计算机科学中的共代数方法的研究综述

代数理论已经在抽象数据类型、程序语义等计算机科学领域有了广泛的应用,而代数的对偶概念--共代数,则直到20世纪90年代中后期才被越来越多的计算机学者关注.代数从"构造"的角度研究数据类型,而共代数则从"观察"的角度考察系统及其性质.共代数方法对研究基于状态的系统有独特的优越性,可以对系统的行为等价、不确定性等从数学上进行深入的探讨.目前,共代数理论已经逐步应用在自动机理论、并发程序的语义、面向对象程序的规范等领域.对共代数的基本概念、范畴理论基础、共代数逻辑及应用等方面的最新研究成果进行了介绍,以引起国内相关研究领域的学者对计算机科学中的共代数方法的关注.     

Automated structural analysis of SCR‐style software requirements specifications using PVS

The importance of effective requirements analysis techniques cannot be overemphasized when developing software requiring high levels of assurance. Requirements analysis can be largely classified as either structural or functional. The former investigates whether definitions and uses of variables and functions are consistent, while the latter addresses whether requirements accurately reflect users' needs. Verification of structural properties for large and complex software requirements is often repetitive, especially if requirements are subject to frequent changes. While inspection has been successfully applied to many industrial applications, the authors found inspection to be ineffective when reviewing requirements to find errors violating structural properties. Moreover, current tools used in requirements engineering provide only limited support in automatically enforcing structural correctness of the requirements. Such experience has motivated research to automate straightforward but tedious activities. This paper demonstrates that a theorem prover, PVS (Prototype Verification System), is useful in automatically verifying structural correctness of software requirements specifications written in SCR (Software Cost Reduction)‐style. Requirements are automatically translated into a semantically equivalent PVS specification. Users need not be experts in formal methods or power users of PVS. Structural properties to be proved are expressed in PVS theorems, and the PVS proof commands are used to carry out the proof automatically. Since these properties are application independent, the same verification procedure can be applied to requirements of various software systems. Copyright © 2001 John Wiley & Sons, Ltd.     

RETE网络中的优化编译模式及其PVS形式验证

In the compilation of rule program to the intermediate code-RETE network,optimizing compilation is an important compiler schema,and is a necessary step in the compiler verification.In this paper,we discuss optimization schemas in rule program compilation,and prove the semantic equivalence theorems of these schemas.Firstly,the structure of RETE network and its PVS specification are represented.Secondly,three kinds of optimization schemas are listed.Then algorithms evaluating semantics of target RETE network are given.Finally,we prove the semantic equivalence theorems with theorem prover PVS (Prototype Verification System).     

Implicit induction in conditional theories

We propose a new procedure for proof by induction in conditional theories where case analysis is simulated by term rewriting. This technique reduces considerably the number of variables of a conjecture to be considered for applying induction schemes. Our procedure is presented as a set of inference rules whose correctness has been formally proved. Moreover, when the axioms are ground convergent and the functions are completely defined, it is possible to apply the system for refuting conjectures. The procedure is even refutationally complete for conditional equations with Boolean preconditions over free constructors. The method is entirely implemented in the proverSPIKE. This system has solved interesting problems in a completely automatic way, that is, without interaction with the user and without ad hoc heuristics. It has also proved the challenging Gilbreath card trick, with only two easy lemmas.Preliminary versions of the results have been presented at the 13th International Joint Conference on Artificial Intelligence, Chambéry (France), 1993 (Bouhoula and Rusinowith, 1993).     

Knuth-Bendix completion of theories of commuting group endomorphisms

Knuth-Bendix completions of the equational theories of k?2 commuting group endomorphisms are obtained, using automated theorem proving and modern termination checking. This improves on modern implementations of completion, where the orderings implemented cannot orient the commutation rules. The result has applications in decision procedures for automated verification.     

超长整数运算的PVS规范与验证

超长整数的运算是现代密码系统的应用基础,运算的正确性关系到密码系统的应用价值。为了验证超长整数算法的设计与需求目标之间的一致性,利用原型验证工具PVS对算法的正确性进行了证明。在介绍了超长整数的加法和减法算法并分析了其设计思想之后,给出了超长整数及其算法的形式规范,通过把算法需要满足的性质描述为定理,将算法的一致性验证问题转化为逻辑定理证明的问题,在PVS定理证明器上完成了相关定理的证明,从而表明这些算法是满足设计需求的。     

重写对策在基于HOL的形式化证明中的应用

讨论了重写对策在基于高阶逻辑定理证明系统HOL的形式化证明过程中的应用.通过REWRITE_ TAC对策、ASM_ REWRITE_ TAC对策和RW_ TAC对策,详细分析了重写对策的功能、应用方法、应用环境、应用中可能出现的问题以及解决办法,给出了DB.match搜索和DB.find搜索等重写对策的定理参数的选择方法,并进行了分析与比较.进一步说明了重写对策在基于HOL系统的形式化证明中的重要性,以期对HOL系统用户提供一些帮助与启发,促进HOL系统的进一步发展与完善,使形式化方法能够解决更多的实际问题.     

Tree automata with equality constraints modulo equational theories

This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalized membership problem (extending the emptiness problem) is decidable by proving that the saturation of tree automata presentations with suitable paramodulation strategies terminates. Alternatively our results can be viewed as new decidable classes of first-order formula.     

Design and results of the 2nd annual satisfiability modulo theories competition (SMT-COMP 2006)

The Satisfiability Modulo Theories Competition (SMT-COMP) arose from the SMT-LIB initiative to spur adoption of common, community-designed formats, and to spark further advances in satisfiability modulo theories (SMT). The first SMT-COMP was held in 2005 as a satellite event of CAV 2005. SMT-COMP 2006 was held August 17–19, 2006, as a satellite event of CAV 2006. This paper describes the rules and competition format for SMT-COMP 2006, the benchmarks used, the participants, and the results.