29,808 research outputs found
A Note on Shared Randomness and Shared Entanglement in Communication
We consider several models of 1-round classical and quantum communication,
some of these models have not been defined before. We "almost separate" the
models of simultaneous quantum message passing with shared entanglement and the
model of simultaneous quantum message passing with shared randomness. We define
a relation which can be efficiently exactly solved in the first model but
cannot be solved efficiently, either exactly or in 0-error setup in the second
model. In fact, our relation is exactly solvable even in a more restricted
model of simultaneous classical message passing with shared entanglement.
As our second contribution we strengthen a result by Yao that a "very short"
protocol from the model of simultaneous classical message passing with shared
randomness can be simulated in the model of simultaneous quantum message
passing: for a boolean function f, QII(f) \in exp(O(RIIp(f))) log n.
We show a similar result for protocols from a (stronger) model of 1-way
classical message passing with shared randomness: QII(f) \in exp(O(RIp(f))) log
n.
We demonstrate a problem whose efficient solution in the model of
simultaneous quantum message passing follows from our result but not from
Yao's.Comment: Stronger separation, minor changes and fixe
Catalytic quantum error correction
We develop the theory of entanglement-assisted quantum error correcting
(EAQEC) codes, a generalization of the stabilizer formalism to the setting in
which the sender and receiver have access to pre-shared entanglement.
Conventional stabilizer codes are equivalent to dual-containing symplectic
codes. In contrast, EAQEC codes do not require the dual-containing condition,
which greatly simplifies their construction. We show how any quaternary
classical code can be made into a EAQEC code. In particular, efficient modern
codes, like LDPC codes, which attain the Shannon capacity, can be made into
EAQEC codes attaining the hashing bound. In a quantum computation setting,
EAQEC codes give rise to catalytic quantum codes which maintain a region of
inherited noiseless qubits.
We also give an alternative construction of EAQEC codes by making classical
entanglement assisted codes coherent.Comment: 30 pages, 10 figures. Notation change: [[n,k;c]] instead of
[[n,k-c;c]
Understanding Space in Proof Complexity: Separations and Trade-offs via Substitutions
For current state-of-the-art DPLL SAT-solvers the two main bottlenecks are
the amounts of time and memory used. In proof complexity, these resources
correspond to the length and space of resolution proofs. There has been a long
line of research investigating these proof complexity measures, but while
strong results have been established for length, our understanding of space and
how it relates to length has remained quite poor. In particular, the question
whether resolution proofs can be optimized for length and space simultaneously,
or whether there are trade-offs between these two measures, has remained
essentially open.
In this paper, we remedy this situation by proving a host of length-space
trade-off results for resolution. Our collection of trade-offs cover almost the
whole range of values for the space complexity of formulas, and most of the
trade-offs are superpolynomial or even exponential and essentially tight. Using
similar techniques, we show that these trade-offs in fact extend to the
exponentially stronger k-DNF resolution proof systems, which operate with
formulas in disjunctive normal form with terms of bounded arity k. We also
answer the open question whether the k-DNF resolution systems form a strict
hierarchy with respect to space in the affirmative.
Our key technical contribution is the following, somewhat surprising,
theorem: Any CNF formula F can be transformed by simple variable substitution
into a new formula F' such that if F has the right properties, F' can be proven
in essentially the same length as F, whereas on the other hand the minimal
number of lines one needs to keep in memory simultaneously in any proof of F'
is lower-bounded by the minimal number of variables needed simultaneously in
any proof of F. Applying this theorem to so-called pebbling formulas defined in
terms of pebble games on directed acyclic graphs, we obtain our results.Comment: This paper is a merged and updated version of the two ECCC technical
reports TR09-034 and TR09-047, and it hence subsumes these two report
Formal Executable Models for Automatic Detection of Timing Anomalies
A timing anomaly is a counterintuitive timing behavior in the sense that a local fast execution slows down an overall global execution. The presence of such behaviors is inconvenient for the WCET analysis which requires, via abstractions, a certain monotony property to compute safe bounds. In this paper we explore how to systematically execute a previously proposed formal definition of timing anomalies. We ground our work on formal designs of architecture models upon which we employ guided model checking techniques. Our goal is towards the automatic detection of timing anomalies in given computer architecture designs
- …