Abstract
This talk surveys work on classifying the complexity and approximability of problems residing in the Polynomial-Time Hierarchy, above the first level. Along the way, we highlight some prominent natural problems that are believed – but not yet known – to be \(\Sigma^p_2\)-complete. We describe how strong inapproximability results for certain \(\Sigma^p_2\) optimization problems can be obtained using dispersers to build error-correcting codes. Finally we adapt a learning algorithm to produce approximation algorithms for these problems.
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Umans, C. (2006). Optimization Problems in the Polynomial-Time Hierarchy. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_33
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DOI: https://doi.org/10.1007/11750321_33
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