On probabilistic tape complexity and fast circuits for matrix inversion problems

Jung, Hermann

doi:10.1007/3-540-13345-3_25

Cited by 9 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The standard procedure is to recompute the numbers from their residue representations (using the Chinese Remainder Theorem), and to compare them bit by bit. This approach was used by Jung Jung 1984] who made crucial use of the results of Reif Reif 1986] and Borodin Bo 1977]. Using this technique we obtain only S > rat 6 ?…”

Section: Theorem 2 Ka 1989] S >mentioning

confidence: 99%

“…Some time later, Freivalds Fre 1981] proved that the language fa n b n j n 2 Ng can be recognized by a 2-way probabilistic nite automaton with isolated cutpoint (2-PFA). Jung Jung 1984] found a O(log n log log n)-space deterministic simulation for 2U-PFA's and later Wang Wang 1992] provided a much weaker O(n)-space deterministic simulation for 2-PFA's using the Markov chain tree theorem of Leighton and Rivest LR 1986]. In spite of the fact that the classes of languages recognized by PFA's and 2U-PFA's are the same (if their transition probabilities are either all rationals or all reals) Ka 1989], the class of languages recognized by 2-PFA's is larger than the class of languages recognized by PFA's with isolated cutpoint.…”

Section: Introductionmentioning

confidence: 99%

“…In spite of the fact that the classes of languages recognized by PFA's and 2U-PFA's are the same (if their transition probabilities are either all rationals or all reals) Ka 1989], the class of languages recognized by 2-PFA's is larger than the class of languages recognized by PFA's with isolated cutpoint. Jung Jung 1984] obtained an O(log n) deterministic space simulation for 2-PFA's.…”

Section: Introductionmentioning

confidence: 99%

“…This result, together with the fact that f(n)-space PTM's are at least as strong as f(n)-space nondeterministic Turing machines, generalizes Savitch's theorem. In the case of small space-bounded probabilistic complexity classes Jung proved the inclusion of languages recognized by f(n) 2 O(log n) space-bounded PTM in Dspace(log n(f(n)+log log n)) Jung 1984].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Space-Efficient Deterministic Simulation of Probabilistic Automata

Macarie

1998

SIAM J. Comput.

View full text Add to dashboard Cite

Given a description of a probabilistic automaton (one-head probabilistic nite 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 nite automata (PFA). We call (rational) stochastic languages (S > rat) the class of languages recognized by PFA's whose transition probabilities and cutpoints (i.e. recognition thresholds) are rational numbers. The class S > rat contains context-sensitive languages that are not context free, but on the other hand there are context-free languages not included in S > rat. Our main results are as follows: The (proper) inclusion of S > rat in Dspace(log n), which is optimal (i.e. S > rat 6 Dspace(o(log n))). The previous upper bounds were Dspace(n) Dieu 1972], Wang 1992] and Dspace(log n log log n) Jung 1984]. Probabilistic Turing machines with space bound f(n) 2 O(log n) can be deterministically simulated in space O(min(c f(n) log n; log n(f(n) + log log n))), where c is a constant depending on the simulated probabilistic Turing machine. The best previously known simulation required space O(log n(f(n) + log log n)) Jung 1984]. Of independent interest is our technique to compare numbers given in terms of their values modulo a sequence of primes, p 1 < p 2 < < p n = O(n a) (where a is some constant) in O(log n) deterministic space.

show abstract

Section: Theorem 2 Ka 1989] S >mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Space-Efficient Deterministic Simulation of Probabilistic Automata

Macarie

1998

SIAM J. Comput.

View full text Add to dashboard Cite

show abstract

“…As explained earlier, this computation boils down to the matrix computation Q* = liw,l(I -SQ)-l for some substochastic Q . In [21], it is shown that if…”

Section: Each Step Of M ( X ) Is Either a Deterministic Changementioning

confidence: 98%

Randomization and derandomization in space-bounded computation

Saks

Proceedings of Computational Complexity (Formerly Structure in Complexity Theory)

View full text Add to dashboard Cite

This is a survey of space-bounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators that fool probabilistic space-bounded computations, and the application of such generators to obtain deterministic simulations.

show abstract

Multihead two-way probabilistic finite automata

Macarie

1997

Theory of Computing Systems

View full text Add to dashboard Cite

On probabilistic tape complexity and fast circuits for matrix inversion problems

Cited by 9 publications

References 12 publications

Space-Efficient Deterministic Simulation of Probabilistic Automata

Space-Efficient Deterministic Simulation of Probabilistic Automata

Randomization and derandomization in space-bounded computation

Multihead two-way probabilistic finite automata

Contact Info

Product

Resources

About