Arms control specialist Cheryl Rofer argues that the nuclear weapon programs pursued by the dictatorships of Iran and North Korea were "Regime Change Deterrents":
The nuclear strategies of North Korea and Iran, up to now, are not the strategies of aggressors. They have left their options open to grow the programs in the future, but that is only prudent. The programs might be called “minimum deterrence.”
She bases this assessment on the fact that these countries produced or planned to produce a rather small number of weapons. A similar case might have been South Africa's nuclear weapon program, or maybe Pakistan up to a point.
My question is, can we define a cut-off point or area between a "minimum deterrent" nuclear weapons program and a more offensive one?
Candidates for cut off points might be: Numbers of weapons mated to delivery systems at any one time, numbers of warheads bigger than the minimum that allows economical maintenance (what would that number be? 5? 1? a dozen?) or a doctrine when to use these weapons. The biggest factor may be if there's a practical lower limit in size for a nuclear weapons program.
To use the Wikipedia definition of minimal deterrence:
Assuming that decision-makers make cost-benefit analyses when deciding to use force, China's doctrine calls for acquiring a nuclear arsenal only large enough to destroy an adversary’s "strategic points" in such a way that the expected costs of a first strike outweigh the anticipated benefits. [...] For example, the United States’ nuclear force exceeds the requirements of minimal deterrence, and is structured to strike numerous targets in multiple countries and to have the ability to conduct successful counterforce strikes with high confidence.
So we can conclude that somewhere between the nuclear arsenal sizes and structures of North Korea and the USA we have a phase change from minimal deterrence to soemthing else. Can we define a cutoff point, beyond which a nuclear weapon program is built for more than minimum deterrence?