76 lines
2.3 KiB
Python
76 lines
2.3 KiB
Python
# Computes griefing factors of various parameter sets for Casper the
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# Friendly Finality Gadget
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# Case 1: <1/3 non-commit (optimal if epsilon participate)
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def gf1(x1, x2, x3, x4, x5):
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return x2 / x1
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# Case 2: censor <1/3 committers (optimal if 1/3 get censored)
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def gf2(x1, x2, x3, x4, x5):
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return 1.5 * (x1 + x2 / 3) / x2
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# Generalized case 2
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#k = 0.25
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#def gf2(x1, x2, x3, x4, x5):
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# return (x1 * k + x2 * k**2) / (x2 * k * (1-k))
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# Case 3: <1/3 non-prepare (optimal if epsilon participate)
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def gf3(x1, x2, x3, x4, x5):
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return x4 / x3
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# Case 4: censor <1/3 preparers (optimal if 1/3 get censored)
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def gf4(x1, x2, x3, x4, x5):
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return 1.5 * (x3 + x4 / 3) / x4
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# Case 5: finality preventing 1/3 non-commits
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def gf5(x1, x2, x3, x4, x5):
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return 2 * (x5 + x2 / 3) / (x5 + x1 + x2 / 3)
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# Case 6: censor commits
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def gf6(x1, x2, x3, x4, x5):
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# Case 6a: 51% participate
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return max(1 + x2 / (x5 + x1 + x2 / 2),
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# Case 6b: 67% participate
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(x5 + x1 + x2 / 3) / (x5 + x2 / 3) / 2)
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# Case 7: finality and commit-preventing 1/3 non-prepares
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def gf7(x1, x2, x3, x4, x5):
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return 2 * (x5 + x4 / 3) / (x5 + x3 + x4 / 3)
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gfs = (gf1, gf2, gf3, gf4, gf5, gf6, gf7)
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# Get the maximum griefing factor of a set of parameters
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def getmax(*args):
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return max([f(*args) for f in gfs])
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# Get the maximum <50% griefing factor, and enforce a bound
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# of MAX_CENSOR_GF on the griefing factor of >50% coalitions
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def getmax2(*args):
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MAX_CENSOR_GF = 2
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if gf2(*args) > MAX_CENSOR_GF or gf4(*args) > MAX_CENSOR_GF or \
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gf6(*args) > MAX_CENSOR_GF:
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return 999999999999999999
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return max(gf1(*args), gf3(*args), gf5(*args), gf7(*args))
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# Range to test for each parameter
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my_range = [i/12. for i in range(1, 61)]
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best_vals = (1, 0, 0, 0, 0)
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best_score = 999999999999999999
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# print([f(5, 6, 5, 6, 0) for f in gfs])
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for x1 in my_range:
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for x2 in my_range:
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for x3 in my_range:
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for x4 in my_range:
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o = getmax2(x1, x2, x3, x4, 1)
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if o < best_score:
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best_score = o
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best_vals = (x1, x2, x3, x4, 1)
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if o <= 1:
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print((x1, x2, x3, x4, 1), [f(x1, x2, x3, x4, 1) for f in gfs])
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print('result', best_vals, best_score)
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print([f(*best_vals) for f in gfs])
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