  The study of the operational complexity of minimal pumping constants started
in [J. DASSOW and I. JECKER. Operational complexity and pumping lemmas. Acta
Inform., 59:337-355, 2022], where an almost complete picture of the operational
complexity of minimal pumping constants for two different variants of pumping
lemmata from the literature was given. We continue this research by considering
a pumping lemma for regular languages that allows pumping of sub-words at any
position of the considered word, if the sub-word is long enough [S. J. SAVITCH.
Abstract Machines and Grammars. 1982]. First we improve on the simultaneous
regulation of minimal pumping constants induced by different pumping lemmata
including Savitch's pumping lemma. In this way we are able to simultaneously
regulate four different minimal pumping constants. This is a novel result in
the field of descriptional complexity. Moreover, for Savitch's pumping lemma we
are able to completely classify the range of the minimal pumping constant for
the operations Kleene star, reversal, complement, prefix- and suffix-closure,
union, set-subtraction, concatenation, intersection, and symmetric difference.
In this way, we also solve some of the open problems from the paper that
initiated the study of the operational complexity of minimal pumping constants
mentioned above.

Formal Languages and Automata Theory