No weed will grow "through" concrete slab, though of course tree roots and such can breakk it up by lifting it - but all weeds and many trees will have seeds lodge in the cracks and sprout there, and horsetail and trees and some bushes growing from cut off stems will grow up through the cracks. Of course, boiling water (if concrete is not real cold), vinegar (though that damages the concrete too), flame, and herbicides can control that, as can hand pulling.
Ways to kill it, other than the repetitive tilling and mulching (which can take up to a year) - note some of these also kill nearby vegetation including in some cases lawn grasses, some don't - read manufacturer info or label:
1) pure vinegar applied directly to plant and stem will kill any weed - use a medicine dropper or syringe orpaint brush to minimize adjacent plant damage. Will take multiple applications over several weeks as the wide-spread roots continue to push up new stems to try to get sunlight. Best type is agricultural vinegar - 20% solution versus 5% in kitchen vinegar - treat safely per instructions as is a moderately strong acid.
2) For horsetail and mares tail - Kurtail from ProGreen Weed Control in Britain - available at some garden supply houses, more the commercial ones some years ago - don't know if still available in US. Works unbelievably well, but very pricey because comes in highly concentrated form for professional mixing and spraying. Also, grass and weed killers (usually only available at commercial feed and seed type stores) containing Timbrel from Dow AgriSciences. Also, repetitive pulling of the shoots will eventually kill it over the course of a year or two, because without the sunlight it eventually dies off. This is best method for vegetable or flower beds where you don't want to risk killing adjacent plantings. You have to stay on top of it - once plant gets a couple of inchers high it is furnishing energy to the roots again, so you have to get them every few days.
3) For pretty much any weed including horsetail and marestail and clover - post-emergent weed killer with 2,4-D like Dow Frontline or Ortho Bush B Gon (which also works on bamboo if injected into stalks); or Ortho Weed B Gon Max Plus Crab Grass (which also works well on weeds like mustard, lambstail, pineapple plant, clover, crab grass, plantain, etc).
4) For the vinegar and herbicide methods, because horsetail and marestail have very tough outer casings, it works WAY better if you crush the plant before poisoning it - smash between two boards or rocks, or crush several places on stem with a pair of pliers before applying poison. Of course, if you are REALLY fed up with them, then inject with a hypodermic needle into a cut-off top of the stem.