31 lines
2.0 KiB
XML
31 lines
2.0 KiB
XML
#align(center, [
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= Review of "Abstract Interpretations, Numerical Domains" by Silvia Gaspari
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== Matthias Veigel
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])
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=== Summary
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The paper deals with numerical domains and how they work.
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The domains are all based on a concept called latice, which is an ordered set of sets with #sym.tack.t as empty set and #sym.tack.b as set which includes everything from the other sets.
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The different domains specified in this paper are: Interval: number #sym.in [a,b], Polyhedron: lattice of intervals, Zone: x #sym.in [a,b] and x - y < constant, Octagon: Extension of zone domain with #sym.plus.minus x #sym.plus.minus y < constant, Pentagon: x,y are program variables and x #sym.in interval and x < y -> y as upper bound.
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These domains can then be used to constrain variables.
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=== Previous experience
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I have no previous experience with lattices or numerical domains.
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=== General Feedback
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#[
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#set list(marker: [+])
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- Good Structure, Domains ordered from least to most complex
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- Detailed explanation of domains
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- Methodology is clearly described
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]
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#[
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#set list(marker: [--])
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- Many typos
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- Incomplete sentences
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- Inconsistent capitalization
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- The text of figure 1 and figure 2 is hard to read, because it is too small.
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- Figure 1: 0 and +/- are too close together.
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- Section 4.2: Should use #sym.NN,#sym.ZZ,#sym.QQ,#sym.RR instead of N,Z,Q,R (possible with `\mathbb{N}` in latex, `#sym.NN` in typst)
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]
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The paper has a good structure and the different domains are clearly described. A big problem in the paper is the missing explanation for lattices, since most of the paper is build on this concept. I also noticed a few logic mistakes in section 4.1: arithmetic operators: (+) - (-) should result in (+) not #sym.tack.b, (-) - (-) should result in #sym.tack.b not (-), (+) \* (+) should result in (+) not (-). The papers are also not really evaluated yet, only the content in them is summarized currently. Another useful thing to include would be the table from 0:25 in https://www.youtube.com/watch?v=jWUXclaKppk for initial understanding and comparison of the numerical domains.
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