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notebooks: correction of typos

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* tests/python/_partitioned_relabel.ipynb,
  tests/python/_product_weak.ipynb,
  tests/python/acc_cond.ipynb,
  tests/python/aliases.ipynb,
  tests/python/automata.ipynb,
  tests/python/cav22-figs.ipynb,
  tests/python/contains.ipynb,
  tests/python/decompose.ipynb,
  tests/python/formulas.ipynb,
  tests/python/games.ipynb,
  tests/python/highlighting.ipynb,
  tests/python/ltsmin-dve.ipynb,
  tests/python/parity.ipynb,
  tests/python/product.ipynb,
  tests/python/satmin.ipynb,
  tests/python/stutter-inv.ipynb,
  tests/python/synthesis.ipynb,
  tests/python/twagraph-internals.ipynb,
  tests/python/word.ipynb,
  tests/python/zlktree.ipynb: here
This commit is contained in:
Florian Renkin 2023-06-20 15:10:00 +02:00
parent 858629dd3a
commit 6dc11b4715
20 changed files with 242 additions and 82 deletions
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31
tests/python/decompose.ipynb
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@ -12,6 +12,7 @@
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@ -28,9 +29,9 @@
"- an accepting SCC is **strictly inherently weak** if it is *inherently weak* and not complete (in other words: *weak* but not *terminal*)\n",
"- an accepting SCC is **strong** if it is not inherently weak.\n",
"\n",
"The strengths **strong**, **stricly inherently weak**, and **inherently terminal** define a partition of all accepting SCCs. The following Büchi automaton has 4 SCCs, and its 3 accepting SCCs show an example of each strength.\n",
"The strengths **strong**, **strictly inherently weak**, and **inherently terminal** define a partition of all accepting SCCs. The following Büchi automaton has 4 SCCs, and its 3 accepting SCCs show an example of each strength.\n",
"\n",
"Note: the reason we use the word *inherently* is that the *weak* and *terminal* properties are usually defined syntactically: an accepting SCC would be weak if all its transitions belong to the same acceptance sets. This syntactic criterion is a sufficient condition for an accepting SCC to not have any rejecting cycle, but it is not necessary. Hence a *weak* SCC is *inherently weak*; but while an *inherently weak* SCC is not necessarily *weak*, it can be modified to be *weak* without alterning the langage."
"Note: the reason we use the word *inherently* is that the *weak* and *terminal* properties are usually defined syntactically: an accepting SCC would be weak if all its transitions belong to the same acceptance sets. This syntactic criterion is a sufficient condition for an accepting SCC to not have any rejecting cycle, but it is not necessary. Hence a *weak* SCC is *inherently weak*; but while an *inherently weak* SCC is not necessarily *weak*, it can be modified to be *weak* without altering the language."
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@ -214,6 +215,7 @@
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@ -225,7 +227,7 @@
"- `w`: (strictly inherently) weak\n",
"- `s`: strong\n",
"\n",
"For instance if we want to preserve only the **strictly inherently weak** part of this automaton, we should get only the SCC with the self-loop on $b$, and the SCC above it so that we can reach it. However the SCC above is not stricly weak, so it should not accept any word in the new automaton."
"For instance if we want to preserve only the **strictly inherently weak** part of this automaton, we should get only the SCC with the self-loop on $b$, and the SCC above it so that we can reach it. However the SCC above is not strictly weak, so it should not accept any word in the new automaton."
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@ -343,6 +345,7 @@
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@ -682,6 +687,7 @@
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@ -2355,12 +2363,13 @@
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"Note how the two weak automata (i.e., stricly weak and terminal) are now using a Büchi acceptance condition (because that is sufficient for weak automata) while the strong automaton inherited the original acceptance condition.\n",
"Note how the two weak automata (i.e., strictly weak and terminal) are now using a Büchi acceptance condition (because that is sufficient for weak automata) while the strong automaton inherited the original acceptance condition.\n",
"\n",
"When extracting multiple strengths and one of the strength is **strong**, we preserve the original acceptance. For instance extracting **strong** and **inherently terminal** gives the following automaton, where only **stricly inherently weak** SCCs have become rejecting."
"When extracting multiple strengths and one of the strength is **strong**, we preserve the original acceptance. For instance extracting **strong** and **inherently terminal** gives the following automaton, where only **strictly inherently weak** SCCs have become rejecting."
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@ -2741,6 +2750,7 @@
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@ -4577,7 +4590,7 @@
"\n",
"### `Acceptance: 0 t`\n",
"\n",
"This occur frequently whant translating LTL formulas that are safety properties:"
"This occur frequently when translating LTL formulas that are safety properties:"
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