16,730 research outputs found
Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation
We present an efficient proof system for Multipoint Arithmetic Circuit
Evaluation: for every arithmetic circuit of size and
degree over a field , and any inputs ,
the Prover sends the Verifier the values and a proof of length, and
the Verifier tosses coins and can check the proof in about time, with probability of error less than .
For small degree , this "Merlin-Arthur" proof system (a.k.a. MA-proof
system) runs in nearly-linear time, and has many applications. For example, we
obtain MA-proof systems that run in time (for various ) for the
Permanent, Circuit-SAT for all sublinear-depth circuits, counting
Hamiltonian cycles, and infeasibility of - linear programs. In general,
the value of any polynomial in Valiant's class can be certified
faster than "exhaustive summation" over all possible assignments. These results
strongly refute a Merlin-Arthur Strong ETH and Arthur-Merlin Strong ETH posed
by Russell Impagliazzo and others.
We also give a three-round (AMA) proof system for quantified Boolean formulas
running in time, nearly-linear time MA-proof systems for
counting orthogonal vectors in a collection and finding Closest Pairs in the
Hamming metric, and a MA-proof system running in -time for
counting -cliques in graphs.
We point to some potential future directions for refuting the
Nondeterministic Strong ETH.Comment: 17 page
Alternation-Trading Proofs, Linear Programming, and Lower Bounds
A fertile area of recent research has demonstrated concrete polynomial time
lower bounds for solving natural hard problems on restricted computational
models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path,
Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs
of these lower bounds follow a certain proof-by-contradiction strategy that we
call alternation-trading. An important open problem is to determine how
powerful such proofs can possibly be.
We propose a methodology for studying these proofs that makes them amenable
to both formal analysis and automated theorem proving. We prove that the search
for better lower bounds can often be turned into a problem of solving a large
series of linear programming instances. Implementing a small-scale theorem
prover based on this result, we extract new human-readable time lower bounds
for several problems. This framework can also be used to prove concrete
limitations on the current techniques.Comment: To appear in STACS 2010, 12 page
A Casual Tour Around a Circuit Complexity Bound
I will discuss the recent proof that the complexity class NEXP
(nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial
size. The proof will be described from the perspective of someone trying to
discover it.Comment: 21 pages, 2 figures. An earlier version appeared in SIGACT News,
September 201
MS – 247: Sinclair – Donaldson Papers
The Sinclair - Donaldson Collection includes photographs and ephemera saved by Connie Sinclair, an African-American W.A.C. member who served during WWII. It consists of sepia-toned and black and white photographs taken during training and enlistment, many captioned. Among the images are official Army photos, including women in a mess hall, the Nurse Corp at Fort Huachuca, and Native American soldiers at the same location.
Also contained within this collection are military pins, patches, and insignia, including the Pallas Athene and Sinclair’s dog tag; a W.A.C. song book from 1944; and Sinclair’s Service Recognition certificate. Two Service Club scrapbooks from the 1950’s are contained in this collection from Sinclair’s time as director. Also, family photographs, a family record book, letters, poetry, and newspaper clippings from the 50’s and 80’s.https://cupola.gettysburg.edu/findingaidsall/1219/thumbnail.jp
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