Constraint Reasoning for Differential Models by J Cruz

By J Cruz

Evaluating the most important positive aspects of biophysical inadequacy used to be similar with the illustration of differential equations. process dynamics is frequently modeled with the expressive energy of the prevailing period constraints framework. it's transparent that crucial version used to be via differential equations yet there has been no manner of expressing a differential equation as a constraint and combine it in the constraints framework. for that reason, the target of this paintings is concentrated at the integration of standard differential equations in the period constraints framework, which for this goal is prolonged with the hot formalism of Constraint pride Differential difficulties. Such framework permits the specification of standard differential equations, including similar details, through constraints, and gives effective propagation ideas for pruning the domain names in their variables. This enabled the mixing of all such details in one constraint whose variables could therefore be utilized in different constraints of the version. the explicit strategy used for pruning its variable domain names can then be mixed with the pruning equipment linked to the opposite constraints in an total propagation set of rules for lowering the boundaries of all version variables.

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In the context of a constraint system, the points of the search space are complete real valued instantiations of all its variables and the search is directed towards the simultaneous satisfaction of all its constraints. 4 Chapter 1. Introduction All the extensions to the interval constraints framework were proposed in the context of integrating biophysical models within decision support. It would be important to validate our approach in the sense that it provides an important contribution along such a direction.

A 2k-tree is a hierarchical decomposition of the solution space into k-arity F-boxes which summarizes the subset of constraints between the k variables. In most interval constraint approaches the basic structures are F-intervals and the solutions space is represented by enclosing F-boxes. In particular a single real value is represented by a canonical F-interval and the assignment of a single real value to each variable of a set of variables is represented by a canonical F-box. Consequently, canonical F-boxes are the closest representations of CCSP solutions.

An expression E is an inductive structure defined in the following way: (i) a constant is an expression; (ii) a variable is an expression; (iii) if E1,…,Em are expressions and ) is a m-ary basic operator then )(E1,…,Em) is an expression; A real expression is an expression with real constants, real valued variables and real operators. An interval expression is an expression with real interval constants, real interval valued variables and interval operators. ‰ If x1, x2 and x3 are real valued variables then (x1+x2)u(x3-S) is a real expression with three binary real operators (+, u and -) and a real constant (S).

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