Sentence examples for refinement of partitions from inspiring English sources

Fig. 1 Refinement of partitions.

Refinement of partitions (mathcal {P}_{1}) with two blocks and (mathcal {P}_{2}), with three blocks.

Partition obtained based on the reward function from Fig. 4 Fig. 7 Refinement of partitions with ADDs.

Refinement of partitions (mathcal {P}_{1}) and (mathcal {P}_{2}) from Fig. 1, computed using the product (mathcal {P}_{1} otimes mathcal {P}_{2}).

The basic idea behind the enumeration algorithm presented below is to introduce an iterative refinement of partitions of the space of feasible solutions i.e. of the space of hyperpaths and in each part to look for a solution.

where In this case, Cathy's information partition is a refinement of the partition she has when there is no announcement, for in this case, then Cathy knows a priori that if ω1 is the case there will be no announcement and will know immediately that she is clean, and Cathy knows a priori that if ω2 is the case, then she will know immediately from the cook's announcement that she is messy.

A partition (mathcal {P}') is a refinement of a partition (mathcal {P}) if and only if each block of (mathcal {P}') is a subset of some block in (mathcal {P}), i.e., a refinement splits a block B i in sub-blocks generating a finer partition.

A refinement of a partition P = { S1, S2,..., S j } is a partition such that each element of P' is contained in exactly one of the elements of P.

By inequality (38), the sum of the affine distances along these segments is a non-increasing function under refinement of the partition.

To compute the refinement of q labeled partitions represented as ADDs, we need to get the product of ADDs representing these partitions.

The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of a state partition which is a bisimulation on some Kripke structure is well known.