Confluence of Layered Rewrite Systems

We investigate a new, Turing-complete class of layered systems, whose linearized lefthand sides of rules can only be overlapped at the root position. Layered systems define a natural notion of rank for terms: the maximal number of redexes along a path from the root to a leaf. Overlappings are allowed in finite or infinite trees. Rules may be non-terminating, non-left-linear, or non-right- linear. Using a novel unification technique, cyclic unification, we show that rank non-increasing layered systems are confluent provided their cyclic critical pairs have cyclic-joinable decreasing diagrams

Encoding Proofs in Dedukti: the case of Coq proofs

International audienceA main ambition of the Inria project Dedukti is to serve as a common language for representing and type checking proof objects originating from other proof systems. Encoding these proof objects makes heavy use of the rewriting capabilities of LambdaPiModulo, the formal system on which Dedukti is based. So far, the proofs generated by two automatic proofsystems, Zenon and iProver, have been encoded, and can therefore be read and checked by Dedukti. But Dedukti goes far beyond this so-called hammering technique of sending goals to automated provers. Proofs from HOL and Matita can be encoded as well. Some Coq’s proofs can be encoded already, when they do not use universe polymorphism. Our ambition here is to close this remaining gap. To this end, we describe a rewrite-based encoding in LambdaPiModulo of the Calculus of Constructions with a cumulative hierarchy of predicative universes above Prop, which is confluent on open terms

Untyped Confluence in Dependent Type Theories

International audienceWe investigate techniques based on van Oostrom's decreasing diagrams that reduce confluence proofs to the checking of critical pairs in the absence of termination properties, which are useful in dependent type calculi to prove confluence on untyped terms. These techniques are applied to a complex example originating from practice: a faithful encoding, in an extension of LF with rewrite rules on objects and types, of a subset of the calculus of inductive constructions with a cumulative hierarchy of predicative universes above Prop. The rules may be first-order or higher-order, plain or modulo, non-linear on the right or on the left. Variables which occur non-linearly in lefthand sides of rules must take their values in confined types: in our example, the natural numbers. The first-order rules are assumed to be terminating and confluent modulo some theory: in our example, associativity, commutativity and identity. Critical pairs involving higher-order rules must satisfy van Oostrom's decreasing diagram condition wrt their indexes taken as labels

The Fast and the Private: Task-based Dataset Search

Modern dataset search platforms employ ML task-based utility metrics instead of relying on metadata-based keywords to comb through extensive dataset repositories. In this setup, requesters provide an initial dataset, and the platform identifies complementary datasets to augment (join or union) the requester's dataset such that the ML model (e.g., linear regression) performance is improved most. Although effective, current task-based data searches are stymied by (1) high latency which deters users, (2) privacy concerns for regulatory standards, and (3) low data quality which provides low utility. We introduce Mileena, a fast, private, and high-quality task-based dataset search platform. At its heart, Mileena is built on pre-computed semi-ring sketches for efficient ML training and evaluation. Based on semi-ring, we develop a novel Factorized Privacy Mechanism that makes the search differentially private and scales to arbitrary corpus sizes and numbers of requests without major quality degradation. We also demonstrate the early promise in using LLM-based agents for automatic data transformation and applying semi-rings to support causal discovery and treatment effect estimation

Simulated Experiment Study of Factors Influencing the Hydration Activity of f-CaO in Basic Oxygen Furnace Slag

The compositions and formation process of f-CaO in BOF slag were revealed and simulated to understand its expansion rules and why its hydration activity is low. BSE showed the compositions of f-CaO, which included calcium iron phase and calcium iron manganese phase, were diverse. The hydration activity sequence was Ca2Fe2O5 and Ca3Fe1.5Mn1.5O8 in tricomponent f-CaO < CaO in tricomponent f-CaO < monocomponent f-CaO; only Ca2Fe2O5 and Ca3Fe1.5Mn1.5O8 were hard to hydrate, and the volume expansion rates of the tricomponent f-CaO varied with different compositions. Inductively, in BOF slag, the hydration activity sequence was solid solutions CaO-FeOx and CaO-FeOx-MnOy in tricomponent f-CaO < CaO in tricomponent f-CaO < monocomponent f-CaO; the volume expansion rates of tricomponent f-CaO changed with different compositions, and CaO-FeOx and CaO-FeOx-MnOy were difficult to hydrate. The reason why solid solutions CaO-FeOx and CaO-FeOx-MnOy were hard to hydrate was that their hydration reaction driving force, which is the absolute value of standard molar reaction Gibbs functions, decreased

Dynamic uncertainty quantification and risk prediction based on the grey mathematics and outcrossing theory

Embarked from the practical conditions of small samples in time-invariant and time-variant uncertainties, a complete non-probabilistic analysis procedure containing uncertainty quantification, uncertainty propagation, and reliability evaluation is presented in this paper. Firstly, the Grey systematic approach is proposed to determine the boundary laws of static intervals and dynamic interval processes. Through a combination of the policies of the second-order Taylor expansion and the smallest parametric interval set, the structural response histories via quantitative uncertainty results are further confirmed. Additionally, according to the first-passage idea from classical random process theory, the study on the time-dependent reliability measurement on the basis of the interval process model is carried out to achieve a more elaborate estimation for structural safety during its whole life cycle. A numerical example and one experimental application are eventually discussed for demonstration of the usage and reasonability of the methodology developed

An MILP model and a hybrid evolutionary algorithm for integrated operation optimisation of multi-head surface mounting machines in PCB assembly

This paper focuses on an operation optimisation problem for a class of multi-head surface mounting machines in printed circuit board assembly lines. The problem involves five interrelated sub-problems: assigning nozzle types as well as components to heads, assigning feeders to slots and determining component pickup and placement sequences. According to the depth of making decisions, the sub-problems are first classified into two layers. Based on the classification, a two-stage mixed-integer linear programming (MILP) is developed to describe it and a two-stage problem-solving frame with a hybrid evolutionary algorithm (HEA) is proposed. In the first stage, a constructive heuristic is developed to determine the set of nozzle types assigned to each head and the total number of assembly cycles; in the second stage, constructive heuristics, an evolutionary algorithm with two evolutionary operators and a tabu search (TS) with multiple neighbourhoods are combined to solve all the sub-problems simultaneously, where the results obtained in the first stage are taken as constraints. Computational experiments show that the HEA can obtain good near-optimal solutions for small size instances when compared with an optimal solver, Cplex, and can provide better results when compared with a TS and an EA for actual instances

DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation

Recent advances in 3D content creation mostly leverage optimization-based 3D generation via score distillation sampling (SDS). Though promising results have been exhibited, these methods often suffer from slow per-sample optimization, limiting their practical usage. In this paper, we propose DreamGaussian, a novel 3D content generation framework that achieves both efficiency and quality simultaneously. Our key insight is to design a generative 3D Gaussian Splatting model with companioned mesh extraction and texture refinement in UV space. In contrast to the occupancy pruning used in Neural Radiance Fields, we demonstrate that the progressive densification of 3D Gaussians converges significantly faster for 3D generative tasks. To further enhance the texture quality and facilitate downstream applications, we introduce an efficient algorithm to convert 3D Gaussians into textured meshes and apply a fine-tuning stage to refine the details. Extensive experiments demonstrate the superior efficiency and competitive generation quality of our proposed approach. Notably, DreamGaussian produces high-quality textured meshes in just 2 minutes from a single-view image, achieving approximately 10 times acceleration compared to existing methods.Comment: project page: https://dreamgaussian.github.io