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# Computations
## Problem 1
`automata.c`, e.g.
### Input
4
1 1 3
0 1 2
0 3 0
1 1 2
4 0011
### Output
yes
## Problem 2
`nfa.cc` takes a state table of a non-deterministic finite-state automaton, its
final states and a string from stdin and print either `yes` or `no` to stdout
to answer whether this string is recognized by the automaton, e.g.
### Input
12
0 0 0
0 0 1
0 1 3
1 0 0
1 1 1
1 1 3
2 1 0
2 1 2
3 0 0
3 0 1
3 0 2
3 1 1
2
2 3
101
### Output
yes
## Problem 3
`automata-to-grammar.c`
### Input
4
1 1 3
0 1 2
0 3 0
1 1 2
### Output
S -> $
S -> 0T
S -> 1V
T -> 0T
T -> 1U
U -> 0V
U -> 1S
V -> $
V -> 0T
V -> 1U
## Problem 4
`grammar-to-automata.cc` (C++17)
### Input
10
S -> $
S -> 0T
S -> 1V
T -> 0T
T -> 1U
U -> 0V
U -> 1S
V -> $
V -> 0T
V -> 1U
### Output
4
V T U 1
U V S 0
S T V 1
T T U 0
## Problem 5
`turing.cc` (C++17) takes a natural number `n` and `n` 5-tuples representing a
Turing machine (with `-1` being the blank), a natural number `m` and a string
of `m` binaries from stdin, then print the output string to stdout, e.g.
### Input
7
0 0 0 0 1
0 1 1 1 1
0 -1 3 -1 1
1 0 0 0 1
1 1 2 0 -1
1 -1 3 -1 1
2 1 3 0 1
6
0 1 0 1 1 0
### Output
010000
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