17 lines
426 B
Plaintext
17 lines
426 B
Plaintext
Undecidability of validity problem in FOL
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PCP - examples
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PCP to validity reduction
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Let x and y be the strings over {0,1}.
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Let K be an instance of PCP.
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That is ((x_1,y_1),(x_2,y_2).....(x_k,y_k))
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where for all i \in {1,..,k} x_i, y_i are strings over {0,1}.
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Then the set of indices i_1,i_2,..i_n \in {1,..,k} is a solution if
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x_{i_1}x_{i_2}...x_{i_n}= y_{i_1}y_{i_2}...y_{i_n}.
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From instance k construct \phi_k.
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