19,083 research outputs found
Factorization of Spanning Trees on Feynman Graphs
In order to use the Gaussian representation for propagators in Feynman
amplitudes, a representation which is useful to relate string theory and field
theory, one has to prove first that each - parameter (where is
the parameter associated to each propagator in the -representation of
the Feynman amplitudes) can be replaced by a constant instead of being
integrated over and second, prove that this constant can be taken equal for all
propagators of a given graph. The first proposition has been proven in one
recent letter when the number of propagators is infinite. Here we prove the
second one. In order to achieve this, we demonstrate that the sum over the
weighted spanning trees of a Feynman graph can be factorized for disjoint
parts of . The same can also be done for cuts on , resulting in a
rigorous derivation of the Gaussian representation for super-renormalizable
scalar field theories. As a by-product spanning trees on Feynman graphs can be
used to define a discretized functional space.Comment: 47 pages, Plain Tex, 3 PostScript figure
The Parikh Property for Weighted Context-Free Grammars
Parikh's Theorem states that every context-free grammar (CFG) is equivalent
to some regular CFG when the ordering of symbols in the words is ignored. The
same is not true for the so-called weighted CFGs, which additionally assign a
weight to each grammar rule. If the result holds for a given weighted CFG ,
we say that satisfies the Parikh property. We prove constructively that the
Parikh property holds for every weighted nonexpansive CFG. We also give a
decision procedure for the property when the weights are over the rationals.Comment: 29 pages, 2 figures, long version of FSTTCS'18 pape
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
A Dynamic Programming Approach To Length-Limited Huffman Coding
The ``state-of-the-art'' in Length Limited Huffman Coding algorithms is the
-time, -space one of Hirschberg and Larmore, where is the length restriction on the code. This is a very clever, very problem
specific, technique. In this note we show that there is a simple
Dynamic-Programming (DP) method that solves the problem with the same time and
space bounds. The fact that there was an time DP algorithm was
previously known; it is a straightforward DP with the Monge property (which
permits an order of magnitude speedup). It was not interesting, though, because
it also required space. The main result of this paper is the
technique developed for reducing the space. It is quite simple and applicable
to many other problems modeled by DPs with the Monge property. We illustrate
this with examples from web-proxy design and wireless mobile paging
Relational Graph Models at Work
We study the relational graph models that constitute a natural subclass of
relational models of lambda-calculus. We prove that among the lambda-theories
induced by such models there exists a minimal one, and that the corresponding
relational graph model is very natural and easy to construct. We then study
relational graph models that are fully abstract, in the sense that they capture
some observational equivalence between lambda-terms. We focus on the two main
observational equivalences in the lambda-calculus, the theory H+ generated by
taking as observables the beta-normal forms, and H* generated by considering as
observables the head normal forms. On the one hand we introduce a notion of
lambda-K\"onig model and prove that a relational graph model is fully abstract
for H+ if and only if it is extensional and lambda-K\"onig. On the other hand
we show that the dual notion of hyperimmune model, together with
extensionality, captures the full abstraction for H*
From spanning forests to edge subsets
We give some insight into Tutte's definition of internally and externally
active edges for spanning forests. Namely we prove, that every edge subset can
be constructed from the edges of exactly one spanning forest by deleting a
unique subset of the internally active edges and adding a unique subset of the
externally active edges.Comment: 11 page
A Chomsky-Sch\"utzenberger representation for weighted multiple context-free languages
We prove a Chomsky-Sch\"utzenberger representation theorem for multiple
context-free languages weighted over complete commutative strong bimonoids.Comment: This is an extended and corrected version of a paper with the same
title presented at the 12th International Conference on Finite-State Methods
and Natural Language Processing (FSMNLP 2015
Efficient Local Unfolding with Ancestor Stacks
The most successful unfolding rules used nowadays in the partial evaluation
of logic programs are based on well quasi orders (wqo) applied over (covering)
ancestors, i.e., a subsequence of the atoms selected during a derivation.
Ancestor (sub)sequences are used to increase the specialization power of
unfolding while still guaranteeing termination and also to reduce the number of
atoms for which the wqo has to be checked. Unfortunately, maintaining the
structure of the ancestor relation during unfolding introduces significant
overhead. We propose an efficient, practical local unfolding rule based on the
notion of covering ancestors which can be used in combination with a wqo and
allows a stack-based implementation without losing any opportunities for
specialization. Using our technique, certain non-leftmost unfoldings are
allowed as long as local unfolding is performed, i.e., we cover depth-first
strategies.Comment: Number of pages: 32 Number of figures: 7 Number of Tables:
Computing q-gram Frequencies on Collage Systems
Collage systems are a general framework for representing outputs of various
text compression algorithms. We consider the all -gram frequency problem on
compressed string represented as a collage system, and present an -time -space algorithm for calculating the frequencies for all
-grams that occur in the string. Here, and are respectively the size
and height of the collage system
Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
This article studies Markovian stochastic motion of a particle on a graph
with finite number of nodes and periodically time-dependent transition rates
that satisfy the detailed balance condition at any time. We show that under
general conditions, the currents in the system on average become quantized or
fractionally quantized for adiabatic driving at sufficiently low temperature.
We develop the quantitative theory of this quantization and interpret it in
terms of topological invariants. By implementing the celebrated Kirchhoff
theorem we derive a general and explicit formula for the average generated
current that plays a role of an efficient tool for treating the current
quantization effects.Comment: 22 pages, 7 figure
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