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compute.cpp
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// 逻辑完备集的计算
// 电路中的对称门与非对称门相关的内容会不会有什么启发？
// https://en.wikipedia.org/wiki/Functional_completeness
// https://blog.csdn.net/u013795675/article/details/44480789
#include <bits/stdc++.h>
std::vector<std::string> basic_input2{
"0101",
"0011",
"0000",
"1111"};
std::vector<std::string> basic_input3{
"01010101",
"00110011",
"00001111"
"00000000",
"11111111"};
std::unordered_map<std::string, std::string> gate_map2{
{"0000", "const0"},
{"0001", "and2"},
{"0010", "us2_1"},
{"0011", "us2_2"},
{"0100", "us2_3"},
{"0101", "us2_4"},
{"0110", "xor2"},
{"0111", "or2"},
{"1000", "nor2"},
{"1001", "xnor2"},
{"1010", "us2_5"},
{"1011", "us2_6"},
{"1100", "us2_7"},
{"1101", "us2_8"},
{"1110", "nand2"},
{"1111", "const1"},
};
std::unordered_set<std::string> basic_symmetry_gates{
{"0001"},
{"0110"},
{"0111"},
{"1000"},
{"1001"},
{"1110"}};
std::string uint_2_string(uint32_t u, uint8_t length)
{
std::string res;
for (int i = length - 1; i >= 0; --i)
{
res += u & (1 << i) ? '1' : '0';
}
return res;
}
/**
* @brief apply the inverter for the given gate
*/
std::string apply_inverter(std::string entry)
{
std::string res;
uint i = 0;
for (i = 0u; i < entry.size(); ++i)
{
if (entry[i] == '0')
res += '1';
else
res += '0';
}
return res;
}
/**
* @brief compute the truth table for the given gate
* @param entry the Boolean function (truth table) of the given gate
* @param a the input truth table
* @param b the input truth table
* @return the truth table of the given gate
*/
std::string compute_new_tt_2(std::string entry, const std::string &a, const std::string &b)
{
std::string res;
uint i = 0;
for (i = 0u; i < 4; ++i)
{
if (a[i] == '0' && b[i] == '0')
res += entry[0];
if (a[i] == '0' && b[i] == '1')
res += entry[1];
if (a[i] == '1' && b[i] == '0')
res += entry[2];
if (a[i] == '1' && b[i] == '1')
res += entry[3];
}
return res;
}
std::string compute_new_tt_3(std::string entry, const std::string &a, const std::string &b, const std::string &c)
{
std::string res;
uint i = 0;
for (i = 0u; i < 8; ++i)
{
if (a[i] == '0' && b[i] == '0' && c[i] == '0')
res += entry[0];
if (a[i] == '0' && b[i] == '0' && c[i] == '1')
res += entry[1];
if (a[i] == '0' && b[i] == '1' && c[i] == '0')
res += entry[2];
if (a[i] == '0' && b[i] == '1' && c[i] == '1')
res += entry[3];
if (a[i] == '1' && b[i] == '0' && c[i] == '0')
res += entry[4];
if (a[i] == '1' && b[i] == '0' && c[i] == '1')
res += entry[5];
if (a[i] == '1' && b[i] == '1' && c[i] == '0')
res += entry[6];
if (a[i] == '1' && b[i] == '1' && c[i] == '1')
res += entry[7];
}
return res;
}
void explore_2_1()
{
uint i = 0u, j = 0u, k = 0u;
bool added = true;
std::vector<std::string> fcs_s;
std::vector<std::string> fcs_us;
for (i = 0u; i < 16u; ++i)
{
std::string entry = uint_2_string(i, 4);
std::vector<std::string> tmp_basic_input2 = basic_input2;
std::set<std::string> tmp_set(tmp_basic_input2.begin(), tmp_basic_input2.end());
added = true;
while (added)
{
added = false;
for (j = 0; j < tmp_basic_input2.size(); ++j)
{
for (k = 0; k < tmp_basic_input2.size(); ++k)
{
std::string newTT = compute_new_tt_2(entry, tmp_basic_input2[j], tmp_basic_input2[k]);
if (tmp_set.find(newTT) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT);
tmp_set.insert(newTT);
added = true;
}
}
}
}
if (tmp_basic_input2.size() == 16u)
{
if (basic_symmetry_gates.find(entry) != basic_symmetry_gates.end())
fcs_s.emplace_back(entry);
else
fcs_us.emplace_back(entry);
}
}
std::cout << "symmetry gates:" << std::endl;
for (auto fc : fcs_s)
{
std::cout << "\t" << gate_map2[fc] << std::endl;
}
std::cout << "unsymmetry gates:" << std::endl;
for (auto fc : fcs_us)
{
std::cout << "\t" << gate_map2[fc] << std::endl;
}
}
void explore_2_2()
{
uint i = 0u, j = 0u, k = 0u, l = 0u;
bool added = true;
std::set<std::tuple<std::string, std::string>> fcs;
for (i = 0u; i < 16u; ++i)
{
for (l = i + 1; l < 16u; ++l)
{
std::string entry1 = uint_2_string(i, 4);
std::string entry2 = uint_2_string(l, 4);
std::vector<std::string> tmp_basic_input2 = basic_input2;
std::set<std::string> tmp_set(tmp_basic_input2.begin(), tmp_basic_input2.end());
added = true;
while (added)
{
added = false;
for (j = 0; j < tmp_basic_input2.size(); ++j)
{
for (k = 0; k < tmp_basic_input2.size(); ++k)
{
std::string newTT1 = compute_new_tt_2(entry1, tmp_basic_input2[j], tmp_basic_input2[k]);
std::string newTT2 = compute_new_tt_2(entry2, tmp_basic_input2[j], tmp_basic_input2[k]);
if (tmp_set.find(newTT1) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT1);
tmp_set.insert(newTT1);
added = true;
}
if (tmp_set.find(newTT2) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT2);
tmp_set.insert(newTT2);
added = true;
}
}
}
}
if (tmp_basic_input2.size() == 16u)
{
std::vector<std::string> entries({entry1, entry2});
std::sort(entries.begin(), entries.end());
fcs.insert(std::make_tuple(entries[0], entries[1]));
}
}
}
for (auto fc : fcs)
{
std::cout << "\t" << gate_map2[std::get<0>(fc)] << ", " << gate_map2[std::get<1>(fc)] << std::endl;
}
}
void explore_2_3()
{
uint i = 0u, l = 0u, m = 0u, j = 0u, k = 0u, u = 0u;
bool added = true;
std::set<std::tuple<std::string, std::string, std::string>> fcs;
for (i = 0u; i < 16u; ++i)
{
for (l = i + 1; l < 16u; ++l)
{
for (m = l + 1; m < 16u; ++m)
{
std::string entry1 = uint_2_string(i, 4);
std::string entry2 = uint_2_string(l, 4);
std::string entry3 = uint_2_string(m, 4);
std::vector<std::string> tmp_basic_input2 = basic_input2;
std::set<std::string> tmp_set(tmp_basic_input2.begin(), tmp_basic_input2.end());
added = true;
while (added)
{
added = false;
for (j = 0; j < tmp_basic_input2.size(); ++j)
{
for (k = 0; k < tmp_basic_input2.size(); ++k)
{
std::string newTT1 = compute_new_tt_2(entry1, tmp_basic_input2[j], tmp_basic_input2[k]);
std::string newTT2 = compute_new_tt_2(entry2, tmp_basic_input2[j], tmp_basic_input2[k]);
std::string newTT3 = compute_new_tt_2(entry3, tmp_basic_input2[j], tmp_basic_input2[k]);
if (tmp_set.find(newTT1) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT1);
tmp_set.insert(newTT1);
added = true;
}
if (tmp_set.find(newTT2) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT2);
tmp_set.insert(newTT2);
added = true;
}
if (tmp_set.find(newTT3) == tmp_set.end())
{
tmp_basic_input2.emplace_back(newTT3);
tmp_set.insert(newTT3);
added = true;
}
}
}
}
if (tmp_basic_input2.size() == 16u)
{
std::vector<std::string> entries({entry1, entry2, entry3});
std::sort(entries.begin(), entries.end());
fcs.insert(std::make_tuple(entries[0], entries[1], entries[2]));
}
}
}
}
for (auto fc : fcs)
{
std::cout << "\t" << gate_map2[std::get<0>(fc)] << ", " << gate_map2[std::get<1>(fc)] << ", " << gate_map2[std::get<2>(fc)] << std::endl;
}
}
void explore_3_1()
{
uint i = 0u, j = 0u, k = 0u, l = 0u;
bool added = true;
std::vector<std::string> fcs;
for (i = 0u; i < 256u; ++i)
{
std::string entry = uint_2_string(i, 8);
std::vector<std::string> tmp_basic_input3 = basic_input3;
std::set<std::string> tmp_set(tmp_basic_input3.begin(), tmp_basic_input3.end());
std::cout << "try entry: " << entry << std::endl;
added = true;
while (added)
{
added = false;
for (j = 0; j < tmp_basic_input3.size(); ++j)
{
for (k = 0; k < tmp_basic_input3.size(); ++k)
{
for (l = 0; l < tmp_basic_input3.size(); ++l)
{
std::string newTT = compute_new_tt_3(entry, tmp_basic_input3[j], tmp_basic_input3[k], tmp_basic_input3[l]);
if (tmp_set.find(newTT) == tmp_set.end())
{
tmp_basic_input3.emplace_back(newTT);
tmp_set.insert(newTT);
added = true;
}
}
}
}
}
if (tmp_basic_input3.size() == 16u)
{
fcs.emplace_back(entry);
}
}
for (auto fc : fcs)
{
std::cout << fc << std::endl;
}
}
int main(int argc, char **argv)
{
std::cout << "Funational Completeness exploration for 2-inputs gate:" << std::endl;
std::cout << "One gate:" << std::endl;
explore_2_1();
std::cout << "Two gates:" << std::endl;
explore_2_2();
std::cout << "Three gates:" << std::endl;
explore_2_3();
// std::cout << "Funational Completeness exploration for 3-inputs gate:" << std::endl;
// explore_3_1();
return 1;
}