Physical consequences of P≠\neqNP and the DMRG-annealing conjecture

Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and, thus, these theorems do not apply directly to it. But {\em classical simulations} of physical processes are programs running on Turing machines and, as such, are subject to them. In this work, computational complexity theory is applied to classical simulations of systems performing an adiabatic quantum computation (AQC), based on an annealed extension of the density matrix renormalization group (DMRG). We conjecture that the computational time required for those classical simulations is controlled solely by the {\em maximal entanglement} found during the process. Thus, lower bounds on the growth of entanglement with the system size can be provided. In some cases, quantum phase transitions can be predicted to take place in certain inhomogeneous systems. Concretely, physical conclusions are drawn from the assumption that the complexity classes {\bf P} and {\bf NP} differ. As a by-product, an alternative measure of entanglement is proposed which, via Chebyshev's inequality, allows to establish strict bounds on the required computational time.Comment: Accepted for publication in JSTA

Correlation of Geometrical Specifications for Flexible Quality Control in the Manufacturing of Plastic Products

This article presents an analysis to meet the demand for process-optimized applications in industrial plastic production. Since in an injection molding process primarily plastic products are created, which underlie a strict quality control, machine technicians thereby carry out worker operator control in order to ensure even production drawing quality. Thereby injection molding products are qualified among others via component dimensions. Due to the complex accessibility of molded part geometry, these controls underlie high and varying sensor influence. Due to technology advancement and increasingly accurate quality requirements, the demand for process-optimized quality controls is continuously growing. First, the complexity of geometrical quality control from workpieces is presented. Practical and simulative tests to determine the correlation of geometric specifications are examined by means of a variable injection molding process. Finally, the new control dimensions\u27 relevance shall be implemented via appropriate correlation evidence

Marine propeller optimisation through user interaction and machine learning for advanced blade design scenarios

The complexity of the marine propeller design process is well recognised and is related to contradicting requirements of the stakeholders, complex physical phenomena, and fast analysis tools, where the latter are preferred due to the strict time limitations under which the entire process is carried out. With all this in mind, an optimisation methodology has been proposed and presented earlier that combines user interactivity with machine learning and proved to be useful for a simple blade design scenario. More specifically, the blade designer manually evaluates the cavitation of the designs during the optimisation and this information is systematically returned into the optimisation algorithm, a process called interactive optimisation. As part of the optimisation, a machine learning pipeline has been implemented in this study, which is used for cavitation evaluation prediction in order to solve the user fatigue problem that is connected to interactive optimisation processes. The proposed methodology is investigated for two case studies of advanced design scenarios, relevant for a real commercial situation, that regard controllable-pitch propellers for ROPAX vessels, and the aim is to obtain a set of optimal, competent blade designs. Both cases represent scenarios with several design variables, objectives and constraints and with conditions that have either suction side or pressure side cavitation. The results show that the proposed methodology can be used as a support tool for the blade designers to, under strict time constraints, find a suitable set of propeller designs, some of which can be considered equal or even superior to the delivered design

In Defense of DEFECT or Cooperation does not Justify the Solution Concept

The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoners' dilemma, when preferences are lexicographic in the complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity.Cooperation; prisoners' dilemma; automata; evolution.

gCSP: A Graphical Tool for Designing CSP systems

For broad acceptance of an engineering paradigm, a graphical notation and a supporting design tool seem necessary. This paper discusses certain issues of developing a design environment for building systems based on CSP. Some of the issues discussed depend specifically on the underlying theory of CSP, while a number of them are common for any graphical notation and supporting tools, such as provisions for complexity management and design overview