0000000000033914
AUTHOR
Richard F. Bonner
showing 6 related works from this author
Ambainis-Freivalds’ Algorithm for Measure-Once Automata
2001
An algorithm given by Ambainis and Freivalds [1] constructs a quantum finite automaton (QFA) with O(log p) states recognizing the language Lp = {ai| i is divisible by p} with probability 1 - Ɛ , for any Ɛ > 0 and arbitrary prime p. In [4] we gave examples showing that the algorithm is applicable also to quantum automata of very limited size. However, the Ambainis-Freivalds algoritm is tailored to constructing a measure-many QFA (defined by Kondacs andWatrous [2]), which cannot be implemented on existing quantum computers. In this paper we modify the algorithm to construct a measure-once QFA of Moore and Crutchfield [3] and give examples of parameters for this automaton. We show for the lang…
Probabilities to Accept Languages by Quantum Finite Automata
1999
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.
Quantum inductive inference by finite automata
2008
AbstractFreivalds and Smith [R. Freivalds, C.H. Smith Memory limited inductive inference machines, Springer Lecture Notes in Computer Science 621 (1992) 19–29] proved that probabilistic limited memory inductive inference machines can learn with probability 1 certain classes of total recursive functions, which cannot be learned by deterministic limited memory inductive inference machines. We introduce quantum limited memory inductive inference machines as quantum finite automata acting as inductive inference machines. These machines, we show, can learn classes of total recursive functions not learnable by any deterministic, nor even by probabilistic, limited memory inductive inference machin…
Nonstochastic languages as projections of 2-tape quasideterministic languages
1998
A language L (n) of n-tuples of words which is recognized by a n-tape rational finite-probabilistic automaton with probability 1-e, for arbitrary e > 0, is called quasideterministic. It is proved in [Fr 81], that each rational stochastic language is a projection of a quasideterministic language L (n) of n-tuples of words. Had projections of quasideterministic languages on one tape always been rational stochastic languages, we would have a good characterization of the class of the rational stochastic languages. However we prove the opposite in this paper. A two-tape quasideterministic language exists, the projection of which on the first tape is a nonstochastic language.
Quantum Finite Multitape Automata
1999
Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automata. This …
Quantum versus Probabilistic One-Way Finite Automata with Counter
2001
The paper adds the one-counter one-way finite automaton [6] to the list of classical computing devices having quantum counterparts more powerful in some cases. Specifically, two languages are considered, the first is not recognizable by deterministic one-counter one-way finite automata, the second is not recognizable with bounded error by probabilistic one-counter one-way finite automata, but each recognizable with bounded error by a quantum one-counter one-way finite automaton. This result contrasts the case of one-way finite automata without counter, where it is known [5] that the quantum device is actually less powerful than its classical counterpart.