updated README

README.md

@@ -5,7 +5,7 @@ Quantitative Timed Pattern Matching
 [![License: GPL v3](https://img.shields.io/badge/License-GPLv3-blue.svg)](./LICENSE)
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-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 <br />
 **-i** *file*, **--input** *file* Read a signal from *file*. <br />
 **-f** *file*, **--automaton** *file* Read a timed automaton from *file*. <br />
-**-a**, **--abs** absolute time mode. <br />
+**-a**, **--abs** absolute time mode. In this mode, the "time" entry shows the (absolute) timestamp of the end of each piece.<br />
 **--maxmin** Use max-min semiring robust semantics (default). <br />
 **--minplus** Use min-plus semiring robust semantics. <br />
 **--maxplus** Use max-plus semiring robust semantics. <br />
@@ -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:
+
+![TSWA taken from the paper](./doc/paper.svg)
+
 How to make compile_commands.json
 ---------------------------------