I put roots in, but probably not things like couch grass or mint....
Roots usually have lots of soil clinging to them and the soil microbes seem to help with the rotting process. In fact its a good idea to put a thin layer of soil into the bin at intervals.

I always thought the heat generated from composting would destroy all plant matter. Here's what I just read:

'High temperatures are necessary to destroy pathogens and weed seeds in compost piles. Heat is released in the aerobic process that takes place as organic matter rots. However, excessively high temperatures remove some of the nitrogen in the compost.'

Read more at Gardening Know How: My Compost Is Too Hot: What To Do About Overheated Compost Piles https://www.gardeningknowhow.com/composting/basics/overheated-compost-piles.htm

Sadly the temperature needed to destroy Japanese knotweed roots is higher than most garden heaps achieve. Not even sure that the commercial ones make it either.
We have a Non-compost heap. All roots, like Dock, dandelion,couch, ground elder go on it. The heap is permanently covered with plastic sheeting. After about 5 years the material in it is good compost. But we certainly do not put the roots of persistent weeds in the ordinary heap.r

I seem to remember that it is illegal to dispose of jap.knotweed in council bins etc as it doesn't get destroyed in the council heaps either. Certainly when my eldest lived in Wales her rented property had it all over the back garden. because she did nothing with it the landlord tried to keep her £500 deposit. she fought him on the grounds that it was illegal for her to dump/bin it. she won her case.

the only roots that don't go in my bins are dandelion, that little yellow flowered oxalis, creeping sowthistle and any bits of bind weed I come across. otherwise it all goes in.

I don't put celandine roots in the compost (adding to Seaburngirl's list)....

Thankyou all. I think I will start to put a few roots in but not the pernicious ones mentioned. Stera, I like the notion that there are microbes in the soil clinging to the roots so they could improve the compost. Bathgate, I'm sure my compost bin doesn't get too hot; sometimes I wonder whether it gets hot enough.
SBG, I worked in housing for years and it seemed to me that some landlords would try anything to keep the deposit. If the Jap Knotweed was already in there when your daughter signed up I would argue that it was up to the owner to remove it (try to!). However, the point about being unable to bin it was a brilliant stroke.

When we talk about heat produced in compost - I believe that Dalek bins never actually get hot enough to destroy weed seeds. I would love to be wrong - anybody ready to say Nay?

sadly my dalek ones never seem to get too hot so I don't put flower heads in of dandelions or chickweed as they can continue to mature for several days in the compost bin. so I am not going to argue there Stera.

yes the Jap Knotweed was already well established pushing up the concrete back yard, but it had been mown /cut off and dumped in a black plastic liner in the dilapidated garage. her dad told her never to go inside it as it looked as if it would collapse at any time. Landlord was a waste of space, rarely doing any fixing of things that needed doing. when the washing machine broke he didn't fix it as there was a launderette on the corner of the next street.

I would say that the majority of composting in Britain, certainly in garden terms, is what is known as 'cold composting'. It does decompose material, but much slower than in 'hot systems' and obviously does not destroy nearly as many pathogens either.

Stera mine is a BIG Yay to Dalek Bin Composting, I have four bins and the dalek one gets the hottest, it steams when I am turning it, have to admit that one is in the sun nearly all day, whereas my others are hidden away in the cubby behind the conifers, it obviously makes a huge difference, its also the one that gets turned more through the course of the year and being the easiest to get at,
is the one that gets the scrap vegetables, tea leaves, hoover dust etc.....as well as the weeds and grasscuttings...

I've found turning in daleks very difficult actually. Full sun and occasional grass cuttings do heat them up but the bin nearest the kitchen is definitely cold composting. I do find occasional reptiles in them too which makes me a bit chary of sticking a fork in...I don't put weed seeds in any of them if I can avoid it. I wish I'd had big wooden bins now that hold more and get warmer...

Stera I agree as regards the wooden bins, like the ones Monty has but possibly not as big, so much easier to work...
Anything that I think will create problems, ie , bindweed, seedheads and suchlike go in my council garden waste bin, years ago they would have gone in an incinerator, problem solved, frowned upon now....

Makes sense. We haven't got a council bin - we have so many branches etc from annual trimming, wind damage etc that we can't manage without two or three bonfires a year and there is far too much to go in a bin anyway. . We try to do it on a day when the wind blows the smoke away from any neighbours and in Spring we wait until all the babies in the rookery have fledged and gone. So anything noxious goes on the heap to dry into firelighters. OH can't get on with the shredder (it can't deal with the thick stuff anyway) and is very reluctant to have a trailer so that we could use the council tip for the big stuff- our access is difficult for anything like that. We are very fortunate that bonfires are not banned here.

They're not exactly banned Stera, just frowned upon, apart from the odd one on Bonfire Night, we never see any around here, I know what you mean about the shredder, have got one and its been used twice in the last five years, that was to get rid of the old apple and willow tree, luckily my nephew has many magic tools so he cut all the big bits up for us, he took most away also to store for his log burner, much to our relief, the shredder was only used for the smaller bits , very, very noisy and took ages....

At least you don't have to worry about 'White Snakeroot'. It's a tenacious poisonous weed that wants to take over my garden. My sickle is the only thing that works.

I have three compost bins, all behind a shed and sun in the evening for a while. It takes at least 18 months for the waste to turn into compost but when it does - wow! Fantastic. I had one of those tools for turning the compost and it was brilliant but now the 'wings' have fallen off (probably due to lack of cleaning) I find it near impossible.

SBG. I often advised clients to go to CAB about their rights as tenants. They have access to experts in housing and would often write to landlords on the tenant's behalf. My son is now renting and insisted that his private landlord replace their washing machine. Fortunately, he's not a bad landlord.

I wonder why your turning thing worked and mine didn't - perhaps you had a more up market version! I do get good compost eventually but as the kitchen waste always goes into the bin near the house the rotted stuff is only in the lower part, and very hard to get without lifting the bin off altogether, which needs OH...

It's all about science. You need to have a little brown, a little green, a little moisture & sufficient oxygen getting into the center.

Stera I have always found the proper turning tool impossible, I am not tall enough or strong enough come to that, I use a broken halfmoon tool instead, push it down into the centre of my compost, give it a twirl which creates a whirlpool in the centre, then scrape the top layer into said hole, do that a few times until the fresh is worked in....