realy the only way is to lift the sidewalk and put black membrane down that lets the water through but not the light.saying that though some weeds will quite litteraly grow in any slightly damp place with the tiniest bit of soil etc.ive got a picture on here of a plant growing out of wear a little bit of morter has fallen out between bricks that is fairly comparitivly new brickwork in a block of flats . so the answer is yes if you have membrane under your sidewalk and you keep it very clean and brushed.if its a cement path with know gaps which im guessing yours isnt then again if you brush and clean it regulerly yes.i guess if you want to keep it as natural as possible then either use bleach or salt with water thats hot when you do clean up as both kill weeds and break down without causing much harm .i hope ive helped take care bye for now .

Noseypotter's right - the only other thing you can do is fill in the cracks with a mortar mix, so there's nowhere for plant seeds to get in.

well there is not much of a natural way from keeping weeds out. you could try applying a pre-emergent this will keep the weed seeds from germenating causing it to die. if you already have weeds growing in the cracks you could use vinegar diluted with water one part water two part vinegar should be fine.

Whatever you use, you have to persist, as weeds will grow anywhere in the shallowest of soils and smallest of cracks. Look at the trees growing out of bare rock on mountainsides and crags!
Ordinary table salt is one of the best and cheapest ways, but use plenty and keep using it.
Otherwise, a flame gun is very effective, but only until the weeds start growing again.
It's boring, but you have to keep at it to keep weeds completely in check.

great minds hay bertie lol