Hi all,

first the typo candidates:

in (17) page 23 there are two ’ missing:

1st line …[[L:x->(L’) instead of [[L:x->(L),

2nd line at the end: A:a’ instead of A.a

and in (18) 1st line [[L:x-a’ ->(L’ instead of [[L:x ->(L

or did I misunderstand it?

Now the question to the broader understanding:

I wonder why the partial whitdrawal is so complicated. The operations make sense and I understood that it’s possible in this way.

However, applying what has been discussed near Figures 14 and 5, a simple \Tau(L,A,a’) should work - not?

To see it, line (13) could be finalized and then, in the adjudicator notation similar to figure 5 would read:

Adjudicator:

Address | Balance | outcome

L |x |A:a+a’, B:b,\xi:c

applying

\Tau(L,A,a’) gives what we want

Adjudicator:

Address | Balance | outcome

L |x |A:a, B:b,\chi:c

A |a’ |

The paper approachs requires in step to (16) also to finalize L on chain. However the result is that the channel \chi later ‘lives’ in L’ and no more in L.

Using the proposed 2 steps above, A could whitdraw a’ while still having \chi in the original L (which does not need to be discarded).

Or did I overlook something?

Another approach which came to my mind at first is the inverse of the toping-up sequence when introducing a rule that the one at the end (or likewise the one at the top of the priority list) can draw out overfunds

- update the state to move A to the end (or likewise to the front) and reduce its balance (off-chain operation)

[L->(B:b), \chis:c, A:a]

now a’ is free and could (according to the rule) be wihtdrawn by A

In conclusion I’d like to keep \chi in L and have a ‘symmetric’ approach for deposit and withdrawal.

I’d be grateful for any hints/ discussion

Alex

P.S. I categorized as protocol design because there is no nitro category