Lecture Notes in Computer Science 3472

84 Henrik Björklund
(3) If φ has at least one nonterminal child φ ′ ,letφ ← φ ′ and restart from step
2. If φ has no nonterminal children that have not been searched, and φ is
the root of the tree, then terminate. If φ has no nonterminal children that
have not been searched but φ is not the root, then set φ ← parent(φ) and
restart from step 3.
In other words, the procedure looks one step ahead before deepening the
search. Naik [Nai97] claims that this approach mostly solves the major problem
with pure depth first search, that longer sequences are found before shorter
sequences for the same state. While this is true in some cases, it somewhat
overstates the merit of the method. For some machines, the procedure will still
be likely to find long sequences before much shorter ones.
If we are only interested in relatively short sequences, like in the conformance
testing algorithm by Sabnani and Dahbura discussed in Section 3.4.1 [SD88], the
search depth of Naik’s algorithm can of course be limited.
3.4.3 Genetic Algorithms
Guo, Hierons, Harman, and Derderian recently suggested the use of genetic
algorithms to find UIO sequences [GHHD04]. The basic idea of genetic algorithms
is to mimic the process of natural selection in nature. An algorithm keeps
a collection of possible solutions to the problem at hand, called the population,
and measures the quality of its members using a fitness function. Thebestindividuals
in the population are paired together using recombination to form the
next generation. Random changes of individuals, called mutations, can also be
applied to individuals. For a survey on the theory of genetic algorithms, see
[Müh97].
In more detail, an individual is assumed to be a sequence of some kind,
and all individuals are generally assumed to have the same length. To start
computation, an initial population is generated randomly, and the fitness of each
individual is computed using the fitness function. To form the next generation,
two individuals are selected in some way that gives preference to high fitness
values. The algorithm has a set value for crossover probability p. Withthis
probability, the two parents are mixed to form an offspring. With probability
1−p, a copy of one of the parents are instead added to the next generation. This
is repeated until the new population is full. According to some other probability
distribution, each individual in the new generation is mutated, i.e., randomly
changed. This is intended to prevent the process from getting stuck in local
minima. The algorithm proceeds to create a preset number of further generation,
and then returns the final population. Ideally, all individuals are then identical
and represent an optimal solution to the problem.
In the approach of Guo et al. [GHHD04], the population is a set of input
sequences, all of the same length. The idea is to use a fitness function that
rewards sequences whose prefixes are the input components of UIO sequences
for many states, while punishing unnecessarily long sequences. All sequences
in the population are assumed to have the same length k. Given a sequence