560 research outputs found
On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms
An inductive theorem proving method for constrained term rewriting systems,
which is based on rewriting induction, needs a decision procedure for
reduction-completeness of constrained terms. In addition, the sufficient
complete property of constrained term rewriting systems enables us to relax the
side conditions of some inference rules in the proving method. These two
properties can be reduced to intersection emptiness problems related to sets of
ground instances for constrained terms. This paper proposes a method to
construct deterministic, complete, and constraint-complete constrained tree
automata recognizing ground instances of constrained terms.Comment: In Proceedings TTATT 2013, arXiv:1311.505
Reversible Computation in Term Rewriting
Essentially, in a reversible programming language, for each forward
computation from state to state , there exists a constructive method to
go backwards from state to state . Besides its theoretical interest,
reversible computation is a fundamental concept which is relevant in many
different areas like cellular automata, bidirectional program transformation,
or quantum computing, to name a few.
In this work, we focus on term rewriting, a computation model that underlies
most rule-based programming languages. In general, term rewriting is not
reversible, even for injective functions; namely, given a rewrite step , we do not always have a decidable method to get from
. Here, we introduce a conservative extension of term rewriting that
becomes reversible. Furthermore, we also define two transformations,
injectivization and inversion, to make a rewrite system reversible using
standard term rewriting. We illustrate the usefulness of our transformations in
the context of bidirectional program transformation.Comment: To appear in the Journal of Logical and Algebraic Methods in
Programmin
Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
Making use of the operator product expansion, we derive a general class of
sum rules for the imaginary part of the single-particle self-energy of the
unitary Fermi gas. The sum rules are analyzed numerically with the help of the
maximum entropy method, which allows us to extract the single-particle spectral
density as a function of both energy and momentum. These spectral densities
contain basic information on the properties of the unitary Fermi gas, such as
the dispersion relation and the superfluid pairing gap, for which we obtain
reasonable agreement with the available results based on quantum Monte-Carlo
simulations.Comment: 44 pages, 11 figures, 2 tables; published versio
Self-Adaptive Named Entity Recognition by Retrieving Unstructured Knowledge
Although named entity recognition (NER) helps us to extract domain-specific
entities from text (e.g., artists in the music domain), it is costly to create
a large amount of training data or a structured knowledge base to perform
accurate NER in the target domain. Here, we propose self-adaptive NER, which
retrieves external knowledge from unstructured text to learn the usages of
entities that have not been learned well. To retrieve useful knowledge for NER,
we design an effective two-stage model that retrieves unstructured knowledge
using uncertain entities as queries. Our model predicts the entities in the
input and then finds those of which the prediction is not confident. Then, it
retrieves knowledge by using these uncertain entities as queries and
concatenates the retrieved text to the original input to revise the prediction.
Experiments on CrossNER datasets demonstrated that our model outperforms strong
baselines by 2.35 points in F1 metric.Comment: EACL2023 (long
Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems
Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past.
In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches
Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems
A narrowing tree for a constructor term rewriting system and a pair of terms is a finite representation for the space of all possible innermost-narrowing derivations that start with the pair and end with non-narrowable terms. Narrowing trees have grammar representations that can be considered regular tree grammars. Innermost narrowing is a counterpart of constructor-based rewriting, and thus, narrowing trees can be used in analyzing constructor-based rewriting to normal forms. In this paper, using grammar representations, we extend narrowing trees to syntactically deterministic conditional term rewriting systems that are constructor systems. We show that narrowing trees are useful to prove two properties of a normal conditional term rewriting system: one is infeasibility of conditional critical pairs and the other is quasi-reducibility
Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting
system (CTRS, for short) over an original signature into an
unconditional term rewriting systems (TRS, for short) over an extended
signature. They are not sound for every CTRS w.r.t. reduction, while
they are complete w.r.t. reduction. Here, soundness w.r.t. reduction
means that every reduction sequence of the corresponding unraveled
TRS, of which the initial and end terms are over the original
signature, can be simulated by the reduction of the original CTRS. In
this paper, we show that an optimized variant of Ohlebusch\u27s
unraveling for deterministic CTRSs is sound w.r.t. reduction if the
corresponding unraveled TRSs are left-linear or both right-linear and
non-erasing. We also show that soundness of the variant implies that
of Ohlebusch\u27s unraveling
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