Few fixes

report/report.tex

@@ -435,7 +435,7 @@ At this point, we can define the \emph{signature of order $n$} ($n \in
         + \text{IO adjacency}
         + \hspace{-2em}\sum\limits_{C_i \in \,\text{neighbours of inputs}}
             \hspace{-2em}\sig_n(C_i) \hspace{1em}
-        - \hspace{-2em}\sum\limits_{C_o \in \,\text{neighbours of inputs}}
+        - \hspace{-2em}\sum\limits_{C_o \in \,\text{neighbours of outputs}}
             \hspace{-2em}\sig_n(C_o)
 \end{align*}
 
@@ -459,11 +459,11 @@ lazy.
 
 To keep those memoized values up to date whenever the structure of the circuit
 is changed (since this is meant to be integrated in a programming language, fl,
-meaning the structure of the circuit will possibly be created, checked for
-signature, altered, then checked again), each circuit keeps track of a
-``timestamp'' of last modification, which is incremented whenever the circuit
-or its children are modified. A memoized data is always stored alongside with a
-timestamp of computation, which invalidates a previous result when needed.
+a standard workflow will possibly be create a circuit, check its signature,
+alter it, then check again), each circuit keeps track of a ``timestamp'' of
+last modification, which is incremented whenever the circuit or its children
+are modified. A memoized data is always stored alongside with a timestamp of
+computation, which invalidates a previous result when needed.
 
 One possible path of investigation for future work, if the computation turns
 out to be still too slow in real-world cases --- which looks unlikely, unless
@@ -481,11 +481,11 @@ Group equality itself is handled as a simple backtracking algorithm, trying to
 establish a match (an isomorphism, that is, a permutation of the gates of one
 of the groups) between the two groups given.
 
-The gates of the two groups are matched by equal signatures, equal number of
-inputs and outputs, based on the signature of default order (that is, 2). A few
-checks are made, \eg{} every matching group must have the same size on both
-sides (if not, then, necessary, the two groups won't match). Then, the worst
-case of number of permutations to check is evaluated.
+The gates of the two groups are matched by equal number of inputs and outputs
+and equal signatures --- based on the signature of default order (that is, 2).
+A few checks are made, \eg{} every matching group must have the same size on
+both sides (if not, then, necessarily, the two groups won't match). Then, the
+worst case of number of permutations to check is evaluated.
 
 If this number is too high, the signature order will be incremented, and the
 matching groups re-created accordingly, until a satisfyingly low number of
@@ -684,8 +684,13 @@ occur).
 
 \subsection{Implementation optimisations}
 
+\paragraph{Pre-check.} The needle will, in most cases, not be found at all in
+a given hierarchy group of the haystack. To avoid wasting computation time, we
+first check that every signature present in the needle is present at least as
+many times in the haystack. This simple check saved a lot of time.
+
 \paragraph{Initial permutation matrix.} The matrix is first filled according to
-the signatures matches. Note that only signatures of order 0 --- \ie{} the
+the signatures' matches. Note that only signatures of order 0 --- \ie{} the
 inner data of a vertex --- can be used here: indeed, we cannot rely on the
 context here, since there can be some context in the haystack that is absent
 from the needle, and we cannot check for ``context inclusion'' with our
@@ -698,11 +703,6 @@ signatures. Thus, two circuits cannot be matched if this condition is not
 respected for each pair of corresponding wires of those circuits, and their
 corresponding cell in the permutation matrix can be nulled.
 
-\paragraph{Pre-check.} The needle will, in most cases, not be found at all in
-a given hierarchy group of the haystack. To avoid wasting computation time, we
-first check that every signature present in the needle is present at least as
-many times in the haystack. This simple check saved a lot of time.
-
 \paragraph{Conversion to adjacency matrix.} The internal structures and graphs
 are represented as inherited classes of \lstcpp{CircuitTree}, connected to
 various \lstcpp{WireId}s. Thus, there is no adjacency matrix easily available,
@@ -731,8 +731,7 @@ the usual test set.
     \textbf{Ordering method} & \textbf{Run time (ms)} & \textbf{Loss (\%)} \\
     Wires by degree decreasing, then gates as they come & 48.8 & --- \\
     As they come, gates then wires & 49.1 & 0.6\% \\
-    Wires by degree decreasing, then gates by degree decreasing & 49.3
-        & 1.0\% \\
+    By degree decreasing, wires then gates & 49.3 & 1.0\% \\
     As they come, wires then gates & 49.3 & 1.0\% \\
     Gates as they come, then wires by degree decreasing & 49.5 & 1.4\% \\
     By degree decreasing, all mixed & 49.5 & 1.4\% \\
@@ -834,11 +833,14 @@ afford really high order signatures (\eg{} 40 or 50, which already means that
 the diameter of the group is 40 or 50) without having a real impact on the
 computation time.
 
+This linearity means that we can increase the signature order without too much
+impact, as we do when computing a group equality.
+
 
 \paragraph{Equality.} To test the circuit group equality, a small piece of
 code takes a circuit, scrambles it as much as possible
 --- without altering its structure ---, \eg{} by renaming randomly its parts,
-by randomly changing the order of the circuits and groups, \ldots The circuit
+by randomly changing the order of the circuits and groups, \ldots{} The circuit
 is then matched with its unaltered counterpart.
 
 For the processor described above, it takes about \textbf{313\,ms} to
@@ -940,12 +942,6 @@ time; and forced me to try to have a code as clean as possible, challenging me
 on small details that were easy to implement, but hard to implement in an
 understandable and bug-proof way.
 
-It also diversified my experience as a student in laboratories, since my only
-other experience was from my 3rd year of Bachelor's degree internship in
-Cambridge.
-
-\todo{Find better}
-
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 \printbibliography{}