文件名称:representations
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The paper deals with representations of the safe states set in the Banker s problem. Using a Petri
Net model we derive formulas for this set (SAFE) directly and for its (smaller) minimal elements
set MIN. Moreover, we partition the set MIN into subclasses, so that two elements of the same
subclass only differ by the permutation of their components. The set SORT, which contains only
one representend of each subclass, is an even smaller representation of the safe states. We also
derive estimates for the size of SORT. Finally we investigate, how our results can be translated to
the multidimensional Banker s Problem, where credits in more than one currency can be given
Net model we derive formulas for this set (SAFE) directly and for its (smaller) minimal elements
set MIN. Moreover, we partition the set MIN into subclasses, so that two elements of the same
subclass only differ by the permutation of their components. The set SORT, which contains only
one representend of each subclass, is an even smaller representation of the safe states. We also
derive estimates for the size of SORT. Finally we investigate, how our results can be translated to
the multidimensional Banker s Problem, where credits in more than one currency can be given
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Banker's Algorithm3.pdf