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Method for definition of lookup tables

  Draft

Overview

A lookup table may be viewed as a set of of parallelized truth tables receiving the same inputs and providing collectively a vector of outputs instead of a single one. In this sense m constraints would be needed to model m outputs. A more efficient and expandable approach however would be to model the lookup table as a memory element with k inputs (address) and m outputs (memory word).

Applicability

Lookup tables are appropiate for functions which outputs depend on a combination of values of the inputs. Lookup tables map input value (ranges) to output values. 

Examples

The following lookup table relates the brake distance and brake time dependent on the train velocity where the standstill corresponds to row #1 (this is simplified because this mapping depends on several other aspects).

rowinput (train velocity)input (estimated brake distance)output (estimated brake time)
#10 km/h0 m0 s
#2<= 20 km/h28 m9 s
#3<= 40 km/h99 m17 s
#4<= 60 km/h215 m24 s
#5<= 80 kn/h375 m32 s
#6<= 100 km/h579 m40 s
#7<= 120 km/h827 m48 s