112 research outputs found
How proofs are prepared at Camelot
We study a design framework for robust, independently verifiable, and
workload-balanced distributed algorithms working on a common input. An
algorithm based on the framework is essentially a distributed encoding
procedure for a Reed--Solomon code, which enables (a) robustness against
byzantine failures with intrinsic error-correction and identification of failed
nodes, and (b) independent randomized verification to check the entire
computation for correctness, which takes essentially no more resources than
each node individually contributes to the computation. The framework builds on
recent Merlin--Arthur proofs of batch evaluation of Williams~[{\em Electron.\
Colloq.\ Comput.\ Complexity}, Report TR16-002, January 2016] with the
observation that {\em Merlin's magic is not needed} for batch evaluation---mere
Knights can prepare the proof, in parallel, and with intrinsic
error-correction.
The contribution of this paper is to show that in many cases the verifiable
batch evaluation framework admits algorithms that match in total resource
consumption the best known sequential algorithm for solving the problem. As our
main result, we show that the -cliques in an -vertex graph can be counted
{\em and} verified in per-node time and space on
compute nodes, for any constant and
positive integer divisible by , where is the
exponent of matrix multiplication. This matches in total running time the best
known sequential algorithm, due to Ne{\v{s}}et{\v{r}}il and Poljak [{\em
Comment.~Math.~Univ.~Carolin.}~26 (1985) 415--419], and considerably improves
its space usage and parallelizability. Further results include novel algorithms
for counting triangles in sparse graphs, computing the chromatic polynomial of
a graph, and computing the Tutte polynomial of a graph.Comment: 42 p
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
From Quantum Query Complexity to State Complexity
State complexity of quantum finite automata is one of the interesting topics
in studying the power of quantum finite automata. It is therefore of importance
to develop general methods how to show state succinctness results for quantum
finite automata. One such method is presented and demonstrated in this paper.
In particular, we show that state succinctness results can be derived out of
query complexity results.Comment: Some typos in references were fixed. To appear in Gruska Festschrift
(2014). Comments are welcome. arXiv admin note: substantial text overlap with
arXiv:1402.7254, arXiv:1309.773
Implications of quantum automata for contextuality
We construct zero-error quantum finite automata (QFAs) for promise problems
which cannot be solved by bounded-error probabilistic finite automata (PFAs).
Here is a summary of our results:
- There is a promise problem solvable by an exact two-way QFA in exponential
expected time, but not by any bounded-error sublogarithmic space probabilistic
Turing machine (PTM).
- There is a promise problem solvable by an exact two-way QFA in quadratic
expected time, but not by any bounded-error -space PTMs in
polynomial expected time. The same problem can be solvable by a one-way Las
Vegas (or exact two-way) QFA with quantum head in linear (expected) time.
- There is a promise problem solvable by a Las Vegas realtime QFA, but not by
any bounded-error realtime PFA. The same problem can be solvable by an exact
two-way QFA in linear expected time but not by any exact two-way PFA.
- There is a family of promise problems such that each promise problem can be
solvable by a two-state exact realtime QFAs, but, there is no such bound on the
number of states of realtime bounded-error PFAs solving the members this
family.
Our results imply that there exist zero-error quantum computational devices
with a \emph{single qubit} of memory that cannot be simulated by any finite
memory classical computational model. This provides a computational perspective
on results regarding ontological theories of quantum mechanics \cite{Hardy04},
\cite{Montina08}. As a consequence we find that classical automata based
simulation models \cite{Kleinmann11}, \cite{Blasiak13} are not sufficiently
powerful to simulate quantum contextuality. We conclude by highlighting the
interplay between results from automata models and their application to
developing a general framework for quantum contextuality.Comment: 22 page
Recursive double-size fixed precision arithmetic
International audienceThis work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture)
Recent Developments in Algorithmic Teaching
Abstract. The present paper surveys recent developments in algorith-mic teaching. First, the traditional teaching dimension model is recalled. Starting from the observation that the teaching dimension model some-times leads to counterintuitive results, recently developed approaches are presented. Here, main emphasis is put on the following aspects derived from human teaching/learning behavior: the order in which examples are presented should matter; teaching should become harder when the memory size of the learners decreases; teaching should become easier if the learners provide feedback; and it should be possible to teach infinite concepts and/or finite and infinite concept classes. Recent developments in the algorithmic teaching achieving (some) of these aspects are presented and compared.
A bi-articular model for scapular-humeral rhythm reconstruction through data from wearable sensors
Patient-specific performance assessment of arm movements in daily life activities is fundamental for neurological rehabilitation therapy. In most applications, the shoulder movement is simplified through a socket-ball joint, neglecting the movement of the scapular-thoracic complex. This may lead to significant errors. We propose an innovative bi-articular model of the human shoulder for estimating the position of the hand in relation to the sternum. The model takes into account both the scapular-toracic and gleno-humeral movements and their ratio governed by the scapular-humeral rhythm, fusing the information of inertial and textile-based strain sensors
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