75,930 research outputs found
The Church Synthesis Problem with Parameters
For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the
Church Synthesis Problem concerns the existence and construction of an operator
Y=F(X) such that ψ(X,F(X)) is universally valid over Nat.
B\"{u}chi and Landweber proved that the Church synthesis problem is
decidable; moreover, they showed that if there is an operator F that solves the
Church Synthesis Problem, then it can also be solved by an operator defined by
a finite state automaton or equivalently by an MLO formula. We investigate a
parameterized version of the Church synthesis problem. In this version ψ
might contain as a parameter a unary predicate P. We show that the Church
synthesis problem for P is computable if and only if the monadic theory of
is decidable. We prove that the B\"{u}chi-Landweber theorem can be
extended only to ultimately periodic parameters. However, the MLO-definability
part of the B\"{u}chi-Landweber theorem holds for the parameterized version of
the Church synthesis problem
PixelFolder: An Efficient Progressive Pixel Synthesis Network for Image Generation
Pixel synthesis is a promising research paradigm for image generation, which
can well exploit pixel-wise prior knowledge for generation. However, existing
methods still suffer from excessive memory footprint and computation overhead.
In this paper, we propose a progressive pixel synthesis network towards
efficient image generation, coined as PixelFolder. Specifically, PixelFolder
formulates image generation as a progressive pixel regression problem and
synthesizes images by a multi-stage paradigm, which can greatly reduce the
overhead caused by large tensor transformations. In addition, we introduce
novel pixel folding operations to further improve model efficiency while
maintaining pixel-wise prior knowledge for end-to-end regression. With these
innovative designs, we greatly reduce the expenditure of pixel synthesis, e.g.,
reducing 90% computation and 57% parameters compared to the latest pixel
synthesis method called CIPS. To validate our approach, we conduct extensive
experiments on two benchmark datasets, namely FFHQ and LSUN Church. The
experimental results show that with much less expenditure, PixelFolder obtains
new state-of-the-art (SOTA) performance on two benchmark datasets, i.e., 3.77
FID and 2.45 FID on FFHQ and LSUN Church, respectively. Meanwhile, PixelFolder
is also more efficient than the SOTA methods like StyleGAN2, reducing about 74%
computation and 36% parameters, respectively. These results greatly validate
the effectiveness of the proposed PixelFolder.Comment: 11 pages, 7 figure
Synthesis of Recursive ADT Transformations from Reusable Templates
Recent work has proposed a promising approach to improving scalability of
program synthesis by allowing the user to supply a syntactic template that
constrains the space of potential programs. Unfortunately, creating templates
often requires nontrivial effort from the user, which impedes the usability of
the synthesizer. We present a solution to this problem in the context of
recursive transformations on algebraic data-types. Our approach relies on
polymorphic synthesis constructs: a small but powerful extension to the
language of syntactic templates, which makes it possible to define a program
space in a concise and highly reusable manner, while at the same time retains
the scalability benefits of conventional templates. This approach enables
end-users to reuse predefined templates from a library for a wide variety of
problems with little effort. The paper also describes a novel optimization that
further improves the performance and scalability of the system. We evaluated
the approach on a set of benchmarks that most notably includes desugaring
functions for lambda calculus, which force the synthesizer to discover Church
encodings for pairs and boolean operations
Synthetic biology—putting engineering into biology
Synthetic biology is interpreted as the engineering-driven building of increasingly complex biological entities for novel applications. Encouraged by progress in the design of artificial gene networks, de novo DNA synthesis and protein engineering, we review the case for this emerging discipline. Key aspects of an engineering approach are purpose-orientation, deep insight into the underlying scientific principles, a hierarchy of abstraction including suitable interfaces between and within the levels of the hierarchy, standardization and the separation of design and fabrication. Synthetic biology investigates possibilities to implement these requirements into the process of engineering biological systems. This is illustrated on the DNA level by the implementation of engineering-inspired artificial operations such as toggle switching, oscillating or production of spatial patterns. On the protein level, the functionally self-contained domain structure of a number of proteins suggests possibilities for essentially Lego-like recombination which can be exploited for reprogramming DNA binding domain specificities or signaling pathways. Alternatively, computational design emerges to rationally reprogram enzyme function. Finally, the increasing facility of de novo DNA synthesis—synthetic biology’s system fabrication process—supplies the possibility to implement novel designs for ever more complex systems. Some of these elements have merged to realize the first tangible synthetic biology applications in the area of manufacturing of pharmaceutical compounds.
Interval-based Synthesis
We introduce the synthesis problem for Halpern and Shoham's modal logic of
intervals extended with an equivalence relation over time points, abbreviated
HSeq. In analogy to the case of monadic second-order logic of one successor,
the considered synthesis problem receives as input an HSeq formula phi and a
finite set Sigma of propositional variables and temporal requests, and it
establishes whether or not, for all possible evaluations of elements in Sigma
in every interval structure, there exists an evaluation of the remaining
propositional variables and temporal requests such that the resulting structure
is a model for phi. We focus our attention on decidability of the synthesis
problem for some meaningful fragments of HSeq, whose modalities are drawn from
the set A (meets), Abar (met by), B (begins), Bbar (begun by), interpreted over
finite linear orders and natural numbers. We prove that the fragment ABBbareq
is decidable (non-primitive recursive hard), while the fragment AAbarBBbar
turns out to be undecidable. In addition, we show that even the synthesis
problem for ABBbar becomes undecidable if we replace finite linear orders by
natural numbers.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Coding for Optimized Writing Rate in DNA Storage
A method for encoding information in DNA sequences is described. The method is based on the precisionresolution framework, and is aimed to work in conjunction with a recently suggested terminator-free template independent DNA synthesis method. The suggested method optimizes the amount of information bits per synthesis time unit, namely, the writing rate. Additionally, the encoding scheme studied here takes into account the existence of multiple copies of the DNA sequence, which are independently distorted. Finally, quantizers for various run-length distributions are designed
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