28,728 research outputs found
Finite state verifiers with constant randomness
We give a new characterization of as the class of languages
whose members have certificates that can be verified with small error in
polynomial time by finite state machines that use a constant number of random
bits, as opposed to its conventional description in terms of deterministic
logarithmic-space verifiers. 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. A
corollary of our main result is that the class of outcome problems
corresponding to O(log n)-space bounded games of incomplete information where
the universal player is allowed a constant number of moves equals NL.Comment: 17 pages. An improved versio
Unbounded-error quantum computation with small space bounds
We prove the following facts about the language recognition power of quantum
Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more
powerful than probabilistic Turing machines for any common space bound
satisfying . For "one-way" Turing machines, where the
input tape head is not allowed to move left, the above result holds for
. We also give a characterization for the class of languages
recognized with unbounded error by real-time quantum finite automata (QFAs)
with restricted measurements. It turns out that these automata are equal in
power to their probabilistic counterparts, and this fact does not change when
the QFA model is augmented to allow general measurements and mixed states.
Unlike the case with classical finite automata, when the QFA tape head is
allowed to remain stationary in some steps, more languages become recognizable.
We define and use a QTM model that generalizes the other variants introduced
earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of
the Fourth International Computer Science Symposium in Russia, pages
356--367, 200
Bounded Counter Languages
We show that deterministic finite automata equipped with two-way heads
are equivalent to deterministic machines with a single two-way input head and
linearly bounded counters if the accepted language is strictly bounded,
i.e., a subset of for a fixed sequence of symbols . Then we investigate linear speed-up for counter machines. Lower
and upper time bounds for concrete recognition problems are shown, implying
that in general linear speed-up does not hold for counter machines. For bounded
languages we develop a technique for speeding up computations by any constant
factor at the expense of adding a fixed number of counters
Succinctness of two-way probabilistic and quantum finite automata
We prove that two-way probabilistic and quantum finite automata (2PFA's and
2QFA's) can be considerably more concise than both their one-way versions
(1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For
this purpose, we demonstrate several infinite families of regular languages
which can be recognized with some fixed probability greater than by
just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with
a constant number of states, whereas the sizes of the corresponding 1PFA's,
1QFA's and 2NFA's grow without bound. We also show that 2QFA's with mixed
states can support highly efficient probability amplification. The weakest
known model of computation where quantum computers recognize more languages
with bounded error than their classical counterparts is introduced.Comment: A new version, 21 pages, late
Linguistics and some aspects of its underlying dynamics
In recent years, central components of a new approach to linguistics, the
Minimalist Program (MP) have come closer to physics. Features of the Minimalist
Program, such as the unconstrained nature of recursive Merge, the operation of
the Labeling Algorithm that only operates at the interface of Narrow Syntax
with the Conceptual-Intentional and the Sensory-Motor interfaces, the
difference between pronounced and un-pronounced copies of elements in a
sentence and the build-up of the Fibonacci sequence in the syntactic derivation
of sentence structures, are directly accessible to representation in terms of
algebraic formalism. Although in our scheme linguistic structures are classical
ones, we find that an interesting and productive isomorphism can be established
between the MP structure, algebraic structures and many-body field theory
opening new avenues of inquiry on the dynamics underlying some central aspects
of linguistics.Comment: 17 page
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms
We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques
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