finished pseudocode

cfg_utils.py

@@ -309,6 +309,7 @@ if __name__ == '__main__':
 # Special case 1: k is T_ij, and thus x_ijk is the last symbol in the production rule.
 # Special case 2: The symbol x_ijk is a terminal symbol.
 
+# The exhaustive case analysis is as follows.
 
 #                        /----------------------------------------------------------\
 #                        |X_ijk is a terminal symbol | X_ijk is a nonterminal symbol|
@@ -325,6 +326,39 @@ if __name__ == '__main__':
 #                        | Fprim(i, j, k+1, N-1)     | symbols in the subset of rule|
 #                        \----------------------------------------------------------/
 
+# We also note that for the degenerate case N=0, we always can and must return the empty array []
+
+# In pseudocode (taken from the paper, with the correction that on top of page 5
+# the "if N==0 then return [1]" seems like it should be "if N==1 then return [1]"):
+
+# Fprim(i, j, k, N):
+# if (N==0) return []
+# if X_ijk is a terminal:
+#    if k==T_ij:
+#        # CASE A
+#        if N==1 return [1], else return [0]
+#    if k != T_ij:
+#        # CASE B
+#        return [sum(Fprim(i, j, k+1, N-1))]
+# else if X_ijk is a nonterminal:
+#    if k=T_ij:
+#        # CASE C
+#        return [sum(Fzero(index of nonterminal at index k, N))]
+#    if k != T_ij
+#        # CASE D
+#        return [sum(Fzero(index of nonterminal at index k, L)) *
+#                sum(Fprim(i, j, k+1, N-L)) for L = [1, N - T_ij + k]]
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