Global Guidance for Local Generalization in Model Checking

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for the theory of Linear Integer Arithmetic and implement them on top of SPACER solver in Z3. Our empirical results show that GSPACER, SPACER extended with global guidance, is significantly more effective than both SPACER and sole global reasoning, and, furthermore, is insensitive to interpolation.Comment: Published in CAV 202

Global Guidance for Local Generalization in Model Checking

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for the theory of Linear Integer Arithmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation

Global guidance for local generalization in model checking

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for Linear Integer Arithmetic and Linear Rational Aritmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Two and Three-Dimensional Finite Element Analysis of Plasticity-Induced Fatigue Crack Closure: A Comprehensive Parametric Study

Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (M(T)), bend (SEB), and compact tension (C(T)) geometries were conducted to study fatigue crack closure and to calculate the crack opening values under plane-strain and plane-stress conditions. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus similar initial forward plastic zone sizes. Mesh refinement studies were performed on all geometries with various element types. For the C(T) geometry, negligible crack opening loads under plane-strain conditions were observed. In contrast, for the M(T) specimen, the plane-strain crack opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for the C(T), SEB, and M(T) specimens. Next, the crack opening values of the C(T), SEB and M(T) specimens were compared under various stress levels and load ratios. The effect of a highly refined mesh on crack opening values was noted and significantly lower crack opening values than those reported in literature were found. A new methodology is presented to calculate crack opening values in planar geometries using the crack surface nodal force distribution under minimum loading as determined from finite element analyses. The calculated crack opening values are compared with values obtained using finite element analysis and more conventional crack opening assessment methodologies. It is shown that the new method is independent of loading increment, integration method (normal and reduced integration), and crack opening assessment location. The compared opening values were in good agreement with strip-yield models

A Proper Orthogonal Decomposition-based inverse material parameter optimization method with applications to cardiac mechanics

We are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex mathematical models of "living cells" are being arranged into representative tissue assemblies and utilized to produce models of integrated tissue and organ function. This enables more sophisticated simulation tools that allows for greater insight into disease and guide the development of modern therapies. The development of realistic computer models of mechanical behaviour for soft biological tissues, such as cardiac tissue, is dependent on the formulation of appropriate constitutive laws and accurate identification of their material parameters. The main focus of this contribution is to investigate a Proper Orthogonal Decomposition with Interpolation (PODI) based method for inverse material parameter optimization in the field of cardiac mechanics. Material parameters are calibrated for a left ventricular and bi-ventricular human heart model during the diastolic filling phase. The calibration method combines a MATLAB-based Levenberg Marquardt algorithm with the in-house PODIbased software ORION. The calibration results are then compared against the full-order solution which is obtained using an in-house code based on the element-free Galerkin method, which is assumed to be the exact solution. The results obtained from this novel calibration method demonstrate that PODI provides the means to drastically reduce computation time but at the same time maintain a similar level of accuracy as provided by the conventional approach

Software-based approximate computing for mathematical functions

The four arithmetic floating-point operations (+,−,÷and×) have been precisely specified in IEEE-754 since 1985, but the situation for floating-point mathematical libraries and even some hardware operations such as fused multiply-add is more nuanced as there are varying opinions on which standards should be followed and when it is acceptable to allow some error or when it is necessary to be correctly-rounded. Deterministic correctly-rounded elementary mathematical functions are important in many applications. Others are tolerant to some level of error and would benefit from less accurate, better-performing approximations. We found that, despite IEEE-754 (2008 and 2019 only)specifying that ‘recommended functions’ such as sin, cos or log should be correctly rounded, the mathematical libraries available through standard interfaces in popular programming languages provide neither correct-rounding nor maximally performing approximations, partly due to the differing accuracy requirements of these functions in conflicting standards provided for some languages, such as C. This dissertation seeks to explore the current methods used for the implementation of mathematical functions, show the error present in them and demonstrate methods to produce both low-cost correctly-rounded solutions and better approximations for specific use-cases. This is achieved by: First, exploring the error within existing mathematical libraries and examining how it is impacting existing applications and the development of programming language standards. We then make two contributions which address the accuracy and standard conformance problems that were found: 1) an approach for a correctly-rounded 32-bit implementation of the elementary functions with minimal additional performance cost on modern hardware; and 2) an approach for developing a better performing incorrectly-rounded solution for use when some error is acceptable and conforming with the IEEE-754 standard is not a requirement. For the latter contribution, we introduce a tool for semi-automated generic code sensitivity analysis and approximation. Next, we target the creation of approximations for the standard activation functions used in neural networks. Identifying that significant time is spent in the computation of the activation functions, we generate approximations with different levels of error and better performance characteristics. These functions are then tested in standard neural networks to determine if the approximations have any detrimental effect on the output of the network. We show that, for many networks and activation functions, very coarse approximations are suitable replacements to train the networks equally well at a lower overall time cost. This dissertation makes original contributions to the area of approximate computing. We demonstrate new approaches to safe-approximation and justify approximate computation generally by showing that existing mathematical libraries are already suffering the downsides of approximation and latent error without fully exploiting the optimisation space available due to the existing tolerance to that error and showing that correctly-rounded solutions are possible without a significant performance impact for many 32-bit mathematical functions

Estimation of stress intensity factors in ship structural connections

Stiffened plated structures such as ships and box girder bridges, result in connection details that contain sharp internal corners. Many failures in ship structure have been found to be associated with fatigue crack propagation at the side shell connections between longitudinal and transverse structure. According to elastic stress analysis, these sharp corners are geometric singularities that have an infinite stress in the corner. A further complication of stiffened structures is that a crack may grow through intersections, e.g. of plates and stiffeners and changes of plate thickness before it causes a catastrophic structural failure. In this thesis, a new approach is developed to simplify the analysis of these issues. The singular stress contribution is, as usual, characterised by Y, the non-dimensional the stress intensity factor but within this method simplified analysis is used to calculate the Y values. The method combines a ratio of non-singular linearized ligament stresses to estimate the effect of large changes in crack length and changes in plate thickness with an empirical methods to estimate the local effect as the crack grows through a change of thickness. The method does not require an analysis of the actual singularity, so saving analysis time and, importantly, giving the engineer some feeling for the result and the possibility of a “back of the envelope” calculation for the SIF or Y. This work is based on running finite element analyses, to determine the Stress Intensity Factor and Y and using the results to test the empirical or analytical methods.The derived methods are useful both for assessment of existing structures and for design application. Comparing the results from the application of this new methodology with the FE method and existing fatigue analysis guidance, the new method is very much quicker and easier to apply. It is though less accurate than FE analysis and so is most appropriate for, (1) preliminary assessment, (2) reliability assessment where many structural and defect variations are to be considered and (3) for checking whether a more detailed analysis is producing sensible results. For design calculations often a stress concentration factor or SCF is needed that can be used with an S-N curve. The actual predicted peak stress and hence SCF will, for finite element analysis, depend on the element size and will normally increase as the element size decreases. The existing guidance on determining an appropriate stress value for fatigue analysis of a sharp corner is commonly in terms of linearly extrapolating finite element calculated surface stresses from a number of plate thicknesses t away from the singularity to the corner. A simpler approach, developed for planar plates with sharp corners, assesses the stress on the basis of the dimensions of the corner. This thesis includes checks on the applicability, to more complicated 3-d geometry, of these previous recommendations for the assessment of corner singularities.Stiffened plated structures such as ships and box girder bridges, result in connection details that contain sharp internal corners. Many failures in ship structure have been found to be associated with fatigue crack propagation at the side shell connections between longitudinal and transverse structure. According to elastic stress analysis, these sharp corners are geometric singularities that have an infinite stress in the corner. A further complication of stiffened structures is that a crack may grow through intersections, e.g. of plates and stiffeners and changes of plate thickness before it causes a catastrophic structural failure. In this thesis, a new approach is developed to simplify the analysis of these issues. The singular stress contribution is, as usual, characterised by Y, the non-dimensional the stress intensity factor but within this method simplified analysis is used to calculate the Y values. The method combines a ratio of non-singular linearized ligament stresses to estimate the effect of large changes in crack length and changes in plate thickness with an empirical methods to estimate the local effect as the crack grows through a change of thickness. The method does not require an analysis of the actual singularity, so saving analysis time and, importantly, giving the engineer some feeling for the result and the possibility of a “back of the envelope” calculation for the SIF or Y. This work is based on running finite element analyses, to determine the Stress Intensity Factor and Y and using the results to test the empirical or analytical methods.The derived methods are useful both for assessment of existing structures and for design application. Comparing the results from the application of this new methodology with the FE method and existing fatigue analysis guidance, the new method is very much quicker and easier to apply. It is though less accurate than FE analysis and so is most appropriate for, (1) preliminary assessment, (2) reliability assessment where many structural and defect variations are to be considered and (3) for checking whether a more detailed analysis is producing sensible results. For design calculations often a stress concentration factor or SCF is needed that can be used with an S-N curve. The actual predicted peak stress and hence SCF will, for finite element analysis, depend on the element size and will normally increase as the element size decreases. The existing guidance on determining an appropriate stress value for fatigue analysis of a sharp corner is commonly in terms of linearly extrapolating finite element calculated surface stresses from a number of plate thicknesses t away from the singularity to the corner. A simpler approach, developed for planar plates with sharp corners, assesses the stress on the basis of the dimensions of the corner. This thesis includes checks on the applicability, to more complicated 3-d geometry, of these previous recommendations for the assessment of corner singularities

Layout-level Circuit Sizing and Design-for-manufacturability Methods for Embedded RF Passive Circuits

The emergence of multi-band communications standards, and the fast pace of the consumer electronics markets for wireless/cellular applications emphasize the need for fast design closure. In addition, there is a need for electronic product designers to collaborate with manufacturers, gain essential knowledge regarding the manufacturing facilities and the processes, and apply this knowledge during the design process. In this dissertation, efficient layout-level circuit sizing techniques, and methodologies for design-for-manufacturability have been investigated. For cost-effective fabrication of RF modules on emerging technologies, there is a clear need for design cycle time reduction of passive and active RF modules. This is important since new technologies lack extensive design libraries and layout-level electromagnetic (EM) optimization of RF circuits become the major bottleneck for reduced design time. In addition, the design of multi-band RF circuits requires precise control of design specifications that are partially satisfied due to manufacturing variations, resulting in yield loss. In this work, a broadband modeling and a layout-level sizing technique for embedded inductors/capacitors in multilayer substrate has been presented. The methodology employs artificial neural networks to develop a neuro-model for the embedded passives. Secondly, a layout-level sizing technique for RF passive circuits with quasi-lumped embedded inductors and capacitors has been demonstrated. The sizing technique is based on the circuit augmentation technique and a linear optimization framework. In addition, this dissertation presents a layout-level, multi-domain DFM methodology and yield optimization technique for RF circuits for SOP-based wireless applications. The proposed statistical analysis framework is based on layout segmentation, lumped element modeling, sensitivity analysis, and extraction of probability density functions using convolution methods. The statistical analysis takes into account the effect of thermo-mechanical stress and process variations that are incurred in batch fabrication. Yield enhancement and optimization methods based on joint probability functions and constraint-based convex programming has also been presented. The results in this work have been demonstrated to show good correlation with measurement data.Ph.D.Committee Chair: Swaminathan, Madhavan; Committee Member: Fathianathan, Mervyn; Committee Member: Lim, Sung Kyu; Committee Member: Peterson, Andrew; Committee Member: Tentzeris, Mano