9,069 research outputs found
Complexity Theory and the Operational Structure of Algebraic Programming Systems
An algebraic programming system is a language built from a fixed algebraic data abstraction and a selection of deterministic, and non-deterministic, assignment and control constructs. First, we give a detailed analysis of the operational structure of an algebraic data type, one which is designed to classify programming systems in terms of the complexity of their implementations. Secondly, we test our operational description by comparing the computations in deterministic and non-deterministic programming systems under certain space and time restrictions
Toward an architecture for quantum programming
It is becoming increasingly clear that, if a useful device for quantum
computation will ever be built, it will be embodied by a classical computing
machine with control over a truly quantum subsystem, this apparatus performing
a mixture of classical and quantum computation.
This paper investigates a possible approach to the problem of programming
such machines: a template high level quantum language is presented which
complements a generic general purpose classical language with a set of quantum
primitives. The underlying scheme involves a run-time environment which
calculates the byte-code for the quantum operations and pipes it to a quantum
device controller or to a simulator.
This language can compactly express existing quantum algorithms and reduce
them to sequences of elementary operations; it also easily lends itself to
automatic, hardware independent, circuit simplification. A publicly available
preliminary implementation of the proposed ideas has been realized using the
C++ language.Comment: 23 pages, 5 figures, A4paper. Final version accepted by EJPD ("swap"
replaced by "invert" for Qops). Preliminary implementation available at:
http://sra.itc.it/people/serafini/quantum-computing/qlang.htm
On the Computational Complexity of MCMC-based Estimators in Large Samples
In this paper we examine the implications of the statistical large sample
theory for the computational complexity of Bayesian and quasi-Bayesian
estimation carried out using Metropolis random walks. Our analysis is motivated
by the Laplace-Bernstein-Von Mises central limit theorem, which states that in
large samples the posterior or quasi-posterior approaches a normal density.
Using the conditions required for the central limit theorem to hold, we
establish polynomial bounds on the computational complexity of general
Metropolis random walks methods in large samples. Our analysis covers cases
where the underlying log-likelihood or extremum criterion function is possibly
non-concave, discontinuous, and with increasing parameter dimension. However,
the central limit theorem restricts the deviations from continuity and
log-concavity of the log-likelihood or extremum criterion function in a very
specific manner.
Under minimal assumptions required for the central limit theorem to hold
under the increasing parameter dimension, we show that the Metropolis algorithm
is theoretically efficient even for the canonical Gaussian walk which is
studied in detail. Specifically, we show that the running time of the algorithm
in large samples is bounded in probability by a polynomial in the parameter
dimension , and, in particular, is of stochastic order in the leading
cases after the burn-in period. We then give applications to exponential
families, curved exponential families, and Z-estimation of increasing
dimension.Comment: 36 pages, 2 figure
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Vector Addition System Reversible Reachability Problem
The reachability problem for vector addition systems is a central problem of
net theory. This problem is known to be decidable but the complexity is still
unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds
complexity are known. In this paper we consider the reversible reachability
problem. This problem consists to decide if two configurations are reachable
one from each other, or equivalently if they are in the same strongly connected
component of the reachability graph. We show that this problem is
EXPSPACE-complete. As an application of the introduced materials we
characterize the reversibility domains of a vector addition system
The combinatorics of biased riffle shuffles
This paper studies biased riffle shuffles, first defined by Diaconis, Fill,
and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds
shuffle and convolve nicely. An upper bound is given for the time for these
shuffles to converge to the uniform distribution; this matches lower bounds of
Lalley. A careful version of a bijection of Gessel leads to a generating
function for cycle structure after one of these shuffles and gives new results
about descents in random permutations. Results are also obtained about the
inversion and descent structure of a permutation after one of these shuffles.Comment: 11 page
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