Effective ways to turn grass weeds into compost

Hi,
I've got a bit of the kikuyu grass http://www.weeds.org.au/cgi-bin/weedident.cgi?tpl=plant.tpl&ibra=all&card 7 as well as other weeds in my lawn. The council planted it as the common nature strip grass and some of it has gotten into my garden.
They grow very quickly - and are very resilient. I've been weeding them out- and throwing them into the rubbish bins.
But can I put it into my compost bin- or will the grass roots survive and grow again? How can I make sure that the weeds' roots, runners, and their seeds rot - and don't grow again.
My old gardener was simply in favor of throwing them away - as the laws here now prohibit open fires which meant he couldn't burn the old weeds.
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YMC said:

The easiest way to make sure the weed seeds rot in the compost bin is to cut or pull the weeds before the seeds are anywhere near mature. And then put the top of the plants in the compost immediately.
Roots/runners should be left out in the sun for several days until they are quite dried up, then composted.
--
Pat in Plymouth MI ('someplace.net' is comcast)

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The best place to use weedy compost is in deep shade where the weeds cannot thrive. Two compost piles, one clean for sun and one weedy for shade solves most of the problem.
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In article

I have three plies somewhat active. Id hazard a guess anything added to planting areas are a few years old. The weeds may grow but the competition weed out the weeds in my piles.
Delusional Bill whose Dad says add more lime.
--
Garden in shade zone 5 S Jersey USA

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