Information Technology Reference
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There is a large variety of similar competitive exercises. Just for illustration,
ask for input data on which
A
returns some constant string hypothesis from
M
+
,whereas
A
returns some pattern with exactly one variable. This exercise
may be easily modified by asking for two, three, or more variables and, perhaps,
by putting constraints on the number of repeated occurrences of one variable.
Note that all the examples mentioned so far refer just to the comparison of
two results generated by
A
and by
A
, respectively. One extension may take
A
generate identical
results or, alternatively, return different hypotheses. Extra constraints as above
may be put on the number of variables and on the frequency of those variable
occurrences. Other extensions result from considering sequences of hypotheses,
possibly until reaching the final learning goal. For instance, one may ask for
some target pattern
p
and investigate sequences of strings from
L
(
p
) such that
certain phenomena may be recognized such as, e.g.,
A
into account asking for input data on which
A
and
A
converging much faster
than
. Such a difference in behavior may be expressed quantitatively.
One of the highlights of didactics would surely be to encourage students to
design attractive competitive exercises to their fellow students. Those exercises
should not just be tasks assigned to other students, but should be investigated
and discussed for gaining insights into the key ideas behind and for their didactic
potentials.
Direct execution is essential to those exercises. Learners should be encouraged
to try out larger numbers of data sets.
Skeptical readers might counter that any collection of programs implementing
the algorithms under consideration would do as well. Although this is basically
true, it is missing the point. Meme media implementations allow for a much
larger variation of experiments including the decomposition of algorithms under
consideration. This aspect has not been demonstrated by means of the pattern
inference algorithms, but may be clearly seen in figure 4, right screenshot, where
some algorithm showing some hole, so to speak, may be completed by fixing the
hole in the one or the other way.
To play with the Lange/Wiehagen algorithm and some of its variations has
been chosen just as a simple case study of exploratory learning about algorithms
using Webbles implementations which allow for direct execution. Even within the
limits of this elementary case study, there are overwhelmingly many options of
formulating playful exercises.
Just for illustration, one may think of short multi-player games as follows.
Some game master is secretly choosing a pattern
p
andispresentingafew
longer inputs (two, at least) from
L
(
p
) to the Lange/Wiehagen algorithm which,
in turn, immediately responds with a certain hypothesis. Now, it is the players'
turn simultaneously. Everyone has the right to guess further string from
L
(
p
).
For correct guesses of strings that really belong to
L
(
p
), they score some points.
Turn by turn, the players proceed toward identifying the hidden target pattern.
Feeding the right string into the algoritm, be it
A
A
, or any other variant,
such that the target pattern is found is rewarded especially and the game ends.
Note that, naturally, the game master may be computerized.
A
,
