On the size of Boyer–Moore automata

In this work we study the size of Boyer–Moore automata introduced in Knuth, Morris & Pratt’s famous paper on pattern matching. We experimentally show that a finite class of binary patterns produce very large Boyer–Moore automata, and find one particular case which we conjecture, generates automata of size Ω(m⁶)$\Omega \left(m^6\right)$. Further experimental results suggest that the maximal size could be a polynomial of O(m⁷)$O\left(m^7\right)$, or even an exponential O(2^0.4m)$O\left(2^{0.4m}\right)$, where m$m$ is the length of the pattern.     

Boyer和Moore获1983年McCarthy奖

两年一度的J.McCarthy奖是为表彰在程序验证领域的杰出工作而设立的。首次奖是根据最近五年在该领域发表的研究工作评定的。美国德克萨斯大学的R.S.Boyer和J S.Moore被评选为首次获奖人。Boyer和Moore从七十年代就合作研究定理证明和程序验证。他们的主要成就是成功地发展了一种可实现高效率的定理证明系统的严谨的逻辑。这种逻辑特别强调了归纳法的使用以表现程序共有的属性。他们的系统是现今最有效的定理证明系统之一。该系统使用启发式来加强其自动定理证明的功能,并允许用户通过人权交换来推导不能由机器完全自动完成的证明。他们还扩充了该系统,使之包括一个FORTRAN验证条件产生程序,使该系统可以处理FORTRAN这     

Rogers–Ramanujan computer searches

We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers–Ramanujan type and identities of false theta functions.     

Accelerating solid–fluid interaction based on the immersed boundary method on multicore and GPU architectures

This work proposes several approaches to accelerate the solid–fluid interaction through the use of the Immersed Boundary method on multicore and GPU architectures. Different optimizations on both architectures have been proposed, focusing on memory management and workload mapping. We have chosen two different test scenarios which consist of single-solid and multiple-solid simulations. The performance analysis has been carried out on an intensive set of test cases to analyze the proposed optimizations using multiple CPUs (2) and GPUs (4). An effective performance is obtained for single-solid executions using one CPU (Intel Xeon E5520) achieving a speedup peak equal to 5.5. It is reached a higher benefit on multiple solids obtaining a top speedup of approximately 5.9 and 9 using one CPU (8 cores) and two CPUs (16 cores), respectively. On GPU (Kepler K20c) architecture, two different approaches are presented as the best alternative: one for single-solid executions and one for multiple-solid executions. The best approach obtained for one solid executions achieves a speedup of approximately 17 with respect the sequential counterpart. In contrast, for multiple-solid executions the benefit is much higher, being this type of problems much more suitable for GPU and reaching a peak speedup of 68, 115 and 162 using 1, 2 and 4 GPUs, respectively.     

Bianchi Type-I Dust-Filled Accelerating Brans–Dicke Cosmology

Spatially homogeneous and anisotropic Bianchi type-I cosmological models of Brans–Dicke (BD) theory of gravitation are investigated. The model represents an accelerating universe at present and is considered to be dominated by dark energy. The cosmological constant Λ is considered as a candidate for dark energy. The derived model agrees at par with the recent SN Ia observations. We have set the BD coupling constant ω to be 40000, according to the solar system tests and evidence. We discuss various physical and geometric properties of the models and compare them with the corresponding general-relativistic models.     

Learning Moore machines from input–output traces

International Journal on Software Tools for Technology Transfer - The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning...     

LMI searches for anticausal and noncausal rational Zames–Falb multipliers

Given a linear time-invariant plant, the search for a suitable multiplier over the class of Zames–Falb multipliers is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames–Falb multipliers. This letter analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers. The addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search. As a result, a search over a noncausal subset of Zames–Falb multipliers is obtained. A comparison between all the search methods proposed in the literature is given.     

Functions of orthogonal projectors involving the Moore–Penrose inverse

Several results scattered in the literature express an oblique projector having given onto and along spaces in terms of a pair of orthogonal projectors. The results were established in various settings, including finite and infinite dimensional vector spaces over either real or complex numbers, but their common feature is that they are valid merely under the assumption of the nonsingularity of certain functions of the involved projectors. In the present paper, these results are unified and reestablished in a generalized form in a complex Euclidean vector space, with the generalization obtained by relaxing the nonsingularity assumption and use of the Moore–Penrose inverse instead of the ordinary inverse. Additionally, several new formulae of the type are provided.     

Accelerating Single Iteration Performance of CUDA-Based 3D Reaction–Diffusion Simulations

The most commonly used approach for solving reaction–diffusion systems relies upon stencil computations. Although stencil computations feature low compute intensity, they place high demands on memory bandwidth. Fortunately, GPU computing allows for the heavy reliance of stencil computations on neighboring data points to be exploited to significantly increase simulation speeds by reducing these memory bandwidth demands. Upon reviewing previously published works, a wide-variety of efforts have been made to optimize NVIDIA CUDA-based stencil computations. However, a critical aspect contributing to algorithm performance is commonly glossed over: the halo region loading technique utilized in conjunction with a given spatial blocking technique. This paper presents an in-depth examination of this aspect and the associated single iteration performance impacts when using symmetric, nearest neighbor 19-point stencils. This is accomplished by closely examining how the simulated space is partitioned into thread blocks and the balance between memory accesses, divergence, and computing threads. The resulting optimization strategy for accelerating 3-dimensional reaction–diffusion simulations offers up to 2.45 times speedup for single-precision floating point numbers in reference to GPU-based speedups found within the previously published work that this paper directly extends. In reference to our multithreaded CPU-based implementation, the resulting optimization strategy offers up to 8.69 times speedup for single-precision floating point numbers.     

Thermodynamic description of the Mg–Eu binary system

Thermodynamic assessment of the Mg–Eu binary system has been carried out by combining first-principles calculations and Miedema’s theory with CALPHAD method. Firstly, the mixing enthalpy of the liquid alloys was calculated by using Miedema’s theory, and formation enthalpies of the intermetallic compounds were calculated by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Subsequently, the liquid phase was described employing a simple substitutional model, of which the excess Gibbs energy was formulated with a Redlich-Kister expression. And the solubility of Eu in HCP_(Mg) and Mg in BCC_(Eu) were neglected. While the intermetallic compounds Mg₁₇Eu₂, Mg₅Eu, Mg₄Eu, Mg₂Eu and MgEu, were treated as stoichiometric compounds. Consequently, a set of self-consistent thermodynamic parameters for all stable phases in the Mg–Eu binary system were obtained, which can reproduce most of the thermodynamic and phase boundary data.     

Kinetic boundary conditions for vapor–gas binary mixture

Using molecular dynamics simulations, the present study investigated the precise characteristics of the binary mixture of condensable gas (vapor) and non-condensable gas (NC gas) molecules creating kinetic boundary conditions (KBCs) at a gas–liquid interface in equilibrium. We counted the molecules utilizing the improved two-boundary method proposed in previous studies by Kobayashi et al. (Heat Mass Trans 52:1851–1859, 2016. doi: 10.1007/s00231-015-1700-6). In this study, we employed Ar for the vapor molecules, and Ne for the NC gas molecules. The present method allowed us to count easily the evaporating, condensing, degassing, dissolving, and reflecting molecules in order to investigate the detailed motion of the molecules, and also to evaluate the velocity distribution function of the KBCs at the interface. Our results showed that the evaporation and condensation coefficients for vapor and NC gas molecules decrease with the increase in the molar fraction of the NC gas molecules in the liquid. We also found that the KBCs can be specified as a function of the molar fraction and liquid temperature. Furthermore, we discussed the method to construct the KBCs of vapor and NC gas molecules.     

Thermodynamic assessment of the Ni–Sc binary system

On the basis of the experimental data of the phase equilibria and the thermochemical properties, a critical evaluation for the Ni–Sc binary system has been carried out using the CALPHAD (Calculation of Phase Diagrams) method. The associated model is used for the liquid phase containing the constituent species Ni, Sc and ScNi. The terminal solid solutions Fcc_A1 (Ni), Hcp_A3 (Sc), and Bcc_A2 (Sc) are described by the solution model with the Redlich–Kister polynomial. The intermetallic compounds, ScNi₅, Sc₂Ni₇, ScNi and Sc₂Ni, are treated as strict stoichiometric compounds. The compound with a homogeneity range, (ScNi₂), is modeled using two sublattices as (Sc,Ni)_0.333(Sc,Ni)_0.667. A set of self-consistent thermodynamic parameters for the Ni–Sc binary system is obtained. The calculated results agree well with the available experimental data from literatures.     

On the pole of non-square transfer function matrix Moore–Penrose pseudo-inverses

An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore–Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet–Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore–Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore–Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.     

Thermodynamic optimization of the binary CaO–ZnO and ternary CaO–ZnO–SiO2 systems

Liquidus phase equilibrium data of the present authors for the CaO–ZnO–SiO₂ system (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃-“Cu₂O”-CaO-SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase; lime (Ca,Zn)O, zincite (Zn,Ca)O, α- and α′-dicalcium silicate (Ca,Zn)₂SiO₄ and tricalcium silicate (Ca,Zn)₃SiO₅ are described within Bragg-Williams formalism; tridymite, cristobalite SiO₂, wollastonite, pseudowollastonite CaSiO₃, rankinite Ca₃Si₂O₇, willemite Zn₂SiO₄, melilite (hardystonite) Ca₂ZnSi₂O₇ and Ca–Zn feldspar CaZnSi₃O₈ are treated as stoichiometric compounds. From these model parameters, the optimized ternary phase diagram is back calculated.