335 research outputs found
On the Computational Complexity of MapReduce
In this paper we study MapReduce computations from a complexity-theoretic
perspective. First, we formulate a uniform version of the MRC model of Karloff
et al. (2010). We then show that the class of regular languages, and moreover
all of sublogarithmic space, lies in constant round MRC. This result also
applies to the MPC model of Andoni et al. (2014). In addition, we prove that,
conditioned on a variant of the Exponential Time Hypothesis, there are strict
hierarchies within MRC so that increasing the number of rounds or the amount of
time per processor increases the power of MRC. To the best of our knowledge we
are the first to approach the MapReduce model with complexity-theoretic
techniques, and our work lays the foundation for further analysis relating
MapReduce to established complexity classes
Lower Bounds for RAMs and Quantifier Elimination
We are considering RAMs , with wordlength , whose arithmetic
instructions are the arithmetic operations multiplication and addition modulo
, the unary function , the binary
functions (with ), ,
, and the boolean vector operations defined on
sequences of length . It also has the other RAM instructions. The size
of the memory is restricted only by the address space, that is, it is
words. The RAMs has a finite instruction set, each instruction is encoded by a
fixed natural number independently of . Therefore a program can run on
each machine , if is sufficiently large. We show that there
exists an and a program , such that it satisfies the following
two conditions.
(i) For all sufficiently large , if running on gets an
input consisting of two words and , then, in constant time, it gives a
output .
(ii) Suppose that is a program such that for each sufficiently large
, if , running on , gets a word of length as an
input, then it decides whether there exists a word of length such that
. Then, for infinitely many positive integers , there exists a
word of length , such that the running time of on at
input is at least
Communication Complexity and Secure Function Evaluation
We suggest two new methodologies for the design of efficient secure
protocols, that differ with respect to their underlying computational models.
In one methodology we utilize the communication complexity tree (or branching
for f and transform it into a secure protocol. In other words, "any function f
that can be computed using communication complexity c can be can be computed
securely using communication complexity that is polynomial in c and a security
parameter". The second methodology uses the circuit computing f, enhanced with
look-up tables as its underlying computational model. It is possible to
simulate any RAM machine in this model with polylogarithmic blowup. Hence it is
possible to start with a computation of f on a RAM machine and transform it
into a secure protocol.
We show many applications of these new methodologies resulting in protocols
efficient either in communication or in computation. In particular, we
exemplify a protocol for the "millionaires problem", where two participants
want to compare their values but reveal no other information. Our protocol is
more efficient than previously known ones in either communication or
computation
Automata theoretic aspects of temporal behaviour and computability in logical neural networks
Imperial Users onl
Hierarchies and Space Measures for Pointer Machines
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Institute of Technology, AFIT/CIR
Formal verification of a microcoded VIPER microprocessor using HOL
The Royal Signals and Radar Establishment (RSRE) and members of the Hardware Verification Group at Cambridge University conducted a joint effort to prove the correspondence between the electronic block model and the top level specification of Viper. Unfortunately, the proof became too complex and unmanageable within the given time and funding constraints, and is thus incomplete as of the date of this report. This report describes an independent attempt to use the HOL (Cambridge Higher Order Logic) mechanical verifier to verify Viper. Deriving from recent results in hardware verification research at UC Davis, the approach has been to redesign the electronic block model to make it microcoded and to structure the proof in a series of decreasingly abstract interpreter levels, the lowest being the electronic block level. The highest level is the RSRE Viper instruction set. Owing to the new approach and some results on the proof of generic interpreters as applied to simple microprocessors, this attempt required an effort approximately an order of magnitude less than the previous one
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Mathematical Logic: Proof Theory, Constructive Mathematics
[no abstract available
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