Propositional Projection Temporal Logic Formula Research Articles

Requirement specification extraction and analysis based on propositional projection temporal logic

AbstractAt present, formal methods significantly facilitate the specification and verification of security requirements in requirement engineering, which can reduce requirement errors in the early stage of system development. Extracting formal specifications from security requirements and then evaluating the quality of the requirements are regarded as a promising solution to ensure software quality. Propositional projection temporal logic (PPTL) with a strong mathematical basis and full regular expressiveness is a suitable language for formal specifications. Inspired by natural language processing and text mining techniques, this paper designs and implements a tool, namely, NL2PPTL, to generate formal coarse‐grained and fine‐grained specifications in terms of PPTL formulas automatically. In specific, the grammatical production rules are defined to construct the syntax tree, and then, the formula is obtained by post‐order traversal of the tree. The satisfiability of the PPTL specifications can be checked utilizing PPTLSAT. In addition, the state transformation model is constructed from fine‐grained specifications, so as to discover scope conflicts and verify the security properties of the requirement case.

Verifying Properties of MapReduce-Based Big Data Processing

Big data techniques are widely used in various fields. To deal with large data sets efficiently, a new programming framework MapReduce has emerged. Thus, new verification challenges arise to improve the reliability of big data processing. In this article, MapReduce processes are implemented by modeling simulation and verification language programs. Then, several data properties such as data soundness, nonconflict, nonduplication, cooperation, and completeness are taken into account. Moreover, these properties are specified by propositional projection temporal logic formulas. To verify these properties, a runtime verification approach at code level based on unified model checking is employed. In addition, two case studies are conducted to demonstrate our approach: sparse matrix multiplication and tracking down suspected patients of an infectious disease.

A sound and complete proof system for a unified temporal logic

Theorem proving is one of the most widely used approaches to the verification of computer systems, and its theoretical basis is generally a proof system for formal derivation of logic formulas. In this paper, we propose a sound and complete proof system for Propositional Projection Temporal Logic (PPTL) with indexed expressions, which is a unified temporal logic that subsumes the well used Linear Temporal Logic (LTL). First, the syntax, semantics and logic laws of PPTL that allows indexed expressions are introduced, and the representation of LTL constructs by PPTL formulas is illustrated. Then, the proof system for the logic is presented which consists of axioms and inference rules for the derivation of both basic constructs and indexed expressions. To show the capability of the proof system, several examples of formal proofs are provided. Finally, the soundness and completeness of the proof system are demonstrated.

Efficient decision procedure for propositional projection temporal logic

The decision problem for Propositional Projection Temporal Logic (PPTL) has been solved successfully, however time complexity of the procedure is increased exponentially to the length of the formula. To solve the problem, a labeled unified complete normal form is introduced as the intermediate form to rewrite a PPTL formula into its equivalent labeled normal form, based on which the labeled normal form graph is constructed, and an efficient decision procedure for PPTL is formalized with the time complexity linear to the length of the formula and the size of the power set of the atomic propositions in the formula. Besides, an example is given to show how the improved decision procedure works.

Verifying Full Regular Temporal Properties of Programs via Dynamic Program Execution

Verification of programs at code level has attracted more and more attentions since the cost is high to extract models from source code. Most of approaches available for code level verification are carried out by inserting assertions into programs and then checking whether the assertions are violated. In this way, only safety properties can be verified, however, other temporal properties of programs such as liveness are hard to be verified. To tackle this problem, a novel runtime verification approach, which can verify full regular temporal properties of a program, is proposed in this paper. With this approach, a program to be verified is written in a modeling, simulation and verification language (MSVL) as a program M and a desired property is specified by a propositional projection temporal logic formula $P$ . The negation of the desired property is then translated to an MSVL program M’ . Thus, whether M violates $P$ can be checked by evaluating whether there exists an acceptable execution of the new MSVL program “ M and M’ .” This problem can efficiently be solved with the MSVL compiler where verification cases are generated via dynamic symbolic execution. Further, we adopt parallel mechanism to handle various execution paths of a program for improving the efficiency. The proposed approach has been implemented in a tool called MSV . Experiments show that the performance of MSV outperforms existing tools such as T2, RiTHM, and LTLAutomizer in verifying temporal properties of real-world programs.

Verifying a scheduling protocol of safety-critical systems

It is of great importance to ensure safety and reliability of the scheduling protocol of safety-critical systems since the failure will cause serious damage. This paper analyzes a real-time scheduling protocol of a safety-critical system and models it using a Modeling, Simulation and Verification Language program. Further, the schedulability and other desired properties are specified using Propositional Projection Temporal Logic formulas. As a result, these properties are proved with theorem proving and further verified using the runtime verification approach at code level.

A canonical form based decision procedure and model checking approach for propositional projection temporal logic

This paper proposes a Canonical Form (CF) for chop formulas of Propositional Projection Temporal Logic (PPTL). Based on CF, an improved algorithm for constructing Labeled Normal Form Graph (LNFG) of a PPTL formula is presented. This improvement leads to a better decision procedure for PPTL with infinite models. In addition, a transformation from LNFGs to Generalized Büchi Automata (GBA) and then Büchi Automata (BA) is formalized. Thus, a SPIN based model checking approach is generalized for PPTL. To illustrate how these algorithms work, several examples are given.

Bounded Model Checking of Traffic Light Control System

Traffic Light Control System (TLCS) is widely used in our daily life. It is of great importance to ensure the correctness of TLCS. In this paper, bounded model checking (BMC) is chosen to verify a simple but practical TLCS. To this end, Propositional Projection Temporal Logic (PPTL) used as the property specification language and the process of BMC for PPTL are briefly introduced. Then, a TLCS is described and its corresponding Kripke structure is given. Finally, two related properties specified by PPTL formulas are verified for the system using the BMC approach. The verification result using our bounded model checker, BMC4PPTL, shows that the behavior of TLCS is consistent with the specification.

A formal proof of the deadline driven scheduler in PPTL axiomatic system

This paper presents an approach for verifying the correctness of the feasibility theorem on the deadline driven scheduler (DDS) with the axiom system of Propositional Projection Temporal Logic (PPTL). To do so, the deadline driven scheduling algorithm is modeled by an MSVL (Modeling, Simulation and Verification Language) program and the feasibility theorem is formulated by PPTL formulas with two parts: a necessary part and a sufficient part. Then, several lemmas are abstracted and proved by means of the axiom system of PPTL. With the help of the lemmas, two parts of the theorem are deduced respectively. This case study convinces us that some real-time properties of systems can be formally verified by theorem proving using the axiom system of PPTL.

A complete proof system for propositional projection temporal logic

The paper presents a proof system for Propositional Projection Temporal Logic (PPTL) with projection-plus. The syntax, semantics, and logical laws of PPTL are introduced together with an axiom system consisting of axioms and inference rules. To facilitate proofs, some of the frequently used theorems are proved. A normal form of PPTL formulas is presented, and the soundness and completeness of the proof system are demonstrated. To show how the axiom system works, a full omega regular property for the mutual exclusion problem is specified by a PPTL formula and then a deductive proof of the property is performed.

Specification and Verification of UML2.0 Sequence Diagrams Based on Event Deterministic Finite Automata

PDF HTML阅读 XML下载 导出引用 引用提醒 基于事件确定有限自动机的UML2.0 序列图描述与验证 DOI: 10.3724/SP.J.1001.2011.04005 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(60433010, 60873018, 60910004, 91018010, 61003078, 61003079, 61133001); 国家重点基础研究发展计划(973)(2010CB328102); 国家教育部博士点基金(200807010012); 中央高校基本科研业务费专项资金(JY10000903004) Specification and Verification of UML2.0 Sequence Diagrams Based on Event Deterministic Finite Automata Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:为了确保软件分析与设计阶段UML2.0 序列图模型的可靠性,采用命题投影时序逻辑(propositional projection temporal logic,简称PPTL)模型检测方法对该模型进行分析和验证.提出了事件确定有限自动机(event deterministic finite automata,简称ETDFA),并使用该自动机为序列图建立形式化模型,通过给出的基于ETDFA 的PPTL 模型检测算法得到验证结果.该方法可以在基于Spin 的PPTL 模型检测器的支持下实现.实例结果表明,该方法可以验证序列图的性质并保证其可靠性. Abstract:To ensure the reliability of UML2.0 sequence diagrams (SD), which are used in software analysis and design, propositional projection temporal logic (PPTL) model checking is adopted in this paper. First, event deterministic finite automata (ETDFA) are proposed and used to describe the formal models of SD. Furthermore, an algorithm for model checking ETDFA with PPTL formulas being the properties is presented. Finally, based on the implementation of PPTL model checker, the ETDFA models of SD are verified. Experimental results show that the proposed method is useful in ensuring the reliability of SD. 参考文献 相似文献 引证文献

Model Checking Cryptographic Protocols with Interval Temporal Logic

This paper investigates model-checking Needham-Schroeder Public-Keyprotocol using Propositio nal Projection Temporal Logic (PPTL). To this end, the ProMeLa model of the protocol is firstly constructed then the properties to verify is specified by PPTL formulas, which is translated into automata and further to Never Claim. The transformation is by the method we present and is implemented by an automatic tool we developed. After that, the verification is done base on SPIN, and the results shows PPTL model checking approach is sound and can be used to verify more generalized communication protocols.

A decision procedure for propositional projection temporal logic with infinite models

This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is given. To this end, Normal Form (NF) and Labeled Normal Form Graph (LNFG) for PPTL formulas are defined, and algorithms for transforming a formula to its normal form and constructing the LNFG for the given formula are presented. Further, the finiteness of LNFGs is proved in details. Moreover, the decision procedure is extended to check the satisfiability of the formulas of Propositional Interval Temporal Logic. In addition, examples are also given to illustrate how the decision procedure works.