wanted: interpretations over vectors-of-arctic-polynomials

... and get "almost linear interpretations" (Hofbauer WST 2018 http://wst2018.webs.upv.es/index.html#proceedings) as an instance.

domain of interpretation is vector of arctic numbers, each letter is interpreted by function that combines argument vector components with (semiring) plus and times (that is, max and plus).

The challenge is to find reasonable conditions that ensure strict monotonicity.

Also, restrict non-linearities to quadratic (product of two vector components) by taking operators of the form x^T A x.

This will result in quadratic deriv. complexity?

The problem is that this class (quadratic polynomials) is not closed w.r.t. composition: interpretations of 2-letter words will be biquadratic, etc., unless add some restrictions.

Note: almost linear functions are nicely closed w.r.t. composition