| Summary: | A linear inference is a valid inequality of Boolean algebra in which each
variable occurs at most once on each side.
In this work we leverage recently developed graphical representations of
linear formulae to build an implementation that is capable of more efficiently
searching for switch-medial-independent inferences. We use it to find four
`minimal' 8-variable independent inferences and also prove that no smaller ones
exist; in contrast, a previous approach based directly on formulae reached
computational limits already at 7 variables. Two of these new inferences derive
some previously found independent linear inferences. The other two (which are
dual) exhibit structure seemingly beyond the scope of previous approaches we
are aware of; in particular, their existence contradicts a conjecture of Das
and Strassburger.
We were also able to identify 10 minimal 9-variable linear inferences
independent of all the aforementioned inferences, comprising 5 dual pairs, and
present applications of our implementation to recent `graph logics'.
|
|---|