diff --git a/README.md b/README.md
index 5c0e34c..2960e10 100644
--- a/README.md
+++ b/README.md
@@ -5,7 +5,7 @@ Quantitative Timed Pattern Matching
[](./LICENSE)
[](https://maswag.github.io/qtpm/doxygen/index.html)
-This is our experimental implementation of *Quantitative Timed Pattern Matching*.
+This is an experimental implementation of *Quantitative Timed Pattern Matching*.
See [FORMATS2019.md](./experiments/README.md) for the experiments in our FORMATS 2019 paper.
Demo on Google Colab is [HERE](https://colab.research.google.com/drive/1y1LU0pKQb5rMcuwwA9VwEb5Ec8I2qvlf)!!
@@ -24,7 +24,7 @@ Usage
**-V**, **--version** Print the version
**-i** *file*, **--input** *file* Read a signal from *file*.
**-f** *file*, **--automaton** *file* Read a timed automaton from *file*.
-**-a**, **--abs** absolute time mode.
+**-a**, **--abs** absolute time mode. In this mode, the "time" entry shows the (absolute) timestamp of the end of each piece.
**--maxmin** Use max-min semiring robust semantics (default).
**--minplus** Use min-plus semiring robust semantics.
**--maxplus** Use max-plus semiring robust semantics.
@@ -44,7 +44,7 @@ This software is tested on Ubuntu 20.04, Ubuntu 22.04, macOS 11, macOS 12, macOS
### Instructions
-```sh
+"`sh
mkdir build
cd build && cmake -DCMAKE_BUILD_TYPE=Release .. && make
```
@@ -54,10 +54,33 @@ Input Format
### Signal
-A signal is a sequence of the following line.
+A signal is a sequence of the following lines.
time v(x1) v(x2) v(x3) ... v(xn)
+Here, the column "time" has different meaning between relative time mode (default) and absolute time mode (enabled by `-a`).
+Consider an example of a signal where during the first 1.0 time unit, the value is 0.0, and during the next 1.0 time unit, the value is 2.0.
+In the relative time mode, such a signal is encoded as follows, where the "time" entry shows the duration of each piece.
+
+```
+1.0 0.0
+1.0 2.0
+```
+
+In the absolute time mode, such a signal is encoded as follows, where the "time" entry shows the (absolute) timestamp of the end of each piece.
+
+```
+1.0 0.0
+2.0 2.0
+```
+
+Note on the accepting states
+----------------------------
+
+To simplify the algorithm, we assume that each matching ends at the same time as a transition to an accepting state is invoked. This assumption does not harm the generality: one can construct a TSWA for such a matching algorithm by making all the states during matching non-accepting, making a fresh accepting state, and making transitions to it so that the transitions to the accepting state are invoked when the matching ends. The following is a typical example of such a TSWA:
+
+
+
How to make compile_commands.json
---------------------------------
diff --git a/doc/paper.svg b/doc/paper.svg
new file mode 100644
index 0000000..9e47670
--- /dev/null
+++ b/doc/paper.svg
@@ -0,0 +1,56 @@
+
+
+
+
+