  Quantum algorithms can be analyzed in a query model to compute Boolean
functions where input is given in a black box and the aim is to compute
function value for arbitrary input using as few queries as possible. We
concentrate on quantum query algorithm designing tasks in this paper. The main
aim of the research was to find new efficient algorithms and develop general
algorithm designing techniques. First, we present several exact quantum query
algorithms for certain problems that are better than classical counterparts.
Next, we introduce algorithm transformation methods that allow significant
enlarging of exactly computable functions sets. Finally, we propose quantum
algorithm designing methods. Given algorithms for the set of sub-functions, our
methods use them to design a more complex one, based on algorithms described
before. Methods are applicable for input algorithms with specific properties
and preserve acceptable error probability and number of queries. Methods offer
constructions for computing AND, OR and MAJORITY kinds of Boolean functions.
