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

Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania

Collections: Computer Technologies and Information Sciences