4,168 research outputs found
Copenhagen Quantum Mechanics Emerges from a Deterministic Schroedinger Theory in 11 Dimensional Spacetime Including Weak Field Gravitation
We construct a world model consisting of a matter field living in 4
dimensional spacetime and a gravitational field living in 11 dimensional
spacetime. The seven hidden dimensions are compactified within a radius
estimated by reproducing the particle - wave characteristic of diffraction
experiments. In the presence of matter fields the gravitational field develops
localized modes with elementary excitations called gravonons which are induced
by the sources (massive particles). The final world model treated here contains
only gravonons and a scalar matter field. The solution of the Schroedinger
equation for the world model yields matter fields which are localized in the 4
dimensional subspace. The localization has the following properties: (i) There
is a chooser mechanism for the selection of the localization site. (ii) The
chooser selects one site on the basis of minor energy differences and
differences in the gravonon structure between the sites, which appear
statistical. (iii) The changes from one localization site to a neighbouring one
take place in a telegraph-signal like manner. (iv) The times at which telegraph
like jumps occur dependent on subtleties of the gravonon structure which appear
statistical. (v) The fact that the dynamical law acts in the configuration
space of fields living in 11 dimensional spacetime lets the events observed in
4 dimensional spacetime appear non-local. In this way the phenomenology of
Copenhagen quantum mechanics is obtained without the need of introducing the
process of collapse and a probabilistic interpretation of the wave function.
Operators defining observables need not be introduced. All experimental
findings are explained in a deterministic way as a consequence of the time
development of the wave function in configuration space according to
Schroedinger's equation
Energy Parity Games
Energy parity games are infinite two-player turn-based games played on
weighted graphs. The objective of the game combines a (qualitative) parity
condition with the (quantitative) requirement that the sum of the weights
(i.e., the level of energy in the game) must remain positive. Beside their own
interest in the design and synthesis of resource-constrained omega-regular
specifications, energy parity games provide one of the simplest model of games
with combined qualitative and quantitative objective. Our main results are as
follows: (a) exponential memory is necessary and sufficient for winning
strategies in energy parity games; (b) the problem of deciding the winner in
energy parity games can be solved in NP \cap coNP; and (c) we give an algorithm
to solve energy parity by reduction to energy games. We also show that the
problem of deciding the winner in energy parity games is polynomially
equivalent to the problem of deciding the winner in mean-payoff parity games,
while optimal strategies may require infinite memory in mean-payoff parity
games. As a consequence we obtain a conceptually simple algorithm to solve
mean-payoff parity games
Observation and Distinction. Representing Information in Infinite Games
We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata.
The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists
Graph Planning with Expected Finite Horizon
Graph planning gives rise to fundamental algorithmic questions such as
shortest path, traveling salesman problem, etc. A classical problem in discrete
planning is to consider a weighted graph and construct a path that maximizes
the sum of weights for a given time horizon . However, in many scenarios,
the time horizon is not fixed, but the stopping time is chosen according to
some distribution such that the expected stopping time is . If the stopping
time distribution is not known, then to ensure robustness, the distribution is
chosen by an adversary, to represent the worst-case scenario.
A stationary plan for every vertex always chooses the same outgoing edge. For
fixed horizon or fixed stopping-time distribution, stationary plans are not
sufficient for optimality. Quite surprisingly we show that when an adversary
chooses the stopping-time distribution with expected stopping time , then
stationary plans are sufficient. While computing optimal stationary plans for
fixed horizon is NP-complete, we show that computing optimal stationary plans
under adversarial stopping-time distribution can be achieved in polynomial
time. Consequently, our polynomial-time algorithm for adversarial stopping time
also computes an optimal plan among all possible plans
Infinite Synchronizing Words for Probabilistic Automata (Erratum)
In [1], we introduced the weakly synchronizing languages for probabilistic
automata. In this report, we show that the emptiness problem of weakly
synchronizing languages for probabilistic automata is undecidable. This implies
that the decidability result of [1-3] for the emptiness problem of weakly
synchronizing language is incorrect.Comment: 5 pages, 3 figure
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