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<p>to <a href="page.php?w=Computational_complexity_theory">computational complexity</a> (in particular <a href="page.php?w=hardness_of_approximation">hardness of approximation</a>) and <a href="page.php?w=cryptography">cryptography</a>.</p>

<p>The definition of a probabilistically checkable proof was explicitly introduced by Arora and Safra in 1992, although their properties were studied earlier.  In 1990 Babai, Fortnow, and Lund proved that <b>PCP</b>[poly(n), poly(n)] = <b><a href="page.php?w=NEXP">NEXP</a></b>, providing the first nontrivial</p><p>
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