Widening Operator Research Articles

Tuning basicity of dual function materials widens operation temperature window for efficient CO2 adsorption and hydrogenation to CH4

Mitigation of CO2 emissions by integrated CO2 capture and utilization (ICCU) is challenging. This work focuses on widening operation temperature window of the hydrogenation of adsorbed CO2 to CH4. For this, a set of dual function materials (DFMs) 4%Ru-x%Na2CO3-y%CaO/γ-Al2O3 are prepared. DFMs are deeply characterized by N2 adsorption-desorption, XRD, H2 chemisorption, TEM, H2-TPR and CO2-TPD. The catalytic behavior, in cycles of CO2 adsorption and hydrogenation to CH4, is evaluated and the temporal evolution of the concentration of reactants and products is analyzed. The presence of both adsorbents in the DFMs improves ruthenium dispersion and the basicity is modulated with the Na2CO3/CaO ratio. Ru-8Na/8Ca improves methane production over the whole temperature window compared to DFMs based only on a unique adsorbent. The best results are assigned to the promotion of contact between the carbonates of medium strength with the metallic sites, which boost the CO2 adsorption and hydrogenation to CH4.

A Nuclear detection method Based on improved You Only Look Once v5s Framework

Extracting human cell smear samples through automated scanners, using target detection algorithm to detect its nucleus is an important content in cell detection. Due to the different shapes, different sizes and complex backgrounds of nuclei in the samples, automatic detection of nuclei is a challenging task. In order to solve the problem of complex small target recognition in nuclear detection and improve detection accuracy, based on the YOLOV5S framework of one-stage target detection, make certain improvement, add new residual module to the original network Neck layer, at the same time carry on network widening operation to the subsequent framework. The algorithm visualizes the results of training and testing through Tensorboard. Experimental results show that the accuracy of the improved YOLOV5S network is 1.6% and 4.4% higher than that of the original YOLOV5S network and YOLOV3 network. the improved network has strong real-time performance and high accuracy, which can meet the actual use requirements.

PPLite: Zero-overhead encoding of NNC polyhedra

We present an alternative Double Description representation for the domain of NNC (not necessarily closed) polyhedra, together with the corresponding Chernikova-like conversion procedure. The representation uses no slack variable at all and provides a solution to a few technical issues caused by the encoding of an NNC polyhedron as a closed polyhedron in a higher dimension space. We then reconstruct the abstract domain of NNC polyhedra, providing all the operators needed to interface it with commonly available static analysis tools: while doing this, we highlight the efficiency gains enabled by the new representation and we show how the canonicity of the new representation allows for the specification of proper, semantic widening operators. A thorough experimental evaluation shows that our new abstract domain achieves significant efficiency improvements with respect to classical implementations for NNC polyhedra.

Analysis on Calculation of Vehicle Operating Cost (VOC) Before and After Flyover & Road Widening Operation at Gedangan Intersection in Sidoarjo Regency

The main road that connects the city of Sidoarjo to Surabaya is the intersection of Gedangan. By 2018 it has reached saturation by having a poor service level. More severe conditions will occur in the next 10-20 years. One of the government’s efforts to overcome the problem of congestion, damage structure is the construction of flyover or other alternatives by widening the road. The purpose of this study is to determine the characteristics of the traffic and to save vehicle operating costs before and after the construction of a flyover at the Gedangan intersection. The method for predicting Vehicle Operating Costs (BOK) is to use PCI method. This study predicts Vehicle Operating Costs (BOK) to determine cost savings. The scenario for predicting BOK is that 80% of the vehicle volume will pass the Fly Over, and 20% still use the existing road. The results showed that the cost savings of Vehicle Operational Costs (BOK) of existing roads compared to the use of flyover in 2019 was IDR 15 Billion. In 2039 the savings are IDR 77 Billion. Another discussion is that if the road is only widened without flyover, then the BOK cost savings in 2019 will be IDR 4 Billion and in 2039 it will be IDR 27 Billion.

Hierarchical Analysis of Loops With Relaxed Abstract Transformers

Numerical computation is often involved in software of embedded control systems, cyber-physical systems, artificial neural network systems, big data processing systems, etc. Automatically discovering numerical loop invariants is fundamental for checking the safety of such software. Abstract interpretation provides a framework to automatically discover sound invariants but which may be not precise enough due to over-approximations. One major source of precision loss is due to the limited linear expressiveness of most widely used numerical abstract domains and the widening operation. This becomes more serious when analyzing all variables simultaneously as a whole for programs that involve nonlinear behaviors. Based on the observation that the dependency among variables in a loop can be hierarchical, in this article, we propose a hierarchical static analysis to analyze a loop by utilizing relaxed abstract transformers. The main idea is to first partition all variables involved in a loop into different hierarchical layers, then compute invariants over the variables layer by layer in a bottom-up manner. During the iterative process, the computed invariants over lower layer variables are then used to relax transfer functions when analyzing the higher layer variables. One benefit of our method lies in that it can generate linear invariants to soundly enclose nonlinear behaviors in a loop. Finally, we present encouraging experimental results on benchmark programs involving nonlinear behaviors.

Optimal Design of PMa-synRM for an Electric Propulsion System Considering Wide Operation Range and Demagnetization

In this paper, optimal design of permanent magnet assisted synchronous reluctance motor (PMa-synRM) for propulsion system is conducted. The main purpose of the design is widening operation region, maintaining advantages of a synchronous reluctance motor with improved noise, vibration, and harshness and demagnetization characteristics appropriate for a propulsion system. First of all, permanent magnet position and combination is optimized considering design purpose. Then, diagnosis of demagnetization has been performed to eliminate the models that are partially demagnetized due to the flux from the armature winding. Finally, a detailed design has been conducted for optimization on the dimensions of the permanent magnet and air-layer. Characteristic analysis of the designed model is conducted and comparison has been made to a reluctance synchronous motor to verify the effectiveness of the design. Calculations have been delivered by numerical analysis based on a finite element method.

Experimental Evaluation of Numerical Domains for Inferring Ranges

Among the numerical abstract domains for detecting linear relationships between program variables, the polyhedra domain is, from a purely theoretical point of view, the most precise one. Other domains, such as intervals, octagons and parallelotopes, are less expressive but generally more efficient. We focus our attention on interval constraints and, using a suite of benchmarks, we experimentally show that, in practice, polyhedra may often compute results less precise than the other domains, due to the use of the widening operator.

A Sums-of-Squares extension of policy iterations

In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative computation of policies, starting from a post-fixpoint. Computing each policy and the associated invariant relies on a sequence of numerical optimizations. While the early research efforts relied on linear programming (LP) to address linear properties of linear programs, the current state of the art is still limited to the analysis of linear programs with at most quadratic invariants, relying on semidefinite programming (SDP) solvers to compute policies, and LP solvers to refine invariants.We propose here to extend the class of programs considered through the use of Sums-of-Squares (SOS) based optimization. Our approach enables the precise analysis of switched systems with polynomial updates and guards. The analysis presented has been implemented in Matlab and applied on existing programs coming from the system control literature, improving both the range of analyzable systems and the precision of previously handled ones.

A program analysis framework for tccp based on abstract interpretation

Abstract The timed concurrent constraint language ( tccp ) is a timed extension of the concurrent constraint paradigm. tccp was defined to model reactive systems, where infinite behaviors arise naturally. In previous works, a semantic framework and abstract diagnosis method for the language have been defined. On the basis of that semantic framework, this paper proposes an abstract semantics that, together with a widening operator, is suitable for the definition of different analyses for tccp programs. The abstract semantics is correct and can be represented as a finite graph where each node represents a hypothetical (abstract) computational step of the program. The widening operator allows us to guarantee the convergence of the abstract fixpoint computation.

Semantic-directed clumping of disjunctive abstract states

To infer complex structural invariants, shape analyses rely on expressive families of logical properties. Many such analyses manipulate abstract memory states that consist of separating conjunctions of basic predicates describing atomic blocks or summaries. Moreover, they use finite disjunctions of abstract memory states in order to account for dissimilar shapes. Disjunctions should be kept small for the sake of scalability, though precision often requires to keep additional case splits. In this context, deciding when and how to merge case splits and to replace them with summaries is critical both for the precision and for the efficiency. Existing techniques use sets of syntactic rules, which are tedious to design and prone to failure. In this paper, we design a semantic criterion to clump abstract states based on their silhouette which applies not only to the conservative union of disjuncts, but also to the weakening of separating conjunction of memory predicates into inductive summaries. Our approach allows to define union and widening operators that aim at preserving the case splits that are required for the analysis to succeed. We implement this approach in the MemCAD analyzer, and evaluate it on real-world C codes from existing libraries, including programs dealing with doubly linked lists, red-black trees and AVL-trees.

Bound Analysis for Whiley Programs

The Whiley compiler can generate naive C code, but the code is inefficient because it uses infinite integers and dynamic array sizes. Our project goal is to build up a compiler that can translate Whiley programs into efficient OpenCL code with fixed-size integer types and fixed-size arrays, for parallel execution on GPUs. This paper presents an abstract interpretation-based bound inference approach along with symbolic analysis for Whiley programs. The source Whiley program is first analyzed by using our symbolic analyzer to find the matching pattern and make any necessary program transformation. Then the bound analyzer is used to analyze the transformed program to make use of primitive integer types rather than third-party infinite integer type (e.g. using GMP arbitrary precision library). The bound analysis results provide conservative estimates of the ranges of integer variables and array sizes so that efficient code can be generated and integer overflows avoided. The bound analyzer combines the bound consistency technique along with a widening operator to give fast time of solving program constraints and of converging to the fixed point. Several example programs are used to illustrate the bound analyzer algorithm and the program transformation.

Efficiently intertwining widening and narrowing

Accelerated fixpoint iteration by means of widening and narrowing is the method of choice for solving systems of equations over domains with infinite ascending chains. The strict separation into an ascending widening and a descending narrowing phase, however, may unnecessarily give up precision that cannot be recovered later. It is also unsuitable for equation systems with infinitely many unknowns — where local solving must be used.As a remedy, we present a novel operator ⍁ that combines a given widening operator ∇ with a given narrowing operator Δ. We present adapted versions of round-robin and worklist iteration as well as local and side-effecting solving algorithms for the combined operator ⍁. We prove that the resulting solvers always return sound results and are guaranteed to terminate for monotonic systems whenever only finitely many unknowns are encountered.

Verification of Programs by Combining Iterated Specialization with Interpolation

We present a verification technique for program safety that combines Iterated Specialization and Interpolating Horn Clause Solving. Our new method composes together these two techniques in a modular way by exploiting the common Horn Clause representation of the verification problem. The Iterated Specialization verifier transforms an initial set of verification conditions by using unfold/fold equivalence preserving transformation rules. During transformation, program invariants are discovered by applying widening operators. Then the output set of specialized verification conditions is analyzed by an Interpolating Horn Clause solver, hence adding the effect of interpolation to the effect of widening. The specialization and interpolation phases can be iterated, and also combined with other transformations that change the direction of propagation of the constraints (forward from the program preconditions or backward from the error conditions). We have implemented our verification technique by integrating the VeriMAP verifier with the FTCLP Horn Clause solver, based on Iterated Specialization and Interpolation, respectively. Our experimental results show that the integrated verifier improves the precision of each of the individual components run separately.

Monitoring the dynamic characteristics of an urban bridge before, during and after widening

The dynamic characteristics of a multi-span pre-stressed concrete urban bridge before, during and after widening operations have been studied. The widening operations have been carried out by adding two new bridges on the either sides of the old bridge. The decks of the new bridges have been structurally separated from the old one by two longitudinal joints on the either side of the old bridge. The dynamic characteristics have been extracted from operational modal tests in three phases during different stages of the widening operations. The dynamic interaction between the new parts and the old part of the bridge has also been investigated. The results show that after the completion of the widening works, and when the whole bridge was placed in service condition, this interaction affects the natural frequencies of almost all the vibration modes of the bridge. It was also found that the longitudinal joints were unable to effectively isolate the new parts from the old part. Finally, in order to achieve a consistent behaviour in the first bending mode of the new and old bridges, a geometrical index has been introduced. This index includes both the effects of stiffness and mass properties of the bridge deck. In widening projects, where the span lengths, material properties and support conditions of the two bridges are taken the same, adopting equal geometrical indices leads to almost equal values of the natural frequencies and similar mode shapes in the first bending mode. The proposed index can be used in the initial design stage for such projects.

Abstract acceleration in linear relation analysis

Linear relation analysis is a classical abstract interpretation based on an over-approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite height, it makes use of a widening operator to enforce the convergence of fixed point computations. Abstract acceleration is a method that computes the precise abstract effect of loops wherever possible and uses widening in the general case. Thus, it improves both the precision and the efficiency of the analysis. This article gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives.

How to combine widening and narrowing for non-monotonic systems of equations

Non-trivial analysis problems require complete lattices with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint iteration by means of widening and narrowing. The strict separation into phases, however, may unnecessarily give up precision that cannot be recovered later. While widening is also applicable if equations are non-monotonic, this is no longer the case for narrowing. A narrowing iteration to improve a given post-fixpoint, additionally, must assume that all right-hand sides are monotonic. The latter assumption, though, is not met in presence of widening. It is also not met by equation systems corresponding to context-sensitive interprocedural analysis, possibly combining context-sensitive analysis of local information with flow-insensitive analysis of globals. As a remedy, we present a novel operator that combines a given widening operator with a given narrowing operator. We present adapted versions of round-robin as well as of worklist iteration, local, and side-effecting solving algorithms for the combined operator and prove that the resulting solvers always return sound results and are guaranteed to terminate for monotonic systems whenever only finitely many unknowns (constraint variables) are encountered.

Stratified Static Analysis Based on Variable Dependencies

In static analysis by abstract interpretation, one often uses widening operators in order to enforce convergence within finite time to an inductive invariant. Certain widening operators, including the classical one over finite polyhedra, exhibit an unintuitive behavior: analyzing the program over a subset of its variables may lead a more precise result than analyzing the original program! In this article, we present simple workarounds for such behavior.

Sweeping in Abstract Interpretation

In this paper we present how sweeping line techniques, which are very popular in computational geometry, can be adapted for static analysis of computer software by abstract interpretation. We expose how concept of the sweeping line can be used to represent elements of a numerical abstract domain of boxes, which is a disjunctive refinement of a well known domain of intervals that allows finite number of disjunctions. We provide a detailed description of the representation along with standard domain operations algorithms. Furthermore we introduce very precise widening operator for the domain.Additionally we show that the presented idea of the representation based on sweeping line technique is a generalisation of the representation that uses Linear Decision Diagrams (LDD), which is one of possible optimisations of our idea. We also show that the presented widening operator is often more precise than the previous one.

Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using template linear constraint domains. Such invariants can be obtained by Kleene iterations that are, in order to guarantee termination, accelerated by widening operators. In many cases, however, applying this form of extrapolation leads to invariants that are weaker than the strongest inductive invariant that can be expressed within the abstract domain in use. Another well-known source of imprecision of traditional abstract interpretation techniques stems from their use of join operators at merge nodes in the control flow graph. The mentioned weaknesses may prevent these methods from proving safety properties. The technique we develop in this article addresses both of these issues: contrary to Kleene iterations accelerated by widening operators, it is guaranteed to yield the strongest inductive invariant that can be expressed within the template linear constraint domain in use. It also eschews join operators by distinguishing all paths of loop-free code segments. Formally speaking, our technique computes the least fixpoint within a given template linear constraint domain of a transition relation that is succinctly expressed as an existentially quantified linear real arithmetic formula. In contrast to previously published techniques that rely on quantifier elimination, our algorithm is proved to have optimal complexity: we prove that the decision problem associated with our fixpoint problem is in the second level of the polynomial-time hierarchy.

Loop invariant synthesis in a combined abstract domain

Automated verification of memory safety and functional correctness for heap-manipulating programs has been a challenging task, especially when dealing with complex data structures with strong invariants involving both shape and numerical properties. Existing verification systems usually rely on users to supply annotations to guide the verification, which can be cumbersome and error-prone by hand and can significantly restrict the usability of the verification system. In this paper, we reduce the need for some user annotations by automatically inferring loop invariants over an abstract domain with both shape and numerical information. Our loop invariant synthesis is conducted automatically by a fixed-point iteration process, equipped with newly designed abstraction mechanism, together with join and widening operators over the combined domain. We have also proven the soundness and termination of our approach. Initial experiments confirm that we can synthesise loop invariants with non-trivial constraints.