n个 变量的布尔函数具有 2 ^ n个 可能的输入。可以通过打印范围内的值的二进制表示形式来枚举这些值
0 <= x < 2^n。
对于这些可能的输入中的每个输入，布尔函数可以输出 0 或 1 。列举所有可能性（即每个可能的真值表）。列出range中的二进制值
0 <= x <2^(2^n)。
这是Python中的算法：
from __future__ import print_functionfrom itertools import product # forms cartesian productsn = 3 # number of variablesprint('All possible truth tables for n =', n)inputs = list(product([0, 1], repeat=n))for output in product([0, 1], repeat=len(inputs)): print() print('Truth table') print('-----------') for row, result in zip(inputs, output): print(row, '-->', result)输出看起来像这样：
All possible truth tables for n = 3Truth table-----------(0, 0, 0) --> 0(0, 0, 1) --> 0(0, 1, 0) --> 0(0, 1, 1) --> 0(1, 0, 0) --> 0(1, 0, 1) --> 0(1, 1, 0) --> 0(1, 1, 1) --> 0Truth table-----------(0, 0, 0) --> 0(0, 0, 1) --> 0(0, 1, 0) --> 0(0, 1, 1) --> 0(1, 0, 0) --> 0(1, 0, 1) --> 0(1, 1, 0) --> 0(1, 1, 1) --> 1Truth table-----------(0, 0, 0) --> 0(0, 0, 1) --> 0(0, 1, 0) --> 0(0, 1, 1) --> 0(1, 0, 0) --> 0(1, 0, 1) --> 0(1, 1, 0) --> 1(1, 1, 1) --> 0Truth table-----------(0, 0, 0) --> 0(0, 0, 1) --> 0(0, 1, 0) --> 0(0, 1, 1) --> 0(1, 0, 0) --> 0(1, 0, 1) --> 0(1, 1, 0) --> 1(1, 1, 1) --> 1... and so on
如果要以代数形式而不是真值表形式输出，则算法是相同的：
from __future__ import print_functionfrom itertools import product # forms cartesian productsn = 3 # number of variablesvariables = 'abcdefghijklmnopqrstuvwxyz'[:n]pairs = [('~'+var, var) for var in variables]print('All possible algebraic expressions for n =', n)inputs = list(product(*pairs))for i, outputs in enumerate(product([0, 1], repeat=len(inputs))): terms = [''.join(row) for row, output in zip(inputs, outputs) if output] if not terms: terms = ['False'] print('Function %d:' % i, ' or '.join(terms))输出看起来像这样：
All possible algebraic expressions for n = 3Function 0: FalseFunction 1: abcFunction 2: ab~cFunction 3: ab~c or abcFunction 4: a~bcFunction 5: a~bc or abcFunction 6: a~bc or ab~cFunction 7: a~bc or ab~c or abcFunction 8: a~b~cFunction 9: a~b~c or abcFunction 10: a~b~c or ab~cFunction 11: a~b~c or ab~c or abcFunction 12: a~b~c or a~bcFunction 13: a~b~c or a~bc or abcFunction 14: a~b~c or a~bc or ab~cFunction 15: a~b~c or a~bc or ab~c or abcFunction 16: ~abcFunction 17: ~abc or abcFunction 18: ~abc or ab~cFunction 19: ~abc or ab~c or abcFunction 20: ~abc or a~bcFunction 21: ~abc or a~bc or abcFunction 22: ~abc or a~bc or ab~cFunction 23: ~abc or a~bc or ab~c or abcFunction 24: ~abc or a~b~cFunction 25: ~abc or a~b~c or abcFunction 26: ~abc or a~b~c or ab~cFunction 27: ~abc or a~b~c or ab~c or abcFunction 28: ~abc or a~b~c or a~bcFunction 29: ~abc or a~b~c or a~bc or abcFunction 30: ~abc or a~b~c or a~bc or ab~cFunction 31: ~abc or a~b~c or a~bc or ab~c or abcFunction 32: ~ab~cFunction 33: ~ab~c or abc... and so on
