# Space-Efficient Deterministic Simulation of Probabilistic Automata

@article{Macarie1998SpaceEfficientDS, title={Space-Efficient Deterministic Simulation of Probabilistic Automata}, author={Ioan I. Macarie}, journal={SIAM J. Comput.}, year={1998}, volume={27}, pages={448-465} }

Given a description of a probabilistic automaton (one-head probabilistic finite-state automaton or probabilistic Turing machine) and an input string x of length n, we ask how much space does a deterministic Turing machine need in order to decide the acceptance of the input string by that automaton?
The question is interesting even in the case of one-head one-way probabilistic finite-state automata (1pfa's). We call (rational) stochastic languages} ($\SS_{rat}^{>}$) the class of languagesâ€¦Â

## 30 Citations

On the Structure of Logspace Probabilistic Complexity Classes

- Computer ScienceSIAM J. Comput.
- 1999

Probabilistic and probabilistic-plus-nondeterministic variants of Savitch's maze threading problem are found which are logspace complete for PL and PPP and which can be recognized by one-way non-sensing two-head finite-state automata with probabilists and nondeterministic states.

Language recognition power and succinctness of affine automata

- Computer ScienceNatural Computing
- 2017

It is shown that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of inner states of quantum and probabilistic automata cannot be bounded.

Postselection Finite Quantum Automata

- Computer ScienceUC
- 2010

It is proved that PALINDROMES can be recognized by MM-quantum finite automata with postselection, and distinguishes quantum automata from probabilistic automata because probabilists with non-isolated cut-point 0 can recognize only regular languages but PALIN DROMES is not a regular language.

Computational limitations of affine automata and generalized affine automata

- Mathematics, Computer ScienceNat. Comput.
- 2021

It is shown that using the endmarker does not increase the computational power of affine automata and that the class of bounded-error affine languages remains the same when the AfAs are restricted to use rational numbers only.

Finite state verifiers with constant randomness

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2013

It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers.

Unary Coded PSPACE-Complete Languages in ASPACE(loglog n)

- Computer ScienceTheory of Computing Systems
- 2018

There exists a binary PSpace-complete languageâ„’ such that the unary coded version of â„’$\mathcal {L}$ is in ASpace(loglog n) so that the standard translation between unary languages accepted with loglog n space and binary languages acceptance with log n space works for alternating machines.

Theory of One Tape Linear Time Turing Machines

- Computer ScienceSOFSEM
- 2004

This paper discusses the computational complexity of one-tape Turing machines of various machine types that halt in time O(n), where the running time of a machine is defined as the height of its computation tree.

Factoring and testing primes in small space

- Computer Science, MathematicsRAIRO Theor. Informatics Appl.
- 2009

It is shown that O(log log n) space is sufficient for a deterministic Turing machine, if it is equipped with an additional pebble movable along the input tape, and also for an alternating machine,if the space restriction applies only to its accepting computation subtrees.

Computing with sublogarithmic space

- Computer Science, Mathematics
- 1998

This work investigates space complexity classes deened by Turing machines that use less than logarithmic space, and considers extension of these computational models by randomness, that means interactive proofs, resp.

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