diff --git a/lectures/hmm/talk.pdf b/lectures/hmm/talk.pdf
index 2f2562b..f76dbb6 100644
Binary files a/lectures/hmm/talk.pdf and b/lectures/hmm/talk.pdf differ
diff --git a/lectures/hmm/talk.tex b/lectures/hmm/talk.tex
index 0109b7d..92e732d 100644
--- a/lectures/hmm/talk.tex
+++ b/lectures/hmm/talk.tex
@@ -198,7 +198,11 @@ \section{Single-sequence hidden Markov models}
  \itemb
  \item probability underflow for long sequences
  \item slow floating-point multiply
- \item motivation for (possibly discretized) log-space scores
+ \item possible solutions:
+  \itemb
+  \item (possibly discretized) log-space scores
+  \item bignum types
+  \iteme
  \iteme
 \end{frame}