Space-Efficient Deterministic Simulation of Probabilistic Automata

  title={Space-Efficient Deterministic Simulation of Probabilistic Automata},
  author={Ioan I. Macarie},
  journal={SIAM J. Comput.},
  • I. Macarie
  • Published 1 April 1998
  • Computer Science
  • SIAM J. Comput.
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 languages… 
On the Structure of Logspace Probabilistic Complexity Classes
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
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
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.
Theory of one-tape linear-time Turing machines
Computational limitations of affine automata and generalized affine automata
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
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)
  • V. Geffert
  • Computer Science
    Theory of Computing Systems
  • 2018
There exists a binary PSpace-complete languageℒ such that the unary coded version of ℒ$\mathcal {L}$ 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
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
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
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.


A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata
It is shown that if a two-way probabilistic finite-state automaton (2pfa) M recognizes a nonregular language L with error probability bounded below $\frac{1}{2}$, then there is a positive constant b
Some Observations on 2-way Probabilistic Finite Automata
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.
A Note on Two-Way Probabilistic Automata
  • Jie Wang
  • Computer Science
    Inf. Process. Lett.
  • 1992
Generalized automata and stochastic languages
This paper is concerned with the so-called generalized automata where the elements of the initial vector, of the final vector and of the matrices are allowed to be arbitrary real numbers and it is proved that a language is accepted by a generalized automaton if and only if it is acceptance by a probabilistic automaton.
Space-bounded hierarchies and probabilistic computations
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.
Computational complexity of probabilistic Turing machines
It is shown how probabilisticlinear-bounded automata can simulate nondeterministic linear-bounding automata and an example is given of a function computable more quickly by Probabilistic Turing machines than by deterministic Turing machines.
Estimating a probability using finite memory
It is proved that the O(1/n) bound is optimal to within a constant factor and it is shown that linear estimation procedures are just as powerful (up to the measure of mean-square error) as arbitrary estimation procedures.
Space-bounded probabilistic turing machine complexity classes are closed under complement (Preliminary Version)
For tape constructible functions S(n)≥log n, if a language L is accepted by an S(n) tape bounded probabilistic Turing machine, then there is an S(n) tape bounded probabilistic Turing machine that