"] = [7.50, 3.50] plt.rcParams["figure.autolayout"] = True year = [2014, 2015, 2016, 2017, 2018, 2019] issues_addressed = [10, 14, 0, 10, 15, 15] issues_pending = [5, 10, 50, ... Read More
ProblemThe given language L={ x | the number of 1's is divisible by 2, and 0's by 3} over an alphabet ∑={0, 1}.SolutionThe language is divided into two parts, first we need to find the number of 1’s divisible by 2 and second find out the number of 0’s divisible by 3, finally combine the two parts to generate a result.Step 1 − DFA for the first part, number of 1’s divisible by 2.Here, q0 on 0 goes to q0 which is a final state, and generates a string 0, accepted by the given language.q0 on 1 goes to q1, ... Read More