357 research outputs found
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Real-Time Vector Automata
We study the computational power of real-time finite automata that have been
augmented with a vector of dimension k, and programmed to multiply this vector
at each step by an appropriately selected matrix. Only one entry
of the vector can be tested for equality to 1 at any time. Classes of languages
recognized by deterministic, nondeterministic, and "blind" versions of these
machines are studied and compared with each other, and the associated classes
for multicounter automata, automata with multiplication, and generalized finite
automata.Comment: 14 page
Exact affine counter automata
© F. Blanchet-Sadri & S. Osborne. We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime
Micro-Futures
One of humankinds oldest quests has been to find the ‘elixir of life’, a mythical potion that, would grant the drinker immortality (and preferably, eternal youth!). One of the most famous tales of a search for this fabled tonic was that of the first emperor of a unified China, Qin Shi Huang (246 BC. to 210 BC), who, in the latter part of his life, is said to have become preoccupied with finding this illusive concoction. This article is presented at a workshop that is taking place in the heartland of what was Qin Shi Huang's empire (China), and touches on a modern day search for an elixir of life, this time a high-tech approach based on computers and artificial intelligence technology, that goes by the name of ‘The Technological Singularity’. However, as fascinating as a search for an elixir of life may be, the real motivation of this paper is to introduce micro-fiction as a methodology for capturing and communicating visions for scientific, business and societal innovations. To those end, The Technological Singularity is described and used as a means to illustrate the workings of micro SciFi-Prototyping (micro-SFPs)
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