6,231 research outputs found
Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata
We consider the possibility of encoding m classical bits into much fewer n
quantum bits so that an arbitrary bit from the original m bits can be recovered
with a good probability, and we show that non-trivial quantum encodings exist
that have no classical counterparts. On the other hand, we show that quantum
encodings cannot be much more succint as compared to classical encodings, and
we provide a lower bound on such quantum encodings. Finally, using this lower
bound, we prove an exponential lower bound on the size of 1-way quantum finite
automata for a family of languages accepted by linear sized deterministic
finite automata.Comment: 12 pages, 3 figures. Defines random access codes, gives upper and
lower bounds for the number of bits required for such (possibly quantum)
codes. Derives the size lower bound for quantum finite automata of the
earlier version of the paper using these result
Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda
Valiant (1975) has developed an algorithm for recognition of context free
languages. As of today, it remains the algorithm with the best asymptotic
complexity for this purpose. In this paper, we present an algebraic
specification, implementation, and proof of correctness of a generalisation of
Valiant's algorithm. The generalisation can be used for recognition, parsing or
generic calculation of the transitive closure of upper triangular matrices. The
proof is certified by the Agda proof assistant. The certification is
representative of state-of-the-art methods for specification and proofs in
proof assistants based on type-theory. As such, this paper can be read as a
tutorial for the Agda system
Green's Relations in Finite Transformation Semigroups
We consider the complexity of Green's relations when the semigroup is given
by transformations on a finite set. Green's relations can be defined by
reachability in the (right/left/two-sided) Cayley graph. The equivalence
classes then correspond to the strongly connected components. It is not
difficult to show that, in the worst case, the number of equivalence classes is
in the same order of magnitude as the number of elements. Another important
parameter is the maximal length of a chain of components. Our main contribution
is an exponential lower bound for this parameter. There is a simple
construction for an arbitrary set of generators. However, the proof for
constant alphabet is rather involved. Our results also apply to automata and
their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1
A Characterization of ET0L and EDT0L Languages
There exists a PT0L language such that the following holds. A language is an ET0L language if and only if there exists a mapping induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that . There exists an infinite collection of EPDT0L languages () such that the family EDT0L is characterized in the following way. A language is an EDT0L language if and only if there exists , a homomorphism and a regular language such that .\u
Information Flow Control in WebKit's JavaScript Bytecode
Websites today routinely combine JavaScript from multiple sources, both
trusted and untrusted. Hence, JavaScript security is of paramount importance. A
specific interesting problem is information flow control (IFC) for JavaScript.
In this paper, we develop, formalize and implement a dynamic IFC mechanism for
the JavaScript engine of a production Web browser (specifically, Safari's
WebKit engine). Our IFC mechanism works at the level of JavaScript bytecode and
hence leverages years of industrial effort on optimizing both the source to
bytecode compiler and the bytecode interpreter. We track both explicit and
implicit flows and observe only moderate overhead. Working with bytecode
results in new challenges including the extensive use of unstructured control
flow in bytecode (which complicates lowering of program context taints),
unstructured exceptions (which complicate the matter further) and the need to
make IFC analysis permissive. We explain how we address these challenges,
formally model the JavaScript bytecode semantics and our instrumentation, prove
the standard property of termination-insensitive non-interference, and present
experimental results on an optimized prototype
The Computational Complexity of Symbolic Dynamics at the Onset of Chaos
In a variety of studies of dynamical systems, the edge of order and chaos has
been singled out as a region of complexity. It was suggested by Wolfram, on the
basis of qualitative behaviour of cellular automata, that the computational
basis for modelling this region is the Universal Turing Machine. In this paper,
following a suggestion of Crutchfield, we try to show that the Turing machine
model may often be too powerful as a computational model to describe the
boundary of order and chaos. In particular we study the region of the first
accumulation of period doubling in unimodal and bimodal maps of the interval,
from the point of view of language theory. We show that in relation to the
``extended'' Chomsky hierarchy, the relevant computational model in the
unimodal case is the nested stack automaton or the related indexed languages,
while the bimodal case is modeled by the linear bounded automaton or the
related context-sensitive languages.Comment: 1 reference corrected, 1 reference added, minor changes in body of
manuscrip
On the Descriptional Complexity of Limited Propagating Lindenmayer Systems
We investigate the descriptional complexity of limited propagating
Lindenmayer systems and their deterministic and tabled variants with respect to
the number of rules and the number of symbols. We determine the decrease of
complexity when the generative capacity is increased. For incomparable
families, we give languages that can be described more efficiently in either of
these families than in the other.Comment: In Proceedings DCFS 2010, arXiv:1008.127
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