For temperature, there is a thermometer, with a simple scale, to measure heat and coldness. It turns out, hot and cold are easy to define relative to one another - they are opposites. One is the absence of the other. Regulation and competition are neither one-dimensional, nor are they opposites. Competition refers to the state of a market, particularly how businesses behave in a market.
Regulation refers to how government interferes with the market.
Absent government intervention, markets may be competitive, monopolistic, or anywhere in between. With government intervention, markets may take on any characteristic, although I believe the likelihood of competition is diminished by substantial government intervention. Consequently, I see nor causality, no necessary and sufficient conditions in any direction between competition and regulation. Non interference Provision of a stable currency Provision of a national defense. The government has other roles that go beyond law enforcement.