I was wondering about this passage in the finite promise game specification
Z is the set of all integers. N is the set of all nonnegative
integers. All letters represent integers.
We say that T:N^k into N is PL if and only if it is piecewise linear
with integer coefficients. I.e., T can be defined by various affine
functions with integer coefficients on each of finitely many pieces,
where each piece is defined by a finite set of linear inequalities
with integer coefficients.