11,107 research outputs found
Quantum Automata and Quantum Grammars
To study quantum computation, it might be helpful to generalize structures
from language and automata theory to the quantum case. To that end, we propose
quantum versions of finite-state and push-down automata, and regular and
context-free grammars. We find analogs of several classical theorems, including
pumping lemmas, closure properties, rational and algebraic generating
functions, and Greibach normal form. We also show that there are quantum
context-free languages that are not context-free.Comment: 21 page
Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory
In this paper we characterize the congruence associated to the direct sum of
all irreducible representations of a finite semigroup over an arbitrary field,
generalizing results of Rhodes for the field of complex numbers. Applications
are given to obtain many new results, as well as easier proofs of several
results in the literature, involving: triangularizability of finite semigroups;
which semigroups have (split) basic semigroup algebras, two-sided semidirect
product decompositions of finite monoids; unambiguous products of rational
languages; products of rational languages with counter; and \v{C}ern\'y's
conjecture for an important class of automata
Weighted Regular Tree Grammars with Storage
We introduce weighted regular tree grammars with storage as combination of
(a) regular tree grammars with storage and (b) weighted tree automata over
multioperator monoids. Each weighted regular tree grammar with storage
generates a weighted tree language, which is a mapping from the set of trees to
the multioperator monoid. We prove that, for multioperator monoids canonically
associated to particular strong bi-monoids, the support of the generated
weighted tree languages can be generated by (unweighted) regular tree grammars
with storage. We characterize the class of all generated weighted tree
languages by the composition of three basic concepts. Moreover, we prove
results on the elimination of chain rules and of finite storage types, and we
characterize weighted regular tree grammars with storage by a new weighted
MSO-logic.Comment: added errat
On the state complexity of closures and interiors of regular languages with subwords and superwords
The downward and upward closures of a regular language are obtained by
collecting all the subwords and superwords of its elements, respectively. The
downward and upward interiors of are obtained dually by collecting words
having all their subwords and superwords in , respectively. We provide lower
and upper bounds on the size of the smallest automata recognizing these
closures and interiors. We also consider the computational complexity of
decision problems for closures of regular languages
Streamable Regular Transductions
Motivated by real-time monitoring and data processing applications, we
develop a formal theory of quantitative queries for streaming data that can be
evaluated efficiently. We consider the model of unambiguous Cost Register
Automata (CRAs), which are machines that combine finite-state control (for
identifying regular patterns) with a finite set of data registers (for
computing numerical aggregates). The definition of CRAs is parameterized by the
collection of numerical operations that can be applied to the registers. These
machines give rise to the class of streamable regular transductions (SR), and
to the class of streamable linear regular transductions (SLR) when the register
updates are copyless, i.e. every register appears at most once the
right-hand-side expressions of the updates. We give a logical characterization
of the class SR (resp., SLR) using MSO-definable transformations from strings
to DAGs (resp., trees) without backward edges. Additionally, we establish that
the two classes SR and SLR are closed under operations that are relevant for
designing query languages. Finally, we study the relationship with weighted
automata (WA), and show that CRAs over a suitably chosen set of operations
correspond to WA, thus establishing that WA are a special case of CRAs.Comment: 53 page
On the enumerating series of an abstract numeration system
It is known that any rational abstract numeration system is faithfully, and
effectively, represented by an N-rational series. A simple proof of this result
is given which yields a representation of this series which in turn allows a
simple computation of the value of words in this system and easy constructions
for the recognition of recognisable sets of numbers. It is also shown that
conversely it is decidable whether an N-rational series corresponds to a
rational abstract numeration system.Comment: presented at the Journ\'ees Montoises d'Informatique Th\'eorique
2010, Sept. 2010, Amiens (France
The Chomsky-Sch\"utzenberger Theorem for Quantitative Context-Free Languages
Weighted automata model quantitative aspects of systems like the consumption
of resources during executions. Traditionally, the weights are assumed to form
the algebraic structure of a semiring, but recently also other weight
computations like average have been considered. Here, we investigate
quantitative context-free languages over very general weight structures
incorporating all semirings, average computations, lattices, and more. In our
main result, we derive the fundamental Chomsky-Sch\"utzenberger theorem for
such quantitative context-free languages, showing that each arises as the image
of a Dyck language and a regular language under a suitable morphism. Moreover,
we show that quantitative context-free language are expressively equivalent to
a model of weighted pushdown automata. This generalizes results previously
known only for semirings. We also investigate when quantitative context-free
languages assume only finitely many values.Comment: This new version combines a conference and a journal paper of the
authors on the same topic, see references [15,16], and supplements them by a
few additional examples and more detailed proofs. It also corrects a mistake
in Theorem 7.7 of the first arxiv version (the property sequential was
missing
Two-Way Automata Making Choices Only at the Endmarkers
The question of the state-size cost for simulation of two-way
nondeterministic automata (2NFAs) by two-way deterministic automata (2DFAs) was
raised in 1978 and, despite many attempts, it is still open. Subsequently, the
problem was attacked by restricting the power of 2DFAs (e.g., using a
restricted input head movement) to the degree for which it was already possible
to derive some exponential gaps between the weaker model and the standard
2NFAs. Here we use an opposite approach, increasing the power of 2DFAs to the
degree for which it is still possible to obtain a subexponential conversion
from the stronger model to the standard 2DFAs. In particular, it turns out that
subexponential conversion is possible for two-way automata that make
nondeterministic choices only when the input head scans one of the input tape
endmarkers. However, there is no restriction on the input head movement. This
implies that an exponential gap between 2NFAs and 2DFAs can be obtained only
for unrestricted 2NFAs using capabilities beyond the proposed new model. As an
additional bonus, conversion into a machine for the complement of the original
language is polynomial in this model. The same holds for making such machines
self-verifying, halting, or unambiguous. Finally, any superpolynomial lower
bound for the simulation of such machines by standard 2DFAs would imply LNL.
In the same way, the alternating version of these machines is related to L =?
NL =? P, the classical computational complexity problems.Comment: 23 page
Development of an MSC language and compiler, volume 1
Higher order programming language and compiler for advanced computer software system to be used with manned space flights between 1972 and 198
The jsonlite Package: A Practical and Consistent Mapping Between JSON Data and R Objects
A naive realization of JSON data in R maps JSON arrays to an unnamed list,
and JSON objects to a named list. However, in practice a list is an awkward,
inefficient type to store and manipulate data. Most statistical applications
work with (homogeneous) vectors, matrices or data frames. Therefore JSON
packages in R typically define certain special cases of JSON structures which
map to simpler R types. Currently there exist no formal guidelines, or even
consensus between implementations on how R data should be represented in JSON.
Furthermore, upon closer inspection, even the most basic data structures in R
actually do not perfectly map to their JSON counterparts and leave some
ambiguity for edge cases. These problems have resulted in different behavior
between implementations and can lead to unexpected output. This paper
explicitly describes a mapping between R classes and JSON data, highlights
potential problems, and proposes conventions that generalize the mapping to
cover all common structures. We emphasize the importance of type consistency
when using JSON to exchange dynamic data, and illustrate using examples and
anecdotes. The jsonlite R package is used throughout the paper as a reference
implementation
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