If We Take Into Account that Constraints Are Soft, Then Processing Constraints Becomes Algorithmically Solvable
Résumé
Constraints are ubiquitous in science and engineering.
Constraints describe the available information about
the state of the system, constraints describe possible relation
between current and future states of the system, constraints
describe which future states we would like to obtain. To solve
problems from engineering and science, it is therefore necessary
to process constraints. We show that if we treat constraints as
hard (crisp), with all the threshold values exactly known, then in
the general case, all the corresponding computational problems
become algorithmically unsolvable. However, these problems
become algorithmically solvable if we take into account that in
reality, constraints are soft: we do not know the exact values of the
corresponding thresholds, we do not know the exact dependence
between the present and future states, etc.