[Docs] Shannon Probabilistic Proofs

docusaurus/docs/protocol/primitives/gateways.md

@@ -1,6 +1,6 @@
 ---
 title: Gateways
-sidebar_position: 4
+sidebar_position: 3
 ---
 
 # Gateways <!-- omit in toc -->

docusaurus/docs/protocol/primitives/probabilistic_proofs/geometric_pdf_vs_cdf.py

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+import matplotlib.pyplot as plt
+import numpy as np
+
+# Define different ProofRequestProbability values
+p_values = [0.1, 0.25, 0.5, 0.75]  # Modify as needed
+k_values = np.arange(0, 21)  # Range of k values starting from 0
+
+# Create subplots side by side
+fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))
+
+# Plot Geometric PDF for different p values
+for p in p_values:
+    q = 1 - p
+    pdf_values = p * (1 - p) ** k_values
+    ax1.plot(k_values, pdf_values, marker="o", linestyle="-", label=f"p = {p}")
+
+ax1.set_title("Geometric PDF: Exactly k Failures Until 1st Success")
+ax1.set_xlabel("Number of Failures before First Success (k)")
+ax1.set_ylabel("Probability Pr(X = k)")
+ax1.set_xticks(k_values)
+ax1.grid(True)
+ax1.legend()
+
+# Plot Geometric CDF for different p values
+for p in p_values:
+    q = 1 - p
+    cdf_values = 1 - (1 - p) ** (k_values + 1)
+    ax2.plot(k_values, cdf_values, marker="o", linestyle="-", label=f"p = {p}")
+
+ax2.set_title("Geometric CDF: ≤ k Failures Until 1st Success")
+ax2.set_xlabel("Number of Failures before First Success (k)")
+ax2.set_ylabel("Cumulative Probability P(X ≤ k)")
+ax2.set_xticks(k_values)
+ax2.grid(True)
+ax2.legend()
+
+# Adjust layout and display the plots
+plt.tight_layout()
+plt.show()

docusaurus/docs/protocol/primitives/probabilistic_proofs/penalty_vs_proof_request_prob.py

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+import matplotlib.pyplot as plt
+import numpy as np
+
+p_values = np.linspace(0.01, 0.5, 100)
+R_values = [10, 100, 1000, 10000]
+
+for R in R_values:
+    S_values = R * ((1 - p_values) / p_values)
+    plt.plot(p_values, S_values, label=f"R = {R} POKT")
+
+plt.xlabel("ProofRequestProbability (p)")
+plt.ylabel("Required Penalty (S POKT)")
+plt.title("Penalty vs. ProofRequestProbability for Different Reward Values")
+plt.legend()
+plt.yscale("log")  # Use logarithmic scale for y-axis (optional)
+plt.grid(True, which="both", ls="--")
+plt.show()