Lecture Notes in Computer Science 3472

596 Therese Berg and Harald Raffelt
the currently observed information plus the domain specific knowledge about
the system to learn.
We present the concept of Assistants using Angluin’s algorithm. It might be
transferred to the other learning algorithms in a similar manner. However, since
not every algorithm stores the result of all membership queries, the effect might
be limited.
The Assistants We present different types of assistants, which differ by the
provided context information.
Assistant 1. The first property of reactive systems that we consider is prefixclosedness.
If the system enters an error state, it will never recover on further
input. So if the system enters a non-accepting state, a sink in the corresponding
automaton, it will never leave it. Hence, the automaton’s language is prefixclosed.
In other words, prefixes of accepted strings are also accepted and extensions
of rejected strings are rejected.
This is used by the first Assistant which states that if a string is a prefix
of a string already in OT with the entry + then the prefix-string will also be
entered as +, without consulting the Teacher. Similarly, a query for a string that
is an extension of a string already classified as rejecting is answered negatively
without consulting the Teacher.
Assistant 2. Sometimes, one deals with systems that provide a sequence of
output symbols to a given sequence of input symbols. These systems may be
modeled as deterministic finite state machines (see also Chapter 21 or Part I of
this book) where the input alphabet comprises sequences of input symbols and
the output alphabet contains sequences of output symbols. These systems can
be understood as DFAs over an alphabet comprising actions that are pairs of
sequences of input and output symbols. However, such an alphabet is large and
the learning algorithm will be expensive. To eliminate the problem we can split
an edge labeled by a sequence of input and output symbols into a sequence of
edges where each edge is labeled with a single symbol, first the input symbols
and then the output symbols. In this way, the number of states increases but
thealphabetiskeptsmall.
Often, these systems are deterministic for a given input. The system under
test always produces the same output on any given sequence of inputs. So replacing
just one output symbol in a string of an input-deterministic language cannot
yield another string of this language. An Assistant can use this knowledge to
determine that a membership query should be answered with a − for a certain
string if in OT the same string with the modification of one output symbol has
the entry +.
Assistant 3. The next Assistant uses the fact that the number of output
events in a given situation is determined, and that we wait with feeding new
input until the system has produced all its responses. Assume that we have in
OT a string labeled + that ends with an input symbol. Then every string that
emerges by changing this input-symbol to any output symbol, will always be
rated as −. This can be checked by a further Assistant.