92,843 research outputs found
Deterministic event-based simulation of quantum phenomena
We propose and analyse simple deterministic algorithms that can be used to construct machines that have primitive learning capabilities. We demonstrate that locally connected networks of these machines can be used to perform blind classification on an event-by-event basis, without storing the information of the individual events. We also demonstrate that properly designed networks of these machines exhibit behavior that is usually only attributed to quantum systems. We present networks that simulate quantum interference on an event-by-event basis. In particular we show that by using simple geometry and the learning capabilities of the machines it is possible to simulate single-photon interference in a Mach-Zehnder interferometer. The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach-Zehnder interferometer. To illustrate that networks of these machines are indeed capable of simulating quantum interference we simulate, event-by-event, a setup involving two chained Mach-Zehnder interferometers, and demonstrate that also in this case the simulation results agree with quantum theory. (C) 2005 Elsevier B.V. All rights reserved.</p
Quantum Pushdown Automata
Quantum finite automata, as well as quantum pushdown automata (QPA) were
first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce
the notion of QPA in a non-equivalent way, including unitarity criteria, by
using the definition of quantum finite automata of Kondacs and Watrous. It is
established that the unitarity criteria of QPA are not equivalent to the
corresponding unitarity criteria of quantum Turing machines. We show that QPA
can recognize every regular language. Finally we present some simple languages
recognized by QPA, not recognizable by deterministic pushdown automata.Comment: Conference SOFSEM 2000, extended version of the pape
ASMs and Operational Algorithmic Completeness of Lambda Calculus
We show that lambda calculus is a computation model which can step by step
simulate any sequential deterministic algorithm for any computable function
over integers or words or any datatype. More formally, given an algorithm above
a family of computable functions (taken as primitive tools, i.e., kind of
oracle functions for the algorithm), for every constant K big enough, each
computation step of the algorithm can be simulated by exactly K successive
reductions in a natural extension of lambda calculus with constants for
functions in the above considered family. The proof is based on a fixed point
technique in lambda calculus and on Gurevich sequential Thesis which allows to
identify sequential deterministic algorithms with Abstract State Machines. This
extends to algorithms for partial computable functions in such a way that
finite computations ending with exceptions are associated to finite reductions
leading to terms with a particular very simple feature.Comment: 37 page
Multi-processor Scheduling to Minimize Flow Time with epsilon Resource Augmentation
We investigate the problem of online scheduling of jobs to minimize flow time and stretch on m identical machines. We consider the case where the algorithm is given either (1 + ε)m machines or m machines of speed (1 + ε), for arbitrarily small ε \u3e 0. We show that simple randomized and deterministic load balancing algorithms, coupled with simple single machine scheduling strategies such as SRPT (shortest remaining processing time) and SJF (shortest job first), are O(poly(1/ε))-competitive for both flow time and stretch. These are the first results which prove constant factor competitive ratios for flow time or stretch with arbitrarily small resource augmentation. Both the randomized and the deterministic load balancing algorithms are non- migratory and do immediate dispatch of jobs.
The randomized algorithm just allocates each incoming job to a random machine. Hence this algorithm is non- clairvoyant, and coupled with SETF (shortest elapsed time first), yields the first non-clairvoyant algorithm which is con- stant competitive for minimizing flow time with arbitrarily small resource augmentation.
The deterministic algorithm that we analyze is due to Avrahami and Azar. For this algorithm, we show O(1/ε)-competitiveness for total flow time and stretch, and also for their Lp norms, for any fixed p ≥ 1
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