 
Summary: Distinguishing tests for nondeterministic and probabilistic machines
(Appeared in the Proceedings of the 27th ACM Symposium on Theory of Computing, pp. 363372, 1995)
Rajeev Alur \Lambda Costas Courcoubetis y Mihalis Yannakakis \Lambda
Abstract
We study the problem of uniquely identifying the ini
tial state of a given finitestate machine from among
a set of possible choices, based on the inputoutput
behavior. Equivalently, given a set of machines, the
problem is to design a test that distinguishes among
them. We consider nondeterministic machines as well
as probabilistic machines. In both cases, we show
that it is Pspacecomplete to decide whether there
is a preset distinguishing strategy (i.e. a sequence of
inputs fixed in advance), and it is Exptimecomplete
to decide whether there is an adaptive distinguish
ing strategy (i.e. when the next input can be cho
sen based on the outputs observed so far). The
probabilistic testing is closely related to probabilistic
games, or Markov Decision Processes, with incom
plete information. We also provide optimal bounds
