Analyses of unsatisfiability for equational logic programming

The problem of unifying pairs of terms with respect to an equational theory (as well as detecting the unsatisfiability of a system of equations) is, in general, undecidable. In this work, we define a framework based on abstract interpretation for the (static) analysis of the unsatisfiability of equation sets. The main idea behind the method is to abstract the process of semantic unification of equation sets based on narrowing. The method consists of building an abstract narrower for equational theories, and executing the sets of equations to be detected for unsatisfiability in the approximated narrower. As an instance of our framework, we define a new analysis whose accuracy is enhanced by some simple loop-checking technique. This analysis can also be actively used for pruning the search tree of an incremental equational constraint solver, and can be integrated with other methods in the literature. Standard methods are shown to be an instance of our framework. To the best of our knowledge, this is the first framework proposed for approximating equational unification.     

命令式动态规划类算法程序推导及机械化验证

动态规划是一种递归求解问题最优解的方法,主要通过求解子问题的解并组合这些解来求解原问题.由于其子问题之间存在大量依赖关系和约束条件,所以验证过程繁琐,尤其对命令式动态规划类算法程序正确性验证是一个难点.基于动态规划类算法Isabelle/HOL函数式建模与验证,通过证明命令式动态规划类算法程序与其的等价性,避免证明正确性时处理复杂的依赖关系和约束条件,提出命令式动态规划类算法程序设计框架及其机械化验证.首先,根据动态规划类算法的优化方法(备忘录方法)和性质(最优子结构性质和子问题重叠性质)描述问题规约、归纳递推关系式和形式化构造出循环不变式,并且基于递推关系式生成IMP (Minimalistic Imperative Programming Language)代码;其次,将问题规约、循环不变式和生成的IMP代码输入VCG (Verification Condition Generator),自动生成正确性的验证条件;然后,在Isabelle/HOL定理证明器中对验证条件进行机械化验证.算法首先设计为命令式动态规划类算法的一般形式,并进一步实例化得到具体算法.最后,例证了所提框架的有效性,为动态规划类算法的自动化推导和验证提供参考价值.     

The patient bed assignment problem solved by autonomous bat algorithm

The patient bed assignment problem consists of managing, in the best possible way, a set of beds with particular features and assigning them to a set of patients with special requirements. This assignment problem can be seen an optimization problem, of which the intended aims are usually to minimize the number of internal movements within a unit and to maximize bed usage according to the levels of criticality of the patients, among others. The usual approaches for solving this problem follow a traditional model based on the constraint programming paradigm, mainly using hard constraints. However, in real-life problems, constraints that should ideally be satisfied are often violated. In this paper, we present a new model for the patient bed assignment problem based on the minimum sum of unsatisfied constraints. This technique enables the consideration of soft constraints in the potential solutions that exhibit the best performance. The aim is to find the assignment that minimizes a weighted sum of the unsatisfied constraints. To this end, we use an autonomous binary version of the bat algorithm, which is an optimization technique inspired by the bio-sonar behaviour of microbats, to find the best set of potential solutions without requiring any expert user knowledge to achieve an efficient solution process. To validate our proposal, we use our model to solve problem instances based on data from several hospitals, and we perform a detailed comparative statistical analysis with a traditional constraint programming solver and several well-known optimization algorithms, including the classic bat algorithm. Promising results show that our approach is capable of efficiently solving 30 instances with decreased solution times.     

Resolution proof transformation for compression and interpolation

Verification methods based on SAT, SMT, and theorem proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal reason that led to unsatisfiability, for computing abstractions, or for deriving Craig interpolants. In this paper we focus on two important aspects that concern efficient handling of proofs of unsatisfiability: compression and manipulation. First of all, since the proof size can be very large in general (exponential in the size of the input problem), it is indeed beneficial to adopt techniques to compress it for further processing. Secondly, proofs can be manipulated as a flexible preprocessing step in preparation for interpolant computation. Both these techniques are implemented in a framework that makes use of local rewriting rules to transform the proofs. We show that a careful use of the rules, combined with existing algorithms, can result in an effective simplification of the original proofs. We have evaluated several heuristics on a wide range of unsatisfiable problems deriving from SAT and SMT test cases.     

一个组合几何最优化未解决问题的半机械化解法

本文证明了一个关于凸n边形面积的不等式猜测在n=8时的正确性,并对n=9的情况做了讨论。首先将这个最优化问题转化为多项式不等式方程组的实解的存在性问题;其次通过分析最优图形给出了一些化简不等式方程组和减少系统自由变元的方法;利用符号计算等方法建立了一个半机械化方法求多项式方程组作为约束条件的非线性规划问题准确
解。     

面向HDL描述基于路径覆盖的模拟矢量自动生成方法研究

提出和实现了一种面向HDL描述基于路径覆盖的模拟矢量自动生成方法,该方法在约束生成时只考虑控制语句的条件表达式，可有效避免生成冗余约束；利用扩展的决策图模型解决了中间信号到初始输入的传播问题和信号依赖关系问题，以及处理各种HDL描述风格的问题；采用约束逻辑编程方法解决了由位、位向量和整型变量组成的约束系统的统一处理问题,实验结果表明该方法能加快模拟矢量生成速度，提高路径覆盖率．生成的模拟矢量也能用于低层次设计验证和故障模拟，加快了设计进度,将该方法的原型系统用于一个32位微处理器核RTL级验证，发现了RTL级设计描述中的错误．     

New techniques for linear arithmetic: cubes and equalities

We present several new techniques for linear arithmetic constraint solving. They are all based on the linear cube transformation, a method presented here, which allows us to efficiently determine whether a system of linear arithmetic constraints contains a hypercube of a given edge length. Our first findings based on this transformation are two sound tests that find integer solutions for linear arithmetic constraints. While many complete methods search along the problem surface for a solution, these tests use cubes to explore the interior of the problems. The tests are especially efficient for constraints with a large number of integer solutions, e.g., those with infinite lattice width. Inside the SMT-LIB benchmarks, we have found almost one thousand problem instances with infinite lattice width. Experimental results confirm that our tests are superior on these instances compared to several state-of-the-art SMT solvers. We also discovered that the linear cube transformation can be used to investigate the equalities implied by a system of linear arithmetic constraints. For this purpose, we developed a method that computes a basis for all implied equalities, i.e., a finite representation of all equalities implied by the linear arithmetic constraints. The equality basis has several applications. For instance, it allows us to verify whether a system of linear arithmetic constraints implies a given equality. This is valuable in the context of Nelson–Oppen style combinations of theories.     

一种C程序断言的全自动静态验证方法

在软件程序中插入断言是保证软件质量的一个简单但有效的方法，人们常使用测试的方法检验程序中的断言是否满足，但测试很难保证验证的完备性。本文提出了一种可以保证完备性的全自动静态断言验证方法，其基本思想是基于程序切片符号执行程序的所有执行路径，并证明路径上的所有断言都满足。为了尽量减少符号执行的语句的数量，使用了基于反例的抽象精化方法，从一个粗略的切片标准开始迭代地符号执行一爷路径，根据验证的反例自动生成下一次迭代过程中使用的精化的切片标准。包含循环的程序可能具有无穷多条程序执行路径，提出的基于符号执行上下文不变式证明的方法可以证明由于循环导致的无穷多条路径中断言都满足，从而使得验证过程可以终止。实验表明，提出的全自动静态断言验证方法不仅可行，而且验证代价较小，具有较强的实用性。     

基于Coq的微内核操作系统程序验证方法研究

机载嵌入式程序的可信属性验证是新一代飞机研制最关注的软件质量保障问题;基于定理证明的程序形式化验证方法是一种可靠和严格的软件正确性验证技术;文中在深入分析微内核操作系统的基础上,应用霍尔逻辑针对机载嵌入式软件核心代码开展程序验证技术研究,根据霍尔逻辑的相关推理规则进行程序验证,并在定理证明辅助工具Coq中形式化表示霍尔逻辑的推理规则,针对机载操作系统的部分程序代码实例进行验证;实验结果表明基于定理证明的程序验证方法可以对软件程序代码的正确性进行验证,从而帮助软件提供商开发高可信的机载嵌入式软件。     

Automatic verification of Java programs with dynamic frames

Framing in the presence of data abstraction is a challenging and important problem in the verification of object-oriented programs Leavens et al. (Formal Aspects Comput (FACS) 19:159–189, 2007). The dynamic frames approach is a promising solution to this problem. However, the approach is formalized in the context of an idealized logical framework. In particular, it is not clear the solution is suitable for use within a program verifier for a Java-like language based on verification condition generation and automated, first-order theorem proving. In this paper, we demonstrate that the dynamic frames approach can be integrated into an automatic verifier based on verification condition generation and automated theorem proving. The approach has been proven sound and has been implemented in a verifier prototype. The prototype has been used to prove correctness of several programming patterns considered challenging in related work.     

基于Mining-SEC方法的电路等价性验证

针对时序电路的等价性验证难题,提出基于Mining-SEC的定界等价性验证方法。将待验证时序电路按时间帧展开为多项式符号代数表示的电路集合,利用时间序列数据挖掘方法挖掘其中的不变量和相应的全局约束,不变量可以是任意多项式。此外还可挖掘电路中的不合法约束和复杂的多项式关系,通过以上方法可以明显降低求解空间。使用基于SMT的验证引擎检验电路等价性。实验结果表明,该方法可以快速地实现验证收敛,得到平均1~2个量级的验证加速,并且可以有效消除虚假验证。     

SCHOOL SCHEDULING USING THRESHOLD ACCEPTING

In this paper, we focus on solving problems modeled after a real-world high school timetable problem. It includes multiple objectives and a variety of constraints. It mainly involves producing an optimal schedule for each teacher and for each class. The conventional integer programming approach seems to have some difficulties with solving such problems. The versatility of our proposed heuristic based on a modification of the threshold accepting method is exemplified through our problem solving. For comparison sake, simulated annealing was also used to solve the same problems.     

Iterative functional modification method for solving a transportation problem

We propose a new method for solving transportation problems based on decomposing the original problem into a number of two-dimensional optimization problems. Since the solution procedure is integer-valued and monotonic in the objective function, the required computation is finite. As a result, we get not only a single optimal solution of the original transportation problem but a system of constraints that can yield all optimal solutions. We give numerical examples that illustrate the constructions of our algorithm.     

Dynamic symmetry-breaking for Boolean satisfiability

With impressive progress in Boolean Satisfiability (SAT) solving and several extensions to pseudo-Boolean (PB) constraints, many applications that use SAT, such as high-performance formal verification techniques are still restricted to checking satisfiability of certain conditions. However, there is also frequently a need to express a preference for certain solutions. Extending SAT-solving to Boolean optimization allows the use of objective functions to describe a desirable solution. Although recent work in 0–1 Integer Linear Programming (ILP) offers extensions that can optimize a linear objective function, this is often achieved by solving a series of SAT or ILP decision problems. Our work articulates some pitfalls of this approach. An objective function may complicate the use of any symmetry that might be present in the given constraints, even when the constraints are unsatisfiable and the objective function is irrelevant. We propose several new techniques that treat objective functions differently from CNF/PB constraints and accelerate Boolean optimization in many practical cases. We also develop an adaptive flow that analyzes a given Boolean optimization problem and picks the symmetry-breaking technique that is best suited to the problem characteristics. Empirically, we show that for non-trivial objective functions that destroy constraint symmetries, the benefit of static symmetry-breaking is lost but dynamic symmetry-breaking accelerates problem-solving in many cases. We also introduce a new objective function, Localized Bit Selection (LBS), that can be used to specify a preference for bit values in formal verification applications.     

InequalityProve及一个公开问题的求解

传统的不等式自动证明方法主要依赖于符号计算,一般只能处理代数类型,或可最终转化为代数类型的不等式,而且效率会随着问题中变量个数的增加迅速降低。为克服这些局限性以满足众多实际问题的需要,并充分挖掘计算机在数值计算方面的能力,我们提出以区间分析为工具进行不等式的自动证明。该方法可以处理类型更为一般的不等式,只需对应的函数具有所需的高阶连续可微性质,并且该方法易于实现并行化。本文主要介绍这一方法在Maple系统上的实现,即InequalityProve,并以一个公开问题为例详细说明运用InequalityProve进行不等式证明的一般过程。     

基于启发式NDFS的模型检测新算法

以带有多个可接受条件的广义Büchi自动机为研究对象,提出基于启发式NDFS的模型检测新算法.该算法结合on-the-fly算法与启发式NDFS算法,能较快地判断出广义Büchi自动机非空性,通过理论证明和实验验证了算法的正确性和可行性.与已有算法相比,在广义Büchi自动机非空的情况下,该算法减少了系统状态空间的搜索,提高了检测效率,且能形成相应反例,为缓解形式化验证中的状态空间爆炸问题提供了有效的解决途径,为安全苛求系统的安全性保障提供了有力支撑,丰富了基于模型的软件形式化开发方法.     

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs.     

可满足性求解器算法基于GPU的加速研究

可满足性求解(SAT)问题被广泛应用于软件验证、理论证明、微处理器验证、模块验证等领域,工业应用实例问题求解变量规模已达到百万数量级,传统的基于CPU的串行和并行SAT求解方法已无法满足如此规模的问题求解。不同于以往的并行SAT研究,利用GPU并行处理的特点和SAT算法的特点,将SAT算法中最耗时的BCP(Boolean Constraint Propagation)过程并行化,设计实现了基于GPU的BCP过程GP_BCP(GPU Paralleled BCP),从而将BCP过程的性能提高了5.4～10.3倍。     

多区间速度约束下的时序数据清洗方法

为进一步优化推广大数据及人工智能技术,作为数据管理与分析的基础,数据质量问题日益成为相关领域的研究热点.通常情况下,数据采集及记录仪的物理故障或技术缺陷等会导致收集到的数据存在一定的错误,而异常错误会对后续的数据分析以及人工智能过程产生不可小视的影响,因此在数据应用之前,需要对数据进行相应的数据清洗修复.现存的平滑修复...     

Watermill: An Optimized Fingerprinting System for Databases under Constraints

his paper presents a watermarking/fingerprinting system for relational databases. It features a built-in declarative language to specify usability constraints that watermarked datasets must comply with. For a subset of these constraints, namely weight-independent constraints, we propose a novel watermarking strategy which consists of translating them into an integer linear program. We show two watermarking strategies: an exhaustive one based on integer linear programming constraint solving and a scalable pairing heuristic. Fingerprinting applications, for which several distinct watermarks need to be computed, benefit from the reduced computation time of our method that precomputes the watermarks only once. Moreover we show that our method enables practical collusion-secure fingerprinting since the precomputed watermarks are based on binary alterations located at exactly the same positions. The paper includes an in-depth analysis of false hits and false misses occurrence probabilities for the detection algorithm. Experiments performed on our open source software Watermill assess the watermark robustness against common attacks, and show that our method outperforms the existing ones concerning the watermark embedding speed.