Nonstochastic languages as projections of 2-tape quasideterministic languages
A language L (n) of n-tuples of words which is recognized by a n-tape rational finite-probabilistic automaton with probability 1-ε, for arbitrary ε > 0, is called quasideterministic. It is proved in [Fr 81], that each rational stochastic language is a projection of a quasideterministic language L (n) of n-tuples of words. Had projections of quasideterministic languages on one tape always been rational stochastic languages, we would have a good characterization of the class of the rational stochastic languages. However we prove the opposite in this paper. A two-tape quasideterministic language exists, the projection of which on the first tape is a nonstochastic language.
Unable to display preview. Download preview PDF.
- [Fr 78]
- [Fr 81]
- [Fr 91]Rūsiņš Freivalds. Complexity of probabilistic versus deterministic automata. ”Lecture Notes in Computer Science”, Springer, 1991, v. 502, p. 565–613Google Scholar
- [RS 59]
- [Mi 66]
- [Ca 57]J.W.S. Cassels. An Introduction to Diophantine Approximation. Cambridge Tracts in Mathematics and Mathematical Physics, vol. 45, 1957.Google Scholar