More on signatures

report/report.tex

@@ -350,6 +350,27 @@ The ``IO adjacency'' term is an additional term in the signatures of order
 above $0$, indicating what input and output pins of the circuit group
 containing the current gate are adjacent to it.
 
+\paragraph{Efficiency.} Every circuit memoizes all it can concerning its
+signature: the inner signature, the IO adjacency, the signatures of order $n$
+already computed, etc.
+
+This memoization, alongside with the exclusive use of elementary operations,
+makes the computation of a signature very fast. The computation is linear in
+the number of gates in a circuit, times the order computed; the computation is
+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.
+
+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 ---,
+would be to try to multithread this computation.
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Group equality}
 \todo{}