A ZPP Lifting Theorem
نویسنده
چکیده
The complexity class ZPP (corresponding to zero-error randomized algorithms with access to one NP oracle query) is known to have a number of curious properties. We further explore this class in the settings of time complexity, query complexity, and communication complexity. r For starters, we provide a new characterization: ZPP equals the restriction of BPP where the algorithm is only allowed to err when it forgoes the opportunity to make an NP oracle query. r Using the above characterization, we prove a query-to-communication lifting theorem, which translates any ZPP decision tree lower bound for a function f into a ZPP communication lower bound for a two-party version of f . r As an application, we use the above lifting theorem to prove that the ZPP communication lower bound technique introduced by Göös, Pitassi, and Watson (ICALP 2016) is not tight. We also provide a “primal” characterization of this lower bound technique as a complexity class.
منابع مشابه
Competing Provers Yield Improved Karp-Lipton Collapse Results
Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2 = S2. Building on this, we strengthen the Kämper– AFK Theorem, namely, we prove that if NP ⊆ (NP ∩ coNP)/poly then the polynomial hierarchy collapses to SNP∩coNP 2 . We also strengthen Yap’s Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to SNP...
متن کاملS2p is subset of ZPPNP
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...
متن کاملOn the Resource Bounded Measure of P/poly
We show that the class of sets having polynomial size circuits, P=poly, has EXPNP-measure zero under each of the following two assumptions: EXPNP 6= ZPP p2 (which holds if the polynomial time hierarchy does not collapse to ZPP p2 ), or NP is not small (does not have EXP-measure zero).
متن کاملGraph Isomorphism Is Low for ZPP(NP) and Other Lowness Results
We show the following new lowness results for the probabilistic class ZPP NP. The class AM \ coAM is low for ZPP NP. As a consequence it follows that Graph Iso-morphism and several group-theoretic problems known to be in AM \ coAM are low for ZPP NP. The class IPPP/poly], consisting of sets that have interactive proof systems with honest provers in P/poly are also low for ZPP NP. We consider lo...
متن کاملOn zero error algorithms having oracle access to one query
It is known that Sp2 ⊆ ZPP NP [3]. The reverse direction of whether ZPP is contained in Sp2 remains open. We show that if the zero-error algorithm is allowed to ask only one query to the NP oracle (for any input and random string), then it can be simulated in Sp2. That is, we prove that ZPP ⊆ Sp2. Next we consider whether the above result can be improved as ZPP ⊆ P and point out a difficulty in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017