Generate a custom data structure
This function acts as a DGS - Data Generating Structure for a certain SOP expression.
generate(expression = "", snames = "", noflevels)
expression |
String: a SOP - sum of products expression. |
snames |
A string containing the sets' names, separated by commas. |
noflevels |
Numerical vector containing the number of levels for each set. |
Using the power of SOP expressions, this function can generate the data for any type of expressions, either Boolean or multi-value.
Causal conditions should always be separated by a product sign "*", unless: - they are single letters, or - the set names are provided, or - the expression is multi-value
All conditions are considered binary crisp, unless the number of levels are provided
in conjunction with the set names, in the order of their specification from the
snames argument.
This is an extension of the function expand(), the process
of data generating process being essentially a Quine expansion to a Disjunctive
Normal Form.
Adrian Dusa
generate(D + ~AB + B~C -> Z) # the positive configurations in their complete DNF expansion: expanded <- expand(D + ~AB + B~C, snames = c(A, B, C, D)) # ~A~B~CD + ~A~BCD + ~AB~CD + ~ABCD + A~B~CD + A~BCD + # AB~CD + ABCD + ~AB~C~D + ~ABC~D + AB~C~D # which has the equivalent simpler, initial expression: simplify(expanded) # D + ~AB + B~C # same structure with different set names # (note the mandatory use of the product sign *) generate(Alpha + ~Beta*Gamma + Gamma*~Delta -> Omicron) # introducing an additional, irrelevant condition # (note the product sign is not mandatory if providing the set names) setnames <- "Alpha, Beta, Gamma, Delta, Epsilon" dat <- generate(Alpha + ~BetaGamma + Gamma~Delta -> Omicron, snames = setnames) head(dat) # Alpha Beta Gamma Delta Epsilon Omicron # 1 0 0 0 0 0 0 # 2 0 0 0 0 1 0 # 3 0 0 0 1 0 0 # 4 0 0 0 1 1 0 # 5 0 0 1 0 0 1 # 6 0 0 1 0 1 1 minimize(dat, outcome = Omicron) # M1: Alpha + ~Beta*Gamma + Gamma*~Delta <-> Omicron
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