On the Structure of Logspace Probabilistic Complexity Classes

@article{Macarie1999OnTS,
  title={On the Structure of Logspace Probabilistic Complexity Classes},
  author={Ioan I. Macarie},
  journal={SIAM J. Comput.},
  year={1999},
  volume={29},
  pages={987-1007}
}
  • I. Macarie
  • Published 1 December 1999
  • Computer Science
  • SIAM J. Comput.
We investigate hierarchical properties and logspace reductions of languages recognized by logspace probabilistic Turing machines, Arthur--Merlin games, and games against nature with logspace probabilistic verifiers. Each logspace complexity class is decomposed into a hierarchy based on corresponding two-way multihead finite-state automata and we (eventually) prove the separation of the hierarchy levels (even for languages over a single-letter alphabet); furthermore, we show efficient reductions… 
1 Citations
Properties of Probabilistic Pushdown Automata

References

SHOWING 1-10 OF 53 REFERENCES
Properties of Multihead Two-way Probabilistic Nite Automata
We present properties of multihead two-way probabilistic nite automata that parallel those of their deterministic and nondeterministic counterparts. We deene multihead proba-bilistic nite automata
On the Power of Finite Automata with Both Nondeterministic and Probabilistic States
TLDR
It is shown that a language has constant 1-tiling complexity if and only if it is regular, from which the result on 1-way input follows, and the last lower bound follows by proving that the characteristic matrix of every nonregular language has rank n for infinitely many n.
Space-Efficient Deterministic Simulation of Probabilistic Automata
TLDR
Two space-efficient (but also parallel-time-efficient) techniques are developed and used to compare deterministically a threshold with entries of the inverse of a given banded matrix.
Some Observations on 2-way Probabilistic Finite Automata
TLDR
New results about the class 2-PFA are presented, which includes all the bounded semilinear languages, and it is shown that a pebble enhances the power of a 2-pfa with unbounded error probability.
Connections among Space-bounded and Multihead Probabilistic Automata
We show that the heads of multihead unbounded-error or bounded-error or one-sided-error probabilistic nite automata are equivalent alternatives to the storage tapes of the corresponding probabilistic
Space-bounded hierarchies and probabilistic computations
TLDR
Two aspects of the power of space-bounded probabilistic Turing machines are studied, one of which raises interesting questions about space hierarchies, and the other demonstrates that any language in the log n space hierarchy can be recognized by an log n Space Turing machine with small error.
Transformational methods and their application to complexity problems
  • B. Monien
  • Computer Science
    Acta Informatica
  • 1976
TLDR
There exists a j such that every language accepted by a nondeterministic one-way one-counter automaton is contained in Dj, which is the family of all languages accepted by deterministic j-head two-way finite automata.
Probabilistic Game Automata
Alternating Multihead Finite Automata
...
...