Getting Started

Let's see an example usage of MONAA. We use timed regular expressions (TREs) [ACM02] in this document. See also this document for the detail of the TREs supported by MONAA.

Consider the following as the input timed word. It is also in example/getting_started/timed_word.txt.

A 0.5
B 0.8
C 1.5
A 2.0
B 3.2
A 3.5
C 4.6

Your first example

Let's detect consecutive occurrences of the events A and B. For example, we can use the TRE (AB)$. An example of the usage and the result is as follows.

../build/monaa -e '(AB)$' < ../examples/getting_started/timed_word.txt

 -0.000000       <= t <   0.500000
  0.800000        < t' <=   1.500000
  0.300000        < t' - t <=   1.500000
=============================
  1.500000       <= t <   2.000000
  3.200000        < t' <=   3.500000
  1.200000        < t' - t <=   2.000000
=============================

MONAA detects the occurrences of A and B in the following two subwords.

A 0.5
B 0.8

A 2.0
B 3.2

In timed pattern matching, the "occurrences" does not mean the subwords but it means the trimming on an open interval. For example, the first occurrence of AB is observed by the trimming on (0.3,1.0). Therefore, the result of MONAA is not a set of subwords but a (possibly infinite) set of open intervals (t,t').

The last character $ of (AB)$ is the end of the trimming. This is useful when giving a constraint on t'.

Timing constraints

We can give a timing constraint on the timed words. When we want to exclude the occurrences of A and B such that the duration between A and B is less than 1, we can use the following TRE.

../build/monaa -e '(A(B)%(1,20))$' < ../examples/getting_started/timed_word.txt

  1.500000       <= t <   2.000000
  3.200000        < t' <=   3.500000
  1.200000        < t' - t <=   2.000000
=============================

Disjunctions

We can also say that the second event may be either B or C. We can use disjunctions for such a purpose.

../build/monaa -e '(A(B|C)%(1,20))$' < ../examples/getting_started/timed_word.txt

  1.500000       <= t <   2.000000
  3.200000        < t' <=   3.500000
  1.200000        < t' - t <=   2.000000
=============================
  3.200000       <= t <   3.500000
  4.600000        < t' <=        inf
  1.100000        < t' - t <=        inf
=============================

Repetition

We can also say that A and (B or C) can occur repeatedly. In other words, the subformula A(B|C) repeats once or more. We can use Kleene plus for such a purpose.

../build/monaa -e '((A(B|C))+%(1,20))$' < ../examples/getting_started/timed_word.txt

  1.500000       <= t <   2.000000
  3.200000        < t' <=   3.500000
  1.200000        < t' - t <=   2.000000
=============================
  1.500000       <= t <   2.000000
  4.600000        < t' <=        inf
  2.600000        < t' - t <=        inf
=============================
  3.200000       <= t <   3.500000
  4.600000        < t' <=        inf
  1.100000        < t' - t <=        inf
=============================

If you want match zero times repetition, i.e., empty events, you can use Kleene star. We note that in the current example, this does not change the result because zero times repetition has zero duration, which is inconsistent with the constraint `%(1,20)``

../build/monaa -e '((A(B|C))*%(1,20))$' < ../examples/getting_started/timed_word.txt

  1.500000       <= t <   2.000000
  3.200000        < t' <=   3.500000
  1.200000        < t' - t <=   2.000000
=============================
  1.500000       <= t <   2.000000
  4.600000        < t' <=        inf
  2.600000        < t' - t <=        inf
=============================
  3.200000       <= t <   3.500000
  4.600000        < t' <=        inf
  1.100000        < t' - t <=        inf
=============================

References

• [ACM02] Timed regular expressions. Eugene Asarin, Paul Caspi, and Oded Maler, Journal of the ACM, Volume 49 Issue 2, March 2002, Pages 172-206