# 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} }

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…

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## References

SHOWING 1-10 OF 53 REFERENCES

Properties of Multihead Two-way Probabilistic Nite Automata

- Computer Science
- 1994

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

- Computer ScienceSIAM J. Comput.
- 1998

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

- Computer ScienceSIAM J. Comput.
- 1998

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

- Computer ScienceFSTTCS
- 1992

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

- Computer Science
- 1994

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

- Computer ScienceSTOC '82
- 1982

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

- Computer ScienceActa Informatica
- 1976

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.

Relationships Between Nondeterministic and Deterministic Tape Complexities

- Computer ScienceJ. Comput. Syst. Sci.
- 1970