Delayed theory combination vs. Nelson-Oppen for satisfiability modulo theories: a comparative analysis

Most state-of-the-art approaches for Satisfiability Modulo Theories $(SMT(\mathcal{T}))$ rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory $\mathcal{T} (\mathcal{T}{\text {-}}solver)$ . Often $\mathcal{T}$ is the combination $\mathcal{T}_1 \cup \mathcal{T}_2$ of two (or more) simpler theories $(SMT(\mathcal{T}_1 \cup \mathcal{T}_2))$ , s.t. the specific ${\mathcal{T}_i}{\text {-}}solvers$ must be combined. Up to a few years ago, the standard approach to $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ was to integrate the SAT solver with one combined $\mathcal{T}_1 \cup \mathcal{T}_2{\text {-}}solver$ , obtained from two distinct ${\mathcal{T}_i}{\text {-}}solvers$ by means of evolutions of Nelson and Oppen’s (NO) combination procedure, in which the ${\mathcal{T}_i}{\text {-}}solvers$ deduce and exchange interface equalities. Nowadays many state-of-the-art SMT solvers use evolutions of a more recent $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ procedure called Delayed Theory Combination (DTC), in which each ${\mathcal{T}_i}{\text {-}}solver$ interacts directly and only with the SAT solver, in such a way that part or all of the (possibly very expensive) reasoning effort on interface equalities is delegated to the SAT solver itself. In this paper we present a comparative analysis of DTC vs. NO for $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ . On the one hand, we explain the advantages of DTC in exploiting the power of modern SAT solvers to reduce the search. On the other hand, we show that the extra amount of Boolean search required to the SAT solver can be controlled. In fact, we prove two novel theoretical results, for both convex and non-convex theories and for different deduction capabilities of the ${\mathcal{T}_i}{\text {-}}solvers$ , which relate the amount of extra Boolean search required to the SAT solver by DTC with the number of deductions and case-splits required to the ${\mathcal{T}_i}{\text {-}}solvers$ by NO in order to perform the same tasks: (i) under the same hypotheses of deduction capabilities of the ${\mathcal{T}_i}{\text {-}}solvers$ required by NO, DTC causes no extra Boolean search; (ii) using ${\mathcal{T}_i}{\text {-}}solvers$ with limited or no deduction capabilities, the extra Boolean search required can be reduced down to a negligible amount by controlling the quality of the $\mathcal{T}$ -conflict sets returned by the ${\mathcal{T}_i}{\text {-}}solvers$ .     

Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.     

Understanding users and their needs

Gaze-control enables people to control a computer by using eye-gaze to select items on screen. Gaze-control is a necessity for people who have lost all motor control of their body and only have control over eye movements. In addition, gaze-control can be the quickest and least tiring option for a far broader group of people with varying disabilities. This paper reports findings from gaze-control user trials involving users from both groups: people who are totally paralyzed, as well as people with a wide range of complex disabilities. The trials conducted involved four different centres supporting people with disabilities in three different European countries. Several gaze-control systems were trialled by a large number of users with varying needs and abilities. The perceived benefits of gaze-control are described, and recommendations for successful assessment and implementation of gaze-control are provided.     

Global asymptotic stabilization of the attitude and the angular rates of an underactuated non-symmetric rigid body

The paper deals with the global stabilization of both the attitude and the angular velocities of an underactuated rigid body. First a stability theorem is proven for a class of systems; subsequently, the equations describing the physics of the rigid body are presented, showing that the rigid body belongs to the considered class of systems, and a sufficient condition for the application of the theorem to the stability of the rigid body equilibrium is pointed out. Finally, some simulation results are reported showing the effectiveness of the proposed methodology.     

Immersive and desktop virtual reality in virtual fashion stores: a comparison between shopping experiences

Virtual Reality - With the high growth and prosperity of e-commerce, the retail industry needs to explore new technologies that improve digital shopping experiences. In the current technological...     

Generation and interpretation of parsimonious predictive models for load forecasting in smart heating networks

Applied Intelligence - Forecasting future heat load in smart district heating networks is a key problem for utility companies that need such predictions for optimizing their operational activities....     

Velocity‐based formulations for standard and quasi‐incompressible hypoelastic‐plastic solids

We present three velocity‐based updated Lagrangian formulations for standard and quasi‐incompressible hypoelastic‐plastic solids. Three low‐order finite elements are derived and tested for non‐linear solid mechanics problems. The so‐called V‐element is based on a standard velocity approach, while a mixed velocity–pressure formulation is used for the VP and the VPS elements. The two‐field problem is solved via a two‐step Gauss–Seidel partitioned iterative scheme. First, the momentum equations are solved in terms of velocity increments, as for the V‐element. Then, the constitutive relation for the pressure is solved using the updated velocities obtained at the previous step. For the VPS‐element, the formulation is stabilized using the finite calculus method in order to solve problems involving quasi‐incompressible materials. All the solid elements are validated by solving two‐dimensional and three‐dimensional benchmark problems in statics as in dynamics. Copyright © 2016 John Wiley & Sons, Ltd.     

The solid-state rearrangement of the Wells-Dawson K6P2W18O62·10H2O to a stable Keggin-type heteropolyanion phase: a catalyst for the selective oxidation of isobutane to isobutene

The thermal and structural stability of the Wells-Dawson-type heteropoly compound K₆P₂W₁₈O₆₂·10H₂O was examined by FT-IR spectroscopy, X-ray powder diffraction, thermogravimetric analysis and HRTEM. It was found that calcination at temperatures higher than 850 K led to the formation of a Keggin-type compound K₃PW₁₂O₄₀, containing small amounts of an additional phase originated from the high-temperature interaction between potassium phosphate (K₃PO₄ formed during the decomposition of the K₆P₂W₁₈O₆₂·10H₂O) and the Keggin-type compound itself. The Keggin-type product showed a higher activity in the selective oxidative dehydrogenation of isobutane to isobutene compared to both the Wells-Dawson precursor and to pure, authentic K₃PW₁₂O₄₀. This higher activity can be tentatively attributed to the presence of an amorphous layer of unknown stoichiometry at the surface of the thermally rearranged Wells-Dawson compound.