Related papers: Using Propagation for Solving Complex Arithmetic C…
Numerical analysis has no satisfactory method for the more realistic optimization models. However, with constraint programming one can compute a cover for the solution set to arbitrarily close approximation. Because the use of constraint…
Box consistency has been observed to yield exponentially better performance than chaotic constraint propagation in the interval constraint system obtained by decomposing the original expression into primitive constraints. The claim was made…
Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…
Numerical methods based on interval arithmetic are efficient means to reliably solve nonlinear systems of equations. Algorithm bc3revise is an interval method that tightens variables' domains by enforcing a property called box consistency.…
We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…
A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion…
Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
We describe the use of array expressions as constraints, which represents a consequent generalisation of the "element" constraint. Constraint propagation for array constraints is studied theoretically, and for a set of domain reduction…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
The Box-Cox transformation is applied to the linear mixed models for analyzing positive and grouped data. The problem in using Box Cox transformation is that the maximum likelihood estimator of the transformation parameter is generally…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…
Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…