We show that the class Sp2 is contained in ZPP NP. The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp–Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPPNP. © 20...

It was previously known that Max Clique cannot be approximated in polynomial time within n1− , for any constant > 0, unless NP = ZPP. In this paper, we extend the reductions used to prove this result and combine the extended reductions with a recent result of Samorodnitsky and Trevisan to show that unless NP ⊆ ZPTIME(2 n(log logn) 3/2)), clique cannot be approximated within n1−O(1/ √ log .

Lower bounds on circuit size were previously established for functions in Σp2, ZPP , Σ exp 2 , ZPEXP NP and MAexp. We investigate the general question: Given a time bound f(n). What is the best circuit size lower bound that can be shown for the classes MA-TIME[f ], ZP-TIME[f ], . . . using the techniques currently known? For the classes MAexp, ZPEXP NP and Σ exp 2 , the answer we get is “halfex...

Plan upravljanja postupkom je novi institut građanskog procesnog prava koji u parnični postupak uveden Zakonom o izmjenama i dopunama Zakona parničnom postupku („Narodne novine“ broj 80/2022, dalje ZID ZPP/22). Kao većinom izmjena dopuna iz navedenog zakona, zakonodavac ovim institutom imao namjeru ubrzati te osigurati koncentraciju postupka kao održavanje procesne discipline kako na strani sud...

We show that, if NP 6= ZPP, for any ε > 0, the toughness of a graph with n vertices is not approximable in polynomial time within a factor of 1 2 (n 2 ). We give a 4-approximation for graphs with toughness bounded by 1 3 and we show that this result cannot be generalized to graphs with a bounded toughness. More exactly we prove that there is no constant approximation for graphs with bounded tou...

OBJECTIVE Patients without tonsils and with Friedman tongue position (FTP) III and IV are poor candidates for uvulopalatopharyngoplasty (UP3). Even when combined with adjunctive hyopharyngeal techniques, results are poor. We assessed a modified uvulopalatoplasty based on a bilateral Z-plasty in treating patients without tonsils who have obstructive sleep apnea/hypopnea syndrome (OSAHS). METHO...

We consider the following class of problems: Given a graph G, find a maximum vertex induced subgraph of G satisfying a nontrivial hereditary property π. We show that this problem cannot be approximated for any such property π, within a factor of n1−2 for any 2 > 0, unless NP = ZPP . This improves the result in [LY93] where it was shown that for any nontrivial hereditary property, the maximum su...