instance, similar to an earlier approach in [@EQU]. We also show some differences from that in [@EQU] for the corresponding index coding instance. Second, their equivalence is proved for a given index coding instance. For a given index coding instance, Gupta and Rajan defined the corresponding network coding instance and showed an equivalence between a network computation problem and a functional index coding problem [@FEQU]. However, the equivalence in [@FEQU] for a given index coding instance has some weak points, which will be explained in this section. In order to mitigate these weak points, for a given index coding instance, we introduce a corresponding network coding instance which differs from that in [@FEQU] and show a different equivalence relationship between them. In the following definition, the equivalence between two problems is described.

NCLE and ICSIE problems are said to be equivalent if and only if the NCLE can be converted to the corresponding ICSIE and vice versa.

Equivalence for a Given Network Coding Instance
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For a given network coding instance, we can construct the corresponding index coding instance in a manner similar to that in the aforementioned research [@EQU]. The differences between our corresponding model and that in [@EQU] 