 
Summary: COMPUTABILITY AND COMPLEXITY
G. N. ARZHANTSEVA AND J. ROLIM
Abstract. One of the most critical question about a problem in
computer science is whether we are capable of solving it or even
worse whether this problem admits a solution or not. The theo
ries of computability and complexity, which are introduced in this
module, have been developed in order to render such questions pre
cise and to discuss them. In complexity theory, the objective is to
classify problems as easy and hard ones, whereas in computability
theory, problems are classified as solvable and nonsolvable ones. In
addition, computability theory introduces several of the concepts
used in complexity theory. Therefore, this module proposes the
integrated study of specific basic issues in both computability and
complexity theory, such as the ChurchTuring thesis, decidability
and reducibility, time and space complexity classes, determinism
and nondeterminism, hierarchy theorems and polynomial classes
(P, NP, PSPACE, etc.), completeness and basic NPhard problems.
University of Geneva, Centre Universitaire d'Informatique, 24, rue
General Dufour, 1211 Gen‘ eve 4, Switzerland
Email address: {arjantse,rolim}@cui.unige.ch
