1,785,747 research outputs found
Logical, mechanical and historical time in economics
Within the economic theory different notions of time imply alternative analytical structures. This article discusses and rejects the methodological dichotomy between âtemporalâ and âa-temporalâ models (equilibrium and disequilibrium models) in economics. Different notions of time are identified âlogical, mechanical and historical time- which enable to specify corresponding sequential methods and to address different questions within the economic theory. Some analytical implications are examined. In the light of the proposed methodological distinction different theories of the rate of interest are evaluated and new light is thrown on the important debate on finance which arose in the â30s among Keynes, Robertson and representatives of the Swedish School (Ohlin).Time and causality in economics; Keynes,Robertson and the Swedish School on finance
On Logical Depth and the Running Time of Shortest Programs
The logical depth with significance of a finite binary string is the
shortest running time of a binary program for that can be compressed by at
most bits. There is another definition of logical depth. We give two
theorems about the quantitative relation between these versions: the first
theorem concerns a variation of a known fact with a new proof, the second
theorem and its proof are new. We select the above version of logical depth and
show the following. There is an infinite sequence of strings of increasing
length such that for each there is a such that the logical depth of the
th string as a function of is incomputable (it rises faster than any
computable function) but with replaced by the resuling function is
computable. Hence the maximal gap between the logical depths resulting from
incrementing appropriate 's by 1 rises faster than any computable function.
All functions mentioned are upper bounded by the Busy Beaver function. Since
for every string its logical depth is nonincreasing in , the minimal
computation time of the shortest programs for the sequence of strings as a
function of rises faster than any computable function but not so fast as
the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451
Bisimulations and Logical Characterizations on Continuous-time Markov Decision Processes
In this paper we study strong and weak bisimulation equivalences for
continuous-time Markov decision processes (CTMDPs) and the logical
characterizations of these relations with respect to the continuous-time
stochastic logic (CSL). For strong bisimulation, it is well known that it is
strictly finer than CSL equivalence. In this paper we propose strong and weak
bisimulations for CTMDPs and show that for a subclass of CTMDPs, strong and
weak bisimulations are both sound and complete with respect to the equivalences
induced by CSL and the sub-logic of CSL without next operator respectively. We
then consider a standard extension of CSL, and show that it and its sub-logic
without X can be fully characterized by strong and weak bisimulations
respectively over arbitrary CTMDPs.Comment: The conference version of this paper was published at VMCAI 201
McTaggart's Argument for the Unreality of Time: A Temporal Logical Analysis
An examination of McTaggartâs [1908] argument for the unreality of time
Protected gates for topological quantum field theories
We study restrictions on locality-preserving unitary logical gates for
topological quantum codes in two spatial dimensions. A locality-preserving
operation is one which maps local operators to local operators --- for example,
a constant-depth quantum circuit of geometrically local gates, or evolution for
a constant time governed by a geometrically-local bounded-strength Hamiltonian.
Locality-preserving logical gates of topological codes are intrinsically fault
tolerant because spatially localized errors remain localized, and hence
sufficiently dilute errors remain correctable. By invoking general properties
of two-dimensional topological field theories, we find that the
locality-preserving logical gates are severely limited for codes which admit
non-abelian anyons; in particular, there are no locality-preserving logical
gates on the torus or the sphere with M punctures if the braiding of anyons is
computationally universal. Furthermore, for Ising anyons on the M-punctured
sphere, locality-preserving gates must be elements of the logical Pauli group.
We derive these results by relating logical gates of a topological code to
automorphisms of the Verlinde algebra of the corresponding anyon model, and by
requiring the logical gates to be compatible with basis changes in the logical
Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio
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