串行线性赋值循环程序的终止性判定

对于并行赋值的线性循环程序,已有文献通过矩阵特征值方法来判定其终止性,但该方法并不适用于常见的串行赋值程序。该文通过把串行赋值程序转换为并行赋值的程序,再利用矩阵特征值和特征向量来对程序的终止性作出判定,从而扩大了该方法的应用范围。     

区间上非线性程序的终止性判定

分析了如下类型程序的终止性:While x∈Ω do {x:=f(x)} end.其中,x是程序变量,Ω是一个区间,f是一个连续函数.这类程序被称为区间上非线性程序.证明了上面程序不终止的必要条件是函数在区间内部或边界上有不动点.如果不动点不在区间的边界,则上述结果是充要条件.仅仅在区间边界上有不动点的情况下,对函数略加限制,也建立了相应结果.特别地,对逐段多项式连续函数程序的终止性给出了完备判定算法.     

有界闭域上的线性赋值循环终止性分析

对有界闭域上的线性赋值循环程序终止性问题进行研究.利用Jordan 标准型技术将原循环程序的终止性问题约减为终止性等价的具有简单结构的循环程序的终止性问题.证明了当线性迭代映射满足一定条件时,该类循环程序不可终止的充分必要条件是：迭代映射在有界闭域上有不动点或周期轨.     

基于迭代轨迹划分的单分支循环程序终止性分析

秩函数作为循环程序终止性分析的重要方法已得到广泛研究。文中着重研究了单分支循环的终止性。首先提出了双向迭代循环概念,将单分支循环分为双向迭代循环和非双向迭代循环。其次,针对双向迭代循环程序,建立了一种划分思路,提出了三段式秩函数的概念,并证明了若该双向迭代循环存在三段式秩函数,则其是终止的。而对非双向迭代循环,引用增函数的划分思路,即利用增函数将原程序空间划分为更小的空间,并通过计算更小空间上的秩函数来证明原程序的终止性。最后,将三段式秩函数的计算问题归结为SVM分类问题,并利用工具Z3或bottema对由SVM所得的候选秩函数进行验证。     

单分支线性约束循环程序的终止性分析

秩函数法是循环终止性分析的主要方法,秩函数的存在表明了循环程序是可终止的.针对单分支线性约束循环程序,提出一种方法对此类循环的终止性进行分析.基于增函数法向空间的计算,该方法将原程序空间上的秩函数计算问题归结为其子空间上的秩函数计算问题.实验结果表明,该方法能有效验证现有文献中大部分循环程序的终止性.     

有界闭区间并上的非线性循环程序的终止性验证

利用符号动力学理论中有关一维离散映射的函数和区间的转换图方法及相关结论,证明一类非线性循环程序不终止的必要条件是在该程序循环区间上有不动点或者周期点存在,并给出相应的终止性验证算法.利用该算法可以验证一维有界闭区间上的非线性循环程序的终止性.最后,给出计算实例演示该算法的算法步骤.     

基于k阶秩函数的线性赋值循环程序的终止性分析

循环程序的终止性是确保循环程序完全正确的必要条件。 如果给定的线性赋值循环程序不存在传统定义的线性秩函数,那么基于传统定义的秩函数终止性证明方法将失效。基于Aⁿx的精确计算,对传统的秩函数概念进行了扩展,提出了k阶秩函数的概念。使用RegularChains软件包给出了合成k阶秩函数的具体方法。实验结果表明,相比于传统定义的线性秩函数,k阶秩函数的适应范围更广。对于 不能用传统定义的秩函数证明其终止性的部分循环程序,可以基于k阶秩函数来证明,从而体现了所提方法的优越性。     

Prolog程序中循环的终止性分析

本文对Prolog程序中的循环进行了分析,提出了一种识别无穷循环的简单直观方法,在此基础上给出了相应的避免或防止办法。     

多分支单变量循环程序的终止性分析

对多分支单变量循环程序的终止性问题进行了研究.证明了在适定的条件下,该类循环程序不可终止性的充分必要条件是迭代映射在循环条件形成的区域中有不动点.特别地,当这类循环程序是多项式循环程序时,在给定条件下,其在实数域上的终止性问题是可判定的.     

PROPER:一个概率程序终止性与正确性分析工具

概率程序将概率推理模型与图灵完备的编程语言相结合,统一了对计算和不确定性知识的形式化描述,能够有效地处理复杂的关系模型和不确定性问题.提供了一种用于分析仿射概率程序的工具PROPER.一方面,它有助于定性和定量地分析仿射概率程序的终止性,可以验证该概率程序是否以概率1终止,估计期望终止时间的上限,并计算步数N,使得N步后给定程序的终止概率呈指数下降;另一方面,它可以估计一个断言成立的概率区间,这有助于分析变量不确定性对概率程序结果的影响.通过实验表明,PROPER对分析各种仿射概率程序是有效的.     

循环展开技术在向量程序中的应用

循环展开是一项常用的循环优化技术。当前针对串行程序的循环展开技术已经比较成熟,但是在实际应用中没有针对向量程序进行有效的循环展开。为了解决这个问题,提出了一种面向向量程序的循环展开技术。首先,针对向量寄存器压力和代码膨胀等限制因素,提出了一种自动计算展开因子的CUFVL算法;其次,根据向量循环展开的特点,制定了完全展开策略;最后结合CUFVL算法和完全展开策略,设计了向量循环展开的总体流程。实验结果表明,该方案能够计算出合适的展开因子,进而对向量程序进行适当的循环展开或完全展开,从而有效提升应用程序的性能。     

Automatic Termination Analysis of Programs Containing Arithmetic Predicates

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is presented for showing termination in this case.The method consists of the following steps: First, a finite abstract domain for representing the range of integers is deduced automatically. Based on this abstraction, abstract interpretation is applied to the program. The result is a finite number of atoms abstracting answers to queries which are used to extend the technique of query-mapping pairs. For each query-mapping pair that is potentially non-terminating, a bounded (integer-valued) termination function is guessed. If traversing the pair decreases the value of the termination function, then termination is established. Simple functions often suffice for each query-mapping pair, and that gives our approach an edge over the classical approach of using a single termination function for all loops, which must inevitably be more complicated and harder to guess automatically. It is worth noting that the termination of McCarthy's 91 function can be shown automatically using our method.In summary, the proposed approach is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Consequently, the whole process of proving termination can be done automatically in the framework of TermiLog and similar systems.     

几种量子程序终止的有效验证

基于文献巨18口提出的量子程序验证方法,讨论了单量子比特系统上比特翻转、去极化、幅值阻尼、相位阻尼等 信道刻画的量子程序的验证,通过选取不同的可观测算子对程序终止的情况进行了详细的讨论。研究表明,由这些量 子信道所描述的量子程序的终止情况不仅依赖于输入态的选取,还依赖于可观测算子的选取。     

A Method for Analyzing Loop Programs

This paper presents a method for automatically analyzing loops, and discusses why it is a useful way to look at loops. The method is based on the idea that there are four basic ways in which the logical structure of a loop is built up. An experiment is presented which shows that this accounts for the structure of a large class of loops. The paper discusses how the method can be used to automatically analyze the structure of a loop, and how the resulting analysis can be used to guide a proof of correctness for the loop. An automatic system is described which performs this type of analysis. The paper discusses the relationship between the structure building methods presented and programming language constructs. A system is described which is designed to assist a person who is writing a program. The intent is that the system will cooperate with a programmer throughout aUl phases of work on a program and be able to communicate with the programmer about it.     

Verifying Termination and Reduction Properties about Higher-Order Logic Programs

We describe two checkers for verifying termination and reduction properties about higher-order logic programs. The reduction checker verifies that the result of a program execution is structurally smaller than (or equal to) the inputs to the program. The termination checker guarantees that the inputs of the recursive calls are structurally smaller than the inputs of the original call, taking into account reduction properties. At the heart of both checkers lies an inference system to reason about structural properties, which are described by higher-order subterm relations. This approach provides a logical foundation for proving properties such as termination and reduction and factors the effort required for each one of them. Moreover, it allows the study of proof-theoretical properties, soundness, and completeness and different optimizations. The termination and reduction checker are implemented as part of the Twelf system and have been used on a wide variety of examples, including proofs about typed assembly language and those in the area of proof-carrying code.     

多项式循环程序的秩函数探测

秩函数法是循环程序终止性分析的主流方法.针对一类多分支多项式循环程序,这类程序的秩函数计算问题被证明可归结为单形上正定多项式的探测问题,从而便于利用线性规划工具Simplex去计算这类程序的秩函数.不同于现有基于柱形代数分解的量词消去算法,该方法能够在可接受的时间内计算更为复杂的多项式秩函数.