Convert NFA to DFA as quickly as possible.
Input
Your input will be an NFA. In order to be able to test your code, it needs to be able to handle an NFA in the following format. This is taken directly from GAP (and slightly simplified).
Automaton( Type, Size, Alphabet, TransitionTable, Initial, Accepting )
For the input, Type will always be "nondet". Size is a positive integer representing the number of states of the automaton. Alphabet is the number of letters of the alphabet. TransitionTable is the transition matrix. The entries are lists of non-negative integers not greater than the size of the automaton are also allowed. Initial and Accepting are, respectively, the lists of initial and accepting states.
Example input:
Automaton("nondet", 4, 2, [[[], [2], [3], [1, 2, 3, 4], [2, 4]],
[[], [1, 3, 4], [1], [2, 4]]], [1], [2, 3])
This is slightly easier to read as a transition table.
| 1 2 3 4
--------------------------------------------------
a | [ 2 ] [ 1, 2, 3, 4 ] [ 2, 4 ]
b | [ 1, 3, 4 ] [ 1 ] [ 2, 4 ]
Initial state: [ 1 ]
Accepting states: [ 2, 3 ]
Output
Your output must be a DFA that is equivalent to the input NFA. There is no need for your DFA to be minimal. For the output, Type will always be "det". Size is a positive integer representing the number of states of the automaton. Alphabet is the number of letters of the alphabet. TransitionTable is the transition matrix. The entries are non-negative integers not greater than the size of the automaton. The states should be labelled by consecutive integers. Initial and Accepting are, respectively, the lists of initial and accepting states. In the case of the example above, this would be:
Automaton("det", 2, 2, [[2, 2], [2, 2]], [1], [])
As a transition table this is:
| 1 2
-----------
a | 2 2
b | 2 2
Initial state: [ 1 ]
Accepting state: [ ]
(It is now clear this is a DFA that will not accept any input strings.)
Test cases:
- Input:
Automaton("nondet",2,4,[[[1], [2]], [[2], []], [[2], []] , [[1], [2]]],[1],[1, 2]))
As a transition matrix:
| 1 2
-------------------
a | [ 1 ] [ 2 ]
b | [ 2 ]
c | [ 2 ]
d | [ 1 ] [ 2 ]
Initial state: [ 1 ]
Accepting states: [ 1, 2 ]
Here is the diagram of the NFA.
Output:
Automaton("det",3, 4,[[1, 2, 3], [2, 3, 3], [2, 3, 3], [1, 2, 3]], [1],[1, 2])
As a transition matrix:
| 1 2 3
--------------
a | 1 2 3
b | 2 3 3
c | 2 3 3
d | 1 2 3
Initial state: [ 1 ]
Accepting states: [ 1, 2 ]
Here is the diagram of the DFA.
- Input:
Automaton("nondet",7,4,[[[1, 3, 4, 5], [2], [3], [3, 4], [3, 5], [], []], [[2, 3, 4, 7], [3], [], [], [3, 7], [3, 4], []], [[2, 3, 5, 6], [3], [], [3, 6], [], [], [3, 5]], [[1, 3, 6, 7], [2], [3], [], [], [3, 6], [3, 7]]],[1],[1, 2, 3, 4, 5, 6, 7])
Output:
- Input:
Automaton("nondet",12, 4,[[[1, 3, 5, 6], [2, 4, 7, 8], [3], [6], [3, 5], [3, 6], [4, 7], [4, 8], [4, 7], [4, 8], [], []], [[2, 3, 5, 10], [3, 4, 7, 12], [6], [], [4, 7], [3, 10], [], [4, 12], [3, 5], [4, 12], [4, 7], []], [[2, 3, 6, 9], [3, 4, 8, 11], [6], [], [3, 9], [4, 8], [4, 11], [], [4, 11], [3, 6], [], [4, 8 ]], [[1, 3, 9, 10], [2, 4, 11, 12], [3], [6], [4, 11], [4, 12], [], [], [3, 9], [3, 10], [4, 11], [4, 12]]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
Output:
Automaton("det",39, 4,[[1, 2, 3, 3, 5, 24, 7, 8, 22, 20, 8, 32, 18, 18, 3, 19, 25, 18, 19, 20, 25, 22, 23, 24, 25, 25, 24, 23, 5, 2, 35, 32, 19, 19, 35, 36, 36, 36, 36], [1, 38, 1, 23, 15, 9, 11, 26, 23, 28, 26, 10, 9, 26, 1, 3, 22, 26, 3, 28, 22, 23, 1, 15, 3, 3, 15, 1, 28, 27, 10, 27, 23, 23, 38, 15, 28, 15, 28], [1, 5, 1, 1, 1, 4, 12, 6, 6, 31, 31, 37, 37, 30, 5, 5, 29, 37, 3, 21, 4, 21, 4, 4, 4, 29, 30, 29, 1, 5, 29, 37, 5, 3, 29, 3, 3, 2, 2], [1, 16, 3, 4, 3, 21, 7, 18, 33, 39, 14, 13, 13, 14, 15, 16, 17, 18, 19, 34, 21, 34, 3, 19, 19, 16, 38, 15, 4, 33, 17, 18, 33, 34, 16, 19, 34, 38, 39]],[7],[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39])
- Input:
Automaton("nondet",25,4,[[[1, 3, 6, 7], [2, 4, 8, 9], [3, 5, 10, 11], [6], [7], [3, 5, 6, 10, 18], [3, 5, 7, 11, 19], [4, 8], [4, 9 ], [5, 10], [5, 11], [4, 5, 8, 10, 22], [4, 5, 9, 11, 23], [5, 10], [5, 11], [], [], [5, 10, 18], [5, 11, 19], [5, 10, 22], [5, 11, 23 ], [], [], [], []], [[2, 3, 6, 13], [3, 4, 8, 15], [4, 5, 10, 17], [7], [], [4, 5, 8, 10, 18], [3, 5, 13, 17, 21], [5, 10], [4, 15], [], [5, 17], [3, 5, 6, 10, 22], [4, 5, 15, 17, 25], [4, 8], [5, 17], [5, 10], [], [], [5, 17, 21], [], [5, 17, 25], [5, 10, 18], [], [5, 10, 22], []], [[2, 3, 7, 12], [3, 4, 9, 14], [4, 5, 11, 16], [7], [], [3, 5, 12, 16, 20], [4, 5, 9, 11, 19], [4, 14], [5, 11], [5, 16], [], [4, 5, 14, 16, 24], [3, 5, 7, 11, 23], [5, 16], [4, 9], [], [5, 11], [5, 16, 20], [], [5, 16, 24], [], [], [5, 11, 19], [], [5, 11, 23]], [[1, 3, 12, 13], [2, 4, 14, 15], [3, 5, 16, 17], [6], [7], [4, 5, 14, 16, 20], [4, 5, 15, 17, 21], [5, 16], [5, 17], [], [], [3, 5, 12, 16, 24], [3, 5, 13, 17, 25], [4, 14], [4, 15], [5, 16], [5, 17], [], [], [], [], [5, 16, 20], [5, 17, 21], [5, 16, 24], [5, 17, 25]]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])
Output:
Automaton("det",266,4,[[1, 127, 50, 50, 115, 249, 50, 8, 257, 10, 151, 12, 13, 14, 81, 78, 34, 106, 137, 107, 21, 22, 82, 89, 71, 43, 43, 62, 63, 63, 44, 10, 179, 171, 214, 265, 206, 38, 137, 152, 21, 151, 71, 22, 41, 41, 47, 13, 49, 50, 50, 210, 50, 210, 116, 90, 64, 49, 207, 207, 207, 62, 232, 64, 64, 89, 151, 236, 236, 70, 71, 236, 116, 260, 128, 75, 13, 38, 77, 133, 14, 82, 13, 13, 77, 235, 64, 64, 231, 206, 138, 91, 91, 206, 90, 264, 137, 169, 10, 10, 41, 71, 232, 228, 232, 21, 21, 107, 106, 110, 111, 266, 256, 114, 114, 116, 251, 251, 116, 114, 114, 111, 266, 260, 122, 182, 127, 128, 129, 213, 132, 132, 129, 49, 49, 138, 138, 138, 249, 71, 43, 43, 210, 235, 183, 214, 132, 265, 206, 138, 232, 64, 64, 153, 153, 64, 152, 152, 82, 236, 236, 82, 116, 116, 64, 207, 266, 64, 231, 169, 171, 250, 227, 70, 175, 175, 176, 10, 47, 178, 178, 110, 111, 266, 260, 122, 266, 127, 213, 49, 49, 152, 257, 153, 257, 90, 90, 183, 250, 264, 62, 228, 229, 82, 82, 206, 64, 266, 249, 249, 249, 242, 213, 214, 64, 116, 114, 114, 50, 50, 236, 236, 261, 115, 152, 251, 8, 228, 229, 229, 231, 232, 237, 235, 235, 236, 237, 235, 235, 235, 235, 235, 235, 242, 242, 242, 115, 251, 249, 250, 116, 116, 116, 207, 64, 265, 266, 257, 256, 266, 264, 261, 260, 264, 265, 266], [1, 125, 1, 114, 114, 121, 115, 3, 23, 19, 13, 15, 230, 28, 201, 202, 16, 84, 123, 103, 105, 208, 114, 84, 172, 199, 199, 119, 83, 83, 123, 170, 16, 31, 27, 26, 25, 104, 102, 23, 28, 13, 120, 208, 48, 103, 19, 230, 239, 1, 114, 218, 115, 219, 82, 140, 23, 208, 204, 216, 216, 119, 174, 119, 119, 84, 13, 115, 115, 50, 120, 50, 82, 204, 262, 79, 230, 104, 203, 85, 28, 114, 230, 230, 203, 3, 23, 119, 96, 96, 96, 123, 102, 140, 208, 3, 200, 200, 98, 97, 103, 120, 119, 120, 119, 28, 105, 103, 105, 54, 3, 23, 141, 1, 250, 50, 82, 114, 50, 1, 250, 3, 3, 219, 219, 125, 54, 263, 124, 124, 27, 124, 223, 208, 239, 25, 208, 208, 120, 120, 217, 217, 217, 120, 120, 142, 142, 141, 140, 140, 174, 174, 174, 204, 216, 23, 119, 23, 250, 114, 114, 250, 162, 162, 159, 205, 159, 159, 208, 123, 170, 1, 219, 50, 208, 208, 123, 177, 177, 19, 170, 173, 172, 172, 199, 199, 23, 186, 185, 184, 184, 23, 120, 216, 23, 140, 208, 120, 1, 3, 119, 120, 114, 114, 250, 239, 119, 3, 121, 3, 120, 219, 212, 212, 23, 50, 1, 250, 1, 114, 50, 114, 219, 114, 23, 114, 3, 120, 114, 114, 208, 119, 125, 121, 3, 50, 54, 120, 3, 120, 121, 3, 120, 218, 219, 217, 114, 114, 3, 1, 250, 250, 250, 253, 252, 173, 172, 120, 125, 3, 3, 219, 219, 3, 54, 3], [1, 1, 249, 249, 6, 1, 1, 247, 7, 130, 167, 17, 11, 66, 33, 33, 131, 136, 10, 32, 150, 9, 112, 36, 149, 112, 149, 56, 167, 37, 181, 130, 35, 147, 139, 51, 139, 11, 10, 234, 147, 37, 148, 113, 136, 136, 146, 24, 249, 1, 1, 249, 249, 249, 139, 6, 238, 127, 134, 238, 134, 9, 148, 238, 134, 167, 36, 50, 249, 247, 73, 249, 51, 139, 112, 167, 76, 76, 11, 167, 80, 73, 67, 66, 66, 135, 58, 58, 112, 139, 233, 100, 100, 2, 6, 95, 10, 32, 130, 130, 99, 94, 94, 56, 149, 150, 147, 150, 136, 51, 51, 51, 7, 51, 51, 51, 7, 6, 139, 139, 139, 2, 58, 134, 139, 7, 1, 112, 112, 249, 238, 238, 112, 249, 127, 238, 233, 238, 1, 149, 112, 149, 249, 135, 7, 139, 238, 51, 139, 238, 112, 238, 233, 234, 234, 134, 234, 190, 112, 50, 249, 73, 139, 51, 238, 134, 51, 134, 148, 32, 147, 145, 145, 145, 258, 259, 180, 130, 146, 189, 189, 51, 51, 134, 134, 139, 2, 1, 249, 127, 249, 191, 191, 191, 188, 188, 188, 188, 198, 197, 196, 196, 195, 187, 187, 139, 233, 134, 127, 127, 127, 49, 249, 139, 243, 211, 211, 211, 210, 210, 210, 210, 95, 209, 241, 209, 126, 117, 117, 9, 112, 112, 50, 50, 50, 50, 50, 50, 49, 49, 127, 127, 127, 249, 249, 249, 7, 7, 1, 247, 51, 139, 211, 134, 134, 51, 51, 7, 7, 2, 126, 145, 139, 247, 51, 51], [1, 51, 3, 4, 4, 7, 7, 50, 73, 61, 11, 12, 40, 109, 101, 93, 45, 18, 19, 20, 21, 64, 161, 29, 193, 118, 193, 65, 11, 42, 19, 59, 30, 46, 163, 164, 163, 40, 39, 57, 46, 42, 246, 60, 18, 21, 61, 158, 72, 50, 51, 53, 53, 3, 55, 55, 57, 246, 156, 64, 65, 64, 155, 64, 65, 11, 29, 68, 69, 236, 160, 72, 73, 55, 157, 11, 154, 154, 40, 11, 46, 160, 225, 192, 192, 86, 87, 88, 157, 118, 155, 19, 39, 74, 161, 239, 92, 92, 166, 254, 20, 144, 88, 240, 65, 109, 108, 21, 21, 50, 50, 73, 73, 50, 247, 236, 73, 161, 72, 3, 5, 54, 86, 239, 3, 51, 50, 64, 64, 161, 165, 64, 157, 161, 245, 165, 60, 64, 51, 240, 161, 240, 4, 144, 51, 55, 57, 73, 55, 57, 157, 157, 155, 57, 64, 156, 64, 87, 118, 160, 161, 248, 163, 164, 165, 168, 164, 168, 60, 19, 108, 3, 3, 72, 64, 60, 19, 194, 194, 61, 59, 247, 247, 193, 193, 5, 74, 7, 69, 244, 69, 156, 240, 65, 74, 74, 246, 143, 219, 86, 88, 144, 222, 222, 226, 72, 60, 239, 52, 54, 143, 239, 72, 72, 215, 221, 219, 224, 219, 220, 221, 222, 239, 220, 215, 222, 54, 160, 160, 161, 64, 64, 160, 68, 236, 236, 236, 160, 239, 240, 244, 245, 246, 69, 72, 161, 51, 160, 50, 50, 248, 118, 226, 255, 255, 248, 248, 160, 160, 245, 245, 72, 72, 236, 236, 236]],[12],[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266])
- Input:
Automaton("nondet",38,4,[[[1, 3, 7, 8], [2, 4, 9, 10], [3, 5, 11, 12], [4, 6, 13, 14], [7], [8], [3, 5, 7, 11, 23], [3, 5, 8, 12, 24], [4, 6, 9, 13, 25], [4, 6, 10, 14, 26], [5, 11], [5, 12], [6, 13], [6, 14], [4, 5, 9, 11, 31], [4, 5, 10, 12, 32], [5, 6, 11, 13, 33], [5, 6, 12, 14, 34], [6, 13], [6, 14], [], [], [5, 11, 23], [5, 12, 24], [6, 13, 25], [6, 14, 26], [5, 11, 31], [5, 12, 32], [6, 13, 33], [6, 14, 34], [6, 13, 25], [6, 14, 26], [], [], [6, 13, 33], [6, 14, 34], [], []], [[2, 3, 7, 16], [3, 4, 9, 18], [4, 5, 11, 20], [5, 6, 13, 22], [8], [], [4, 5, 9, 11, 23], [3, 5, 16, 20, 28], [5, 6, 11, 13, 25], [4, 6, 18, 22, 30], [6, 13], [5, 20], [], [6, 22], [3, 5, 7, 11, 31], [4, 5, 18, 20, 36], [4, 6, 9, 13, 33], [5, 6, 20, 22, 38], [5, 11], [6, 22], [6, 13], [], [6, 13, 25], [5, 20, 28], [], [6, 22, 30], [6, 13, 33], [5, 20, 36], [], [6, 22, 38], [5, 11, 23], [6, 22, 30], [6, 13, 25], [], [5, 11, 31], [6, 22, 38], [6, 13, 33], []], [[2, 3, 8, 15], [3, 4, 10, 17], [4, 5, 12, 19], [5, 6, 14, 21], [8], [], [3, 5, 15, 19, 27], [4, 5, 10, 12, 24], [4, 6, 17, 21, 29], [5, 6, 12, 14, 26], [5, 19], [6, 14], [6, 21], [], [4, 5, 17, 19, 35], [3, 5, 8, 12, 32], [5, 6, 19, 21, 37], [4, 6, 10, 14, 34], [6, 21], [5, 12], [], [6, 14], [5, 19, 27], [6, 14, 26], [6, 21, 29], [], [5, 19, 35], [6, 14, 34], [6, 21, 37], [], [6, 21, 29], [5, 12, 24], [], [6, 14, 26 ], [6, 21, 37], [5, 12, 32], [], [6, 14, 34]], [[1, 3, 15, 16], [2, 4, 17, 18], [3, 5, 19, 20], [4, 6, 21, 22], [7], [8], [ 4, 5, 17, 19, 27], [4, 5, 18, 20, 28], [5, 6, 19, 21, 29], [5, 6, 20, 22, 30], [6, 21], [6, 22], [], [], [3, 5, 15, 19, 35], [3, 5, 16, 20, 36], [4, 6, 17, 21, 37], [4, 6, 18, 22, 38], [5, 19], [5, 20], [6, 21], [6, 22], [6, 21, 29], [6, 22, 30], [], [], [6, 21, 37], [6, 22, 38], [], [], [5, 19, 27], [5, 20, 28], [6, 21, 29], [6, 22, 30], [5, 19, 35], [5, 20, 36], [6, 21, 37], [6, 22, 38]]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38])
Output
- Input:
Automaton("nondet",67,4,[[[1, 3, 8, 9], [2, 4, 10, 11], [3, 5, 12, 13], [4, 6, 14, 15], [5, 7, 16, 17], [8], [8], [3, 5, 8, 12, 28], [3, 5, 9, 13, 29], [4, 6, 10, 14, 30], [4, 6, 11, 15, 31], [5, 7, 12, 16, 32], [5, 7, 13, 17, 33], [6, 14], [6, 15], [ 7, 16], [7, 17], [4, 5, 10, 12, 40], [4, 5, 11, 13, 41], [5, 6, 12, 14, 42], [5, 6, 13, 15, 43], [6, 7, 14, 16, 44], [6, 7, 15, 17, 45], [7, 16], [7, 17], [], [], [5, 7, 12, 16, 28, 32, 52], [5, 7, 13, 17, 29, 33, 53], [6, 14, 30], [6, 15, 31], [7, 16, 32], [7, 17, 33], [5, 7, 12, 16, 40, 44, 56], [5, 7, 13, 17, 41, 45, 57], [6, 14, 42], [6, 15, 43], [7, 16, 44], [7, 17, 45], [6, 7, 14, 16, 30, 32, 60], [6, 7, 15, 17, 31, 33, 61], [7, 16, 32], [7, 17, 33], [], [], [6, 7, 14, 16, 42, 44, 64], [6, 7, 15, 17, 43, 45, 65], [7, 16, 44], [7, 17, 45], [], [], [7, 16, 32, 52], [7, 17, 33, 53], [7, 16, 44, 56], [7, 17, 45, 57], [7, 16, 32, 60], [7, 17, 33, 61], [7, 16, 44, 64], [7, 17, 45, 65], [], [], [], [], [], [], [], []], [[2, 3, 8, 19], [3, 4, 10, 21], [4, 5, 12, 23], [5, 6, 14, 25], [6, 7, 16, 27], [8], [], [4, 5, 10, 12, 28], [3, 5, 19, 23, 35], [5, 6, 12, 14, 30], [4, 6, 21, 25, 37], [6, 7, 14, 16, 32], [5, 7, 23, 27, 39], [7, 16], [6, 25], [], [7, 27], [3, 5, 8, 12, 40], [4, 5, 21, 23, 47], [4, 6, 10, 14, 42], [5, 6, 23, 25, 49], [5, 7, 12, 16, 44], [6, 7, 25, 27, 51], [6, 14], [7, 27], [7, 16], [], [6, 7, 14, 16, 30, 32, 52], [5, 7, 23, 27, 35, 39, 55], [7, 16, 32], [6, 25, 37], [], [7, 27, 39], [6, 7, 14, 16, 42, 44, 56], [5, 7, 23, 27, 47, 51, 59], [7, 16, 44], [6, 25, 49], [], [7, 27, 51], [5, 7, 12, 16, 28, 32, 60], [6, 7, 25, 27, 37, 39, 63], [6, 14, 30], [7, 27, 39], [7, 16, 32], [], [5, 7, 12, 16, 40, 44, 64], [6, 7, 25, 27, 49, 51, 67], [6, 14, 42], [7, 27, 51], [7, 16, 44], [], [], [7, 27, 39, 55], [], [7, 27, 51, 59], [], [7, 27, 39, 63], [], [7, 27, 51, 67], [7, 16, 32, 52], [], [7, 16, 44, 56], [], [7, 16, 32, 60], [], [7, 16, 44, 64], []], [[2, 3, 9, 18], [3, 4, 11, 20], [4, 5, 13, 22], [5, 6, 15, 24], [6, 7, 17, 26], [8], [], [3, 5, 18, 22, 34], [4, 5, 11, 13, 29], [4, 6, 20, 24, 36], [5, 6, 13, 15, 31], [5, 7, 22, 26, 38], [6, 7, 15, 17, 33], [6, 24], [7, 17], [7, 26 ], [], [4, 5, 20, 22, 46], [3, 5, 9, 13, 41], [5, 6, 22, 24, 48], [4, 6, 11, 15, 43], [6, 7, 24, 26, 50], [5, 7, 13, 17, 45], [7, 26], [6, 15], [], [7, 17], [5, 7, 22, 26, 34, 38, 54], [6, 7, 15, 17, 31, 33, 53], [6, 24, 36], [7, 17, 33], [7, 26, 38], [], [ 5, 7, 22, 26, 46, 50, 58], [6, 7, 15, 17, 43, 45, 57], [6, 24, 48], [7, 17, 45], [7, 26, 50], [], [6, 7, 24, 26, 36, 38, 62], [5, 7, 13, 17, 29, 33, 61], [7, 26, 38], [6, 15, 31], [], [7, 17, 33], [6, 7, 24, 26, 48, 50, 66], [5, 7, 13, 17, 41, 45, 65], [7, 26, 50], [6, 15, 43], [], [7, 17, 45], [7, 26, 38, 54], [], [7, 26, 50, 58], [], [7, 26, 38, 62], [], [7, 26, 50, 66], [], [], [7, 17, 33, 53], [], [7, 17, 45, 57], [], [7, 17, 33, 61], [], [7, 17, 45, 65]], [[1, 3, 18, 19], [2, 4, 20, 21], [3, 5, 22, 23 ], [4, 6, 24, 25], [5, 7, 26, 27], [8], [8], [4, 5, 20, 22, 34], [4, 5, 21, 23, 35], [5, 6, 22, 24, 36], [5, 6, 23, 25, 37], [6, 7, 24, 26, 38], [6, 7, 25, 27, 39], [7, 26], [7, 27], [], [], [3, 5, 18, 22, 46], [3, 5, 19, 23, 47], [4, 6, 20, 24, 48], [4, 6, 21, 25, 49], [5, 7, 22, 26, 50], [5, 7, 23, 27, 51], [6, 24], [6, 25], [7, 26], [7, 27], [6, 7, 24, 26, 36, 38, 54], [6, 7, 25, 27, 37, 39, 55], [7, 26, 38], [7, 27, 39], [], [], [6, 7, 24, 26, 48, 50, 58], [6, 7, 25, 27, 49, 51, 59], [7, 26, 50], [7, 27, 51], [], [], [5, 7, 22, 26, 34, 38, 62], [5, 7, 23, 27, 35, 39, 63], [6, 24, 36], [6, 25, 37], [7, 26, 38], [7, 27, 39], [5, 7, 22, 26, 46, 50, 66], [5, 7, 23, 27, 47, 51, 67], [6, 24, 48], [6, 25, 49], [7, 26, 50], [7, 27, 51], [], [], [], [], [], [], [], [], [7, 26, 38, 54], [7, 27, 39, 55], [7, 26, 50, 58], [7, 27, 51, 59], [7, 26, 38, 62], [7, 27, 39, 63], [7, 26, 50, 66], [7, 27, 51, 67]]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67])
Output
- Input:
Automaton("nondet",96,4,[[[1, 3, 9, 10], [2, 4, 11, 12], [3, 5, 13, 14], [4, 6, 15, 16], [5, 7, 17, 18], [6, 8, 19, 20], [7 ], [8], [3, 5, 9, 13, 33], [3, 5, 10, 14, 34], [4, 6, 11, 15, 35], [4, 6, 12, 16, 36], [5, 7, 13, 17, 37], [5, 7, 14, 18, 38], [6, 8, 15, 19, 39], [6, 8, 16, 20, 40], [7, 17], [7, 18], [8, 19], [8, 20], [4, 5, 11, 13, 49], [4, 5, 12, 14, 50], [5, 6, 13, 15, 51], [5, 6, 14, 16, 52], [6, 7, 15, 17, 53], [6, 7, 16, 18, 54], [7, 8, 17, 19, 55], [7, 8, 18, 20, 56], [8, 19], [8, 20], [], [], [5, 7, 13, 17, 33, 37, 65], [5, 7, 14, 18, 34, 38, 66], [6, 8, 15, 19, 35, 39, 67], [6, 8, 16, 20, 36, 40, 68], [7, 17, 37], [7, 18, 38], [8, 19, 39], [8, 20, 40], [5, 7, 13, 17, 49, 53, 73], [5, 7, 14, 18, 50, 54, 74], [6, 8, 15, 19, 51, 55, 75], [6, 8, 16, 20, 52, 56, 76], [7, 17, 53], [7, 18, 54], [8, 19, 55], [8, 20, 56], [6, 7, 15, 17, 35, 37, 81], [6, 7, 16, 18, 36, 38, 82], [7, 8, 17, 19, 37, 39, 83], [7, 8, 18, 20, 38, 40, 84], [8, 19, 39], [8, 20, 40], [], [], [6, 7, 15, 17, 51, 53, 89], [6, 7, 16, 18, 52, 54, 90], [7, 8, 17, 19, 53, 55, 91], [7, 8, 18, 20, 54, 56, 92], [8, 19, 55], [8, 20, 56], [], [], [7, 17, 37, 65], [7, 18, 38, 66 ], [8, 19, 39, 67], [8, 20, 40, 68], [7, 17, 53, 73], [7, 18, 54, 74], [8, 19, 55, 75], [8, 20, 56, 76], [7, 17, 37, 81], [7, 18, 38, 82], [8, 19, 39, 83], [8, 20, 40, 84], [7, 17, 53, 89], [7, 18, 54, 90], [8, 19, 55, 91], [8, 20, 56, 92], [8, 19, 39, 67], [8, 20, 40, 68], [], [], [8, 19, 55, 75], [8, 20, 56, 76], [], [], [8, 19, 39, 83], [8, 20, 40, 84], [], [], [8, 19, 55, 91], [8, 20, 56, 92], [], []], [[2, 3, 9, 22], [3, 4, 11, 24], [4, 5, 13, 26], [5, 6, 15, 28], [6, 7, 17, 30], [7, 8, 19, 32], [8 ], [], [4, 5, 11, 13, 33], [3, 5, 22, 26, 42], [5, 6, 13, 15, 35], [4, 6, 24, 28, 44], [6, 7, 15, 17, 37], [5, 7, 26, 30, 46], [7, 8, 17, 19, 39], [6, 8, 28, 32, 48], [8, 19], [7, 30], [], [8, 32], [3, 5, 9, 13, 49], [4, 5, 24, 26, 58], [4, 6, 11, 15, 51], [ 5, 6, 26, 28, 60], [5, 7, 13, 17, 53], [6, 7, 28, 30, 62], [6, 8, 15, 19, 55], [7, 8, 30, 32, 64], [7, 17], [8, 32], [8, 19], [], [6, 7, 15, 17, 35, 37, 65], [5, 7, 26, 30, 42, 46, 70], [7, 8, 17, 19, 37, 39, 67], [6, 8, 28, 32, 44, 48, 72], [8, 19, 39], [7, 30, 46], [], [8, 32, 48], [6, 7, 15, 17, 51, 53, 73], [5, 7, 26, 30, 58, 62, 78], [7, 8, 17, 19, 53, 55, 75], [6, 8, 28, 32, 60, 64, 80], [8, 19, 55], [7, 30, 62], [], [8, 32, 64], [5, 7, 13, 17, 33, 37, 81], [6, 7, 28, 30, 44, 46, 86], [6, 8, 15, 19, 35, 39, 83], [7, 8, 30, 32, 46, 48, 88], [7, 17, 37], [8, 32, 48], [8, 19, 39], [], [5, 7, 13, 17, 49, 53, 89], [6, 7, 28, 30, 60, 62, 94], [6, 8, 15, 19, 51, 55, 91], [7, 8, 30, 32, 62, 64, 96], [7, 17, 53], [8, 32, 64], [8, 19, 55], [], [8, 19, 39, 67], [7, 30, 46, 70], [], [8, 32, 48, 72], [8, 19, 55, 75], [7, 30, 62, 78], [], [8, 32, 64, 80], [8, 19, 39, 83], [7, 30, 46, 86], [], [8, 32, 48, 88], [8, 19, 55, 91], [7, 30, 62, 94], [], [8, 32, 64, 96], [7, 17, 37, 65], [8, 32, 48, 72], [8, 19, 39, 67], [], [7, 17, 53, 73], [8, 32, 64, 80], [8, 19, 55, 75], [], [7, 17, 37, 81], [8, 32, 48, 88], [8, 19, 39, 83], [], [7, 17, 53, 89], [8, 32, 64, 96 ], [8, 19, 55, 91], []], [[2, 3, 10, 21], [3, 4, 12, 23], [4, 5, 14, 25], [5, 6, 16, 27], [6, 7, 18, 29], [7, 8, 20, 31], [8], [], [3, 5, 21, 25, 41], [4, 5, 12, 14, 34], [4, 6, 23, 27, 43], [5, 6, 14, 16, 36], [5, 7, 25, 29, 45], [6, 7, 16, 18, 38], [6, 8, 27, 31, 47], [7, 8, 18, 20, 40], [7, 29], [8, 20], [8, 31], [], [4, 5, 23, 25, 57], [3, 5, 10, 14, 50], [5, 6, 25, 27, 59], [ 4, 6, 12, 16, 52], [6, 7, 27, 29, 61], [5, 7, 14, 18, 54], [7, 8, 29, 31, 63], [6, 8, 16, 20, 56], [8, 31], [7, 18], [], [8, 20 ], [5, 7, 25, 29, 41, 45, 69], [6, 7, 16, 18, 36, 38, 66], [6, 8, 27, 31, 43, 47, 71], [7, 8, 18, 20, 38, 40, 68], [7, 29, 45], [8, 20, 40], [8, 31, 47], [], [5, 7, 25, 29, 57, 61, 77], [6, 7, 16, 18, 52, 54, 74], [6, 8, 27, 31, 59, 63, 79], [7, 8, 18, 20, 54, 56, 76], [7, 29, 61], [8, 20, 56], [8, 31, 63], [], [6, 7, 27, 29, 43, 45, 85], [5, 7, 14, 18, 34, 38, 82], [7, 8, 29, 31, 45, 47, 87], [6, 8, 16, 20, 36, 40, 84], [8, 31, 47], [7, 18, 38], [], [8, 20, 40], [6, 7, 27, 29, 59, 61, 93], [5, 7, 14, 18, 50, 54, 90], [7, 8, 29, 31, 61, 63, 95], [6, 8, 16, 20, 52, 56, 92], [8, 31, 63], [7, 18, 54], [], [8, 20, 56], [7, 29, 45, 69], [8, 20, 40, 68], [8, 31, 47, 71], [], [7, 29, 61, 77], [8, 20, 56, 76], [8, 31, 63, 79], [], [7, 29, 45, 85], [8, 20, 40, 84], [8, 31, 47, 87], [], [7, 29, 61, 93], [8, 20, 56, 92], [8, 31, 63, 95], [], [8, 31, 47, 71], [7, 18, 38, 66], [], [8, 20, 40, 68], [8, 31, 63, 79], [7, 18, 54, 74], [], [8, 20, 56, 76], [8, 31, 47, 87], [7, 18, 38, 82], [], [8, 20, 40, 84], [8, 31, 63, 95], [7, 18, 54, 90 ], [], [8, 20, 56, 92]], [[1, 3, 21, 22], [2, 4, 23, 24], [3, 5, 25, 26], [4, 6, 27, 28], [5, 7, 29, 30], [6, 8, 31, 32], [8], [8], [4, 5, 23, 25, 41], [4, 5, 24, 26, 42], [5, 6, 25, 27, 43], [5, 6, 26, 28, 44], [6, 7, 27, 29, 45], [6, 7, 28, 30, 46], [7, 8, 29, 31, 47], [7, 8, 30, 32, 48], [8, 31], [8, 32], [], [], [3, 5, 21, 25, 57], [3, 5, 22, 26, 58], [4, 6, 23, 27, 59], [4, 6, 24, 28, 60], [5, 7, 25, 29, 61], [5, 7, 26, 30, 62], [6, 8, 27, 31, 63], [6, 8, 28, 32, 64], [7, 29], [7, 30], [8, 31], [8, 32], [6, 7, 27, 29, 43, 45, 69], [6, 7, 28, 30, 44, 46, 70], [7, 8, 29, 31, 45, 47, 71], [7, 8, 30, 32, 46, 48, 72], [8, 31, 47], [8, 32, 48], [], [], [6, 7, 27, 29, 59, 61, 77], [6, 7, 28, 30, 60, 62, 78], [7, 8, 29, 31, 61, 63, 79], [7, 8, 30, 32, 62, 64, 80], [8, 31, 63], [8, 32, 64], [], [], [5, 7, 25, 29, 41, 45, 85], [5, 7, 26, 30, 42, 46, 86], [6, 8, 27, 31, 43, 47, 87], [6, 8, 28, 32, 44, 48, 88], [7, 29, 45], [7, 30, 46], [8, 31, 47], [8, 32, 48], [5, 7, 25, 29, 57, 61, 93], [5, 7, 26, 30, 58, 62, 94], [6, 8, 27, 31, 59, 63, 95], [6, 8, 28, 32, 60, 64, 96], [7, 29, 61], [7, 30, 62], [8, 31, 63], [8, 32, 64], [8, 31, 47, 71], [8, 32, 48, 72 ], [], [], [8, 31, 63, 79], [8, 32, 64, 80], [], [], [8, 31, 47, 87], [8, 32, 48, 88], [], [], [8, 31, 63, 95], [8, 32, 64, 96 ], [], [], [7, 29, 45, 69], [7, 30, 46, 70], [8, 31, 47, 71], [8, 32, 48, 72], [7, 29, 61, 77], [7, 30, 62, 78], [8, 31, 63, 79], [8, 32, 64, 80], [7, 29, 45, 85], [7, 30, 46, 86], [8, 31, 47, 87], [8, 32, 48, 88], [7, 29, 61, 93], [7, 30, 62, 94], [8, 31, 63, 95], [8, 32, 64, 96]]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96])
- The DFA for 7 plus the NFAs/DFAS for 8, 9, 10, 11 are here as they are too big to paste. For 12, 13, 14, 15 I have only included the NFAs. The files have names k6dfa, k7nfa, k7dfa etc. As an example, the input for problem 7 is k7nfa and the output is k7dfa. Hopefully the rest of the names are clear. If your code is correct for problems 1-11, I am happy to believe it is correct in general.
Score
I will time your code on test cases 1..15 from above of increasing size. Your score will be the largest test case your code can process in less than 10 minutes. If two answers get to the same size then the one that is fastest on that largest test case wins. The test machine is an Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.40GHz. You can use at most 16 of its cores.
Testing
I will check your answers (for the smaller cases) using AreEquivAut .
[Thank you to Christian Sievers for the example NFAs.]