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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Copyright (C) 2009-2020 Authors of CryptoMiniSat, see AUTHORS file
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; version 2
# of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
# 02110-1301, USA.
import optparse
import random
import os
class PlainHelpFormatter(optparse.IndentedHelpFormatter):
def format_description(self, description):
if description:
return description + "\n"
else:
return ""
usage = "usage: %prog [options] "
desc = """Generates an LPN problem
"""
def set_up_parser():
parser = optparse.OptionParser(usage=usage, description=desc,
formatter=PlainHelpFormatter())
parser.add_option("--verbose", "-v", action="store_true", default=False,
dest="verbose", help="Print more output")
# for fuzz-testing
parser.add_option("--seed", "-s", dest="seed", default=None,
help="Genereate with this seed", type=int)
parser.add_option("-n", dest="n", default=None, type=int,
help="Functiion width")
parser.add_option("--pb", dest="pb", default=False, action="store_true",
help="Functiion width")
parser.add_option("-m", dest="samples", default=None, type=int,
help="Number of samples")
parser.add_option("--noise", dest="noise", default=0.1, type=float,
help="Ratio of noise")
parser.add_option("--tolerance", "-t", dest="tolerance", default=None, type=int,
help="Tolerance for error. It is set AUTOMATICALLY if you don't set it here. It will be set to EXACTLY the actual error, so you will get a SAT instance.")
#parser.add_option("--autotolerance", dest="autotolerance", action="store_true", default=False,
#help="Set tolerance automatically to PERFECT match. Default.")
return parser
if __name__ == "__main__":
# parse opts
parser = set_up_parser()
(opts, args) = parser.parse_args()
if opts.seed is None or opts.n is None or opts.samples is None or opts.noise is None:
print("ERROR: You MUST give all of: --seed, -n, -m")
exit(-1)
print("c Seed: %3d" % opts.seed)
print("c n: %3d" % opts.n)
print("c Samples: %3d" % opts.samples)
print("c Noise: %-3.2f" % opts.noise)
random.seed(opts.seed)
# y[i] = set randomly [[output]]
# x[i] = data that SAT solver can manipulate
# val[x][y] = x[i]*y[i]
fun = []
for i in range(opts.n):
fun.append(random.randint(0, 1))
inputs = []
for i in range(opts.samples):
inp = []
for i2 in range(opts.n):
inp.append(random.randint(0, 1))
inputs.append(inp)
real_outputs = []
for i in range(opts.samples):
out = 0
for a,b in zip(fun, inputs[i]):
out ^= a*b
real_outputs.append(out)
num_incorrect_eqs = 0
correct_eqs = []
outputs = []
for i in range(opts.samples):
out = real_outputs[i]
if random.random() < opts.noise:
out = out ^ 1
num_incorrect_eqs+=1
correct_eqs.append(False)
else:
correct_eqs.append(True)
outputs.append(out)
print("c Tncorrect eqs: %3d" %num_incorrect_eqs)
tolerance=None
if opts.tolerance is None:
tolerance = num_incorrect_eqs
print("c -------------------- setting tolerance AUTOMATICALLY, since '--tolerance' was not set")
else:
tolerance = opts.tolerance
print("c Tolerance: %3d" % tolerance)
# print
print("c equations. FUN[i2]*INPUT[i][i2]")
for i in range(opts.samples):
toprint = ""
for i2 in range(opts.n):
toprint += "c %d" % fun[i2]
toprint += "*"
toprint += "%d" % inputs[i][i2]
if i2 != opts.n-1:
toprint += " + "
toprint += " = %d" % outputs[i]
toprint += " -- correct: %s" % correct_eqs[i]
print(toprint)
# variable table (sequential):
# n: function we need to figure out
# inputs -- n+n+n...n exactly opts.samples times. Total: opts.samples*opts.n
# outputs -- opts.samples
# helper functions come here
v = 1
vars_fun = []
for _ in range(opts.n):
vars_fun.append(v)
v+=1
#vars_inputs = []
#for _ in range(opts.samples):
#tmp = []
#for _ in range(opts.n):
#tmp.append(v)
#v+=1
#vars_inputs.append(tmp)
vars_noise = []
for _ in range(opts.samples):
vars_noise.append(v)
v+=1
####################
####### Generate CNF
####################
if opts.pb:
print("* #variable= %d #constraint= 1" % (opts.n+opts.samples))
# compute outputs
for i in range(opts.samples):
vs = []
for i2 in range(opts.n):
# v = inputs[i][i2] * fun[i]
if inputs[i][i2] == 1:
vs.append(vars_fun[i2])
out = "x "
out_pb = "* xor "
for x in vs:
out += "%d " % x
out_pb += "x%d " % x
out_pb += "x%d " % vars_noise[i]
if outputs[i]:
out+="%d " % vars_noise[i]
out_pb+=" 1"
else:
out+="-%d " % vars_noise[i]
out_pb+=" 0"
out +="0"
if opts.pb:
print(out_pb)
else:
print(out)
# get noise
print("c Num equations: ", opts.samples)
print("c Incorrect equations: ", num_incorrect_eqs)
print("c Tolerance: ", tolerance)
if num_incorrect_eqs > tolerance:
print("c this will be UNSAT for sure. Tolerance is smaller than the number of Incorrect euqations.")
if opts.pb:
out = ""
for i in range(opts.samples):
out +="-1 x%d " % vars_noise[i]
out += " >= %d" % (-tolerance)
print(out)
else:
out = "b "
for i in range(opts.samples):
out +="-%d " % vars_noise[i]
out += "0 %d" % (opts.samples-tolerance)
print(out)
# print correct output
out = "c correct output is: "
if num_incorrect_eqs <= tolerance:
out += "SAT "
for i in range(opts.n):
val = fun[i]
if val:
out+= "%d " % vars_fun[i]
else:
out+= "-%d " % vars_fun[i]
else:
out += "UNSAT "
print(out)
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