Show differences from existing methods

[MichaelJFishman]

Some reviews asked how this differs from existing methods. Explain the differences.

[camall3n]

@MichaelJFishman Is the intent to distinguish scoping from these others, or to improve clarity by explaining scoping better in terms of existing techniques?

If it's the former, we should make an additional issue for the latter.

[MichaelJFishman]

@camall3n

At least the latter. Review 2.4 says

I think the suggested technique could be
presented as an actual abstraction, combined with pruning of operators
irrelevant in the abstraction: the suggested technique combines a
projection (not in the sense of the paper) with a domain abstraction
(to a single value). (Some operators would need to be removed and
others would need to be "combined", more on this below.) This would
have the great advantage that all of the properties discussed in
Sections 3.1 and 3.2 would follow automatically from the transformation
being a homomorphism. One would then "only" need to argue why the
transformation additionally allows plan reconstruction from the
transformed to the original task. I recommend reading Sections 2 and 3
of "Merge-and-Shrink: A Compositional Theory of Transformations of
Factored Transition Systems" by Sievers & Helmert (JAIR 2021). While
that work deals with transformations of LTS rather than tasks, I think
the concept is applicable to FDR tasks. Note that they also discuss how
transformations can prune states or operators (Section 8). Furthermore,
the concept of "label reduction" (Section 7) should capture the
"combination of operators" discussed in here.

Edit: This comment is more relevant to #15 .

[MichaelJFishman]

Specific methods to relate to:

• Merge and shrink Find or implement merge & shrink #10
• Irrelevance pruning Find or implement irrelevance pruning #11
• Others (see issues)

[MichaelJFishman]

Rewording:

Use standard verbiage to make our method more clear, and to compare and contrast to existing methods.

[MichaelJFishman]

Expressing PPP using merge-and-shrink is a mess

It seems that expressing PPP as a composition of shrink, prune, label reduce, label prune transformations will a mess. The shrink transformation will throw away information we need at one of the label-pruning steps of PPP. In particular:

Part of a PPP transformation is, in order

1. Ignore effects on vshrink. This is part of a shrink transformation
2. Merge operators that are effect-equivalent Label reduction transformation
3. Delete merged operators that condition on vshrink This relies on pre-shrink-transformation data!

The problem is that for FTS, we’d use the shrink transformation to ignore effects on vshrink, but the shrink transformation will remove any conditioning on vshrink.

We could

1. Apply shrink to FTS X0 to get system X1
2. Collect labels that are now effect-equivalent in X1
3. Map each of these equivalence classes in X1 back to the pre-shrink labels in X0
4. Reduce those pre-shrink labels to get X2
5. Delete any label from this reduced label set (in X2) that conditions on vshrink, in order to get FTS X3
6. Apply a shrink transformation to X3 to get a new FTS X4

But this seems messier than our existing description.

Mermaid graph of this. Solid lines are between FTS, their transformation, and the output FTS. Dashed lines indicate that a transformation definition is based on the source FTS.

graph LR

X0
X1
X2
X3
X4

F0(("shrink"))
F1(("label reduce"))
F2(("label prune"))
F3(("shrink"))

X0 --> F0 --> X1
X1 -.-> F1
X0 -->F1-->X2
X2 --> F2 --> X3
X3 --> F3 --> X4

Loading

graph LR

X0
X1
X2
X3
X4

F0[/"shrink vshrink"/]
F1[/"reduce labels based on the effect-equivalence of their images in X1"/]
F2[/"prune labels which condition on vshrink"/]
F3[/"shrink vshrink"/]

X0 --> F0 --> X1
X1 -.-> F1
X0 -->F1-->X2
X2 --> F2 --> X3
X3 --> F3 --> X4

Loading

Moving forwards

There may be another step left in PPP after the above. I'm not sure, and I don't know if we need to find out.

I think a minimal path is:

1. In the paper say

A PPP transformation is similar to a composition of prune, shrink, label reduction, and label pruning* transformations from helmert-et-al. We can describe our transformation in this way, but the following expression is simpler. See the supplement for a partial expression of PPP in merge-and-shrink.

2. Put a slightly cleaned up version of the above in the supplement.
3. (tangent) Edit the paper to use partial functions instead of mapping some elements to null.

[camall3n]

What does vshrink mean?

[MichaelJFishman]

Set of variables that will be shrunk to a single value each. V_projected or v_irrelevant in the paper/code.

…

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