The New Sudoku Players' Forum

[aran]

Isnt "chain memory" usually called "net"?

yes, exactly.

a stream of implications
where each step stands on its own (no "memory")
is used in "chains"

as soon as we need "memory",
i.e. a step uses results from some earlier step,
this is called a "net"

If the definition which someone has previously given covers single strand chains then so be it.
I would merely point out that :
1. it doesn't correspond to any intuitive notion of the word net (interwoven strands)
2. it isn't imho what most people have in mind when they refer to nets. What they do have in mind imho is branching chains which either
- subsequently merge and then resume as a single chain, or
- which converge/unite on a conclusion eg
strand A=>r1c1=9
strand B=>r5c1=8
strand C=>r8c1=6
hence <689>=37r4c1 which combines with 37r5c3 (which came from strands D,E,F) to conclude <37>=2r6c.
Not quite the same creature as single strand memory.

[Pat]

If the definition which someone has previously given covers single strand chains then so be it---

"Forcing chains: Terminology and Definition" is the discussion where the terminology was established (2006).

it distinguishes between 2 types of "Network" --

• "Forcing Chain"
• "Forcing Net"

-- and does include the "SIN (Single Implication Network)" (a network with one implication-stream),
which may be what you're calling "single strand"---

[aran]

If the definition which someone has previously given covers single strand chains then so be it---

"Forcing chains: Terminology and Definition" is the discussion where the terminology was established (2006).

it distinguishes between 2 types of "Network" --

• "Forcing Chain"
• "Forcing Net"

-- and does include the "SIN (Single Implication Network)" (a network with one implication-stream),
which may be what you're calling "single strand"---

With respect, what you write does not reflect the logic used in what I was calling single strand chains : there is no forcing of any sort.
Excerpts from the post to which you refer :
1. Error Net or SIN (Single Implication Network) - a network with one implication stream that starts with a candidate selected in one node and propagates with or without multiple inferences until a contradiction is revealed. Due to this contradiction, such as 'empty cell', 'one digit appears 2 times in a unit' and 'no place for a digit in a unit', it can be concluded that the candidate selected at the start is invalid. This is also the principle of a "backtest".
2. Forcing Chain - a chain that has 2 or more implication streams that start from one node and end in another node where the outcomes of inferences merge from the 2 implication streams. In a forcing chain, a node can only infer the next successive node downstream.
(the text then gives an example concluding as follows, clearly demonstrating the forcing nature)
r9c6=7 => r9c1=8 => r9c1<>7
r9c6=8 => r8c5=7 => r3c5<>7 => r3c1=7 => r9c1<>7
Therefore r9c1<>7
3. Forcing Net - same as a forcing chain, except that in a forcing net, a node could infer 2 or more nodes downstream. Such inference is regarded as a multiple inference.
(the text then gives an example concluding as follows, clearly demonstrating the forcing nature)
r9c1=5 => r9c7=8 => r7c9=7 (=> r8c8<>7) => r7c8=2 => r8c8=5 => r3c8<>5 => (r3c18=17) => r3c2<>17 => r3c2=8 => r1c3=2 => r5c3=3
r9c1=9 (=> r5c1<>9) => r4c1=7 (=> r5c1<>7) => r3c1=1 => r5c1=2 => r5c3 =3
Therefore r5c3=3.
4. Network - a collective term for forcing chain and forcing net.

In the single strand chain, deductions further along can be made by remembering what has already been determined within the chain. None of that was or is forcing (at least not anymore than not a in a bivalue ab "forces" b).
So in other words, there is memory, there is branching, and there is memory with branching.
Single strand chains use memory alone.