Though Unified Modeling Language (UML) has been widely used in software development, the major problems confronted lie in comprehension and testing. Dependence analysis is an important approach to analyze, understand,...Though Unified Modeling Language (UML) has been widely used in software development, the major problems confronted lie in comprehension and testing. Dependence analysis is an important approach to analyze, understand, test and maintain programs. A new kind of dependence analysis method for UML class diagrams is developed. A set of dependence relations is definedcorresponding to the relations among classes. Thus, the dependence graph of UML class diagram can be constructed from these dependence relations. Based on this model, both slicing and measurement coupling are further given as its two applications.展开更多
Extracting objects from legacy systems is a basic step in system's object orientation to improve the maintainability and understandability of the systems. A new object extraction model using association rules and...Extracting objects from legacy systems is a basic step in system's object orientation to improve the maintainability and understandability of the systems. A new object extraction model using association rules and dependence analysis is proposed. In this model data are classified by association rules and the corresponding operations are partitioned by dependence analysis.展开更多
The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system fa...The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.展开更多
Classes are the basic modules in object-oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about the tightness of the attributes and methods of classes. Th...Classes are the basic modules in object-oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about the tightness of the attributes and methods of classes. This paper discusses the relationships between attributes and attributes, attributes and methods, methods and methods of a class based on dependence analysis. Then the paper presents methods to compute these dependencies. Based on these, the paper proposes a method to measure the class cohesion, which satisfies the properties that a good measurement should have. The approach overcomes the limitations of previous class cohesion measures, which consider only one or two of the three relationships in a class. Keywords cohesion - object-orientation - class - program complexity - dependence analysis Supported by the National Natural Science Foundation of China under Grant No.60073012; the National Basic Research 973 Program of China under Grant No.2002CB312000; the Program for Cross-Century Outstanding Teachers of the Ministry of Education; the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No.20020286004; the Natural Science Foundation of Jiangsu, China, under Grant No.BK2001004; the Jiangsu Key Science and Technology Project under Grant No.BE2001025; the Opening Foundation of State Key Laboratory of Software Engineering in Wuhan University; the Opening Foundation of Jiangsu Key Laboratory of Computer Information Processing Technology in Soochow University.Zheng-Qiang Chen was born in 1976. He received the M.S. and Ph.D. degrees in computer science in 2000 and 2003, respectively. His current research interests include program analysis, understanding and testing as well as other topics related to reverse engineering. He has published more than 30 technical papers.Bao-Wen Xu was born in 1961. He received the M.S. and Ph.D. degrees in computer science in 1984 and 2002, respectively. He is a professor in the Computer Science & Engineering Department of Southeast University, Nanjing, China. His current research interests include programming language, program analysis, understanding, metrics and testing, Web search engine, and other topics related to reverse engineering. He has published more than 200 technical papers and 10 books. He is General Chairs of IEEE FTDCS'2004 and ICYCS'99, PC Chairs of WISA'2004 and WEBSA'2003, PC Members of IEEE COMPSAC'2003,'2002 and '2001, IEEE ICTAI'2003 and IEEE IRI'2003, and Session Chairs of IEEE ICTAI'2003 and COMPSAC'2002.Yu-Ming Zhou was born in 1974. He received the M.S. and Ph.D. degrees in computer science in 1999 and 2003, respectively. His current research interests include program analysis and metrics. He has published more than 20 technical papers.展开更多
To avoid the precision loss caused by combining data- flow facts impossible to occur in the same execution path in dependence analysis for C programs, this paper first proposes a flow-sensitive and context-insensitive...To avoid the precision loss caused by combining data- flow facts impossible to occur in the same execution path in dependence analysis for C programs, this paper first proposes a flow-sensitive and context-insensitive points-to analysis algorithm and then presents a new dependence analysis approach based on it. The approach makes more sufficient consideration on the executa- ble path problem and can avoid invalid combination between points-to relations and between points-to relations and reaching definitions. The results of which are therefore more precise than those of the ordinary dependence analysis approaches.展开更多
Conflict between conservation and community livelihood is a significant issue in China.Based on Sustainable Livelihood Framework(SLA),this study systematically analyzed livelihoods assets of a community in a Yunnan sn...Conflict between conservation and community livelihood is a significant issue in China.Based on Sustainable Livelihood Framework(SLA),this study systematically analyzed livelihoods assets of a community in a Yunnan snub-nosed monkey conservation area and found that the livelihood pentagon of the community was shaped by multiple but frail and unstable income sources,abundant natural resources with restricted use right,underutilized labors,inadequate financial resources,inconvenient physical capital and weak social capital.Villagers'income heavily depended on forest,and grazing and nontimber forest products(NTFP)collection are common and major income sources for villagers.However,differentiation of income dependence on forest among villagers'groups showed that there is no close correlation between the level of income and the level of income dependence on forest.Households'daily life also heavily depended on the forest due to heating and pig-feed cooking;hence,fuelwood cannot be easily replaced by any other energy resource for a long period.展开更多
Classes are the basic modules in Object-Oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about how tightly the attributes and methods of classes cohere w...Classes are the basic modules in Object-Oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about how tightly the attributes and methods of classes cohere with each other. This letter discusses the relationships between attributes and attributes, attributes and methods, methods and methods of a class,and the properties of these relationships. Based on these properties, the letter proposes a new framework to measure the cohesion of a class. The approach overcomes the limitations of previous class cohesion measures, which consider only one or two of the three relationships in a class.展开更多
With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach...With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit.展开更多
The goal of sentiment analysis is to detect the opinion polarities of people towards specific targets.For finegrained analysis aspect-based sentiment analysis(ABSA)is a challenging subtask of sentiment analysis The go...The goal of sentiment analysis is to detect the opinion polarities of people towards specific targets.For finegrained analysis aspect-based sentiment analysis(ABSA)is a challenging subtask of sentiment analysis The goals of most literature are to judge sentiment orientation for a single aspect,but the entities aspects belong to are ignored.Sequence-based methods,such as LSTM,or tagging schemas,such as BIO,always rely on relative distances to target words or accurate positions of targets in sentences It will require more detailed annotations if the target words do not appear in sentences.In this paper,we discuss a scenario where there are multiple entities and shared aspects in multiple sentences.The task is to predict the sentiment polarities of different pairs,ie,(entity,aspect)in each sample and the target entities or aspects are not guaranteed to exist in texts.After converting the long sequences to dependency relation-connected graphs,the dependency distances are embedded automatically to generate contextual representations during iterations We adopt partly densely connected graph convolutional networks with multi-head attention mechanisms to judgethe sentiment polarities for pairs of entities and aspects.The experiments conducted onaChinesedataset demonstrate the effectiveness of the method.Wealso explore the influences of different attention mechanisms and the connection manners of sentences on the tasks.展开更多
Compared with physical models,WRF-Solar,as an excellent numerical forecasting model,includes abundant novel cloud physical and dynamical processes,which enablesenable the high-frequency output of radiation components ...Compared with physical models,WRF-Solar,as an excellent numerical forecasting model,includes abundant novel cloud physical and dynamical processes,which enablesenable the high-frequency output of radiation components which are urgently needed by the solar energy industry.However,the popularisation of WRF-Solar in a wide range of applications,such as the estimation of diffuse radiation,suffers from unpredictable influences of cloud and aerosol optical property parameters.This study assessed the accuracy of the improved numerical weather prediction(WRF-Solar)model in simulating global and diffuse radiation.Aerosol optical properties at 550 nm,which were provided by a moderate resolution imaging spectroradiometer,were used as input to analyse the differences in accuracies obtained by the model with/without aerosol input.The sensitivity of WRF-Solar to aerosol and cloud optical properties and solar zenith angle(SZA)was analysed.The results show the superiority of WRF-Solar to WRF-Dudhia in terms of their root mean square error(RMSE)and mean absolute error(MAE).The coefficients of determination between WRF-Solar and WRF-Dudhia revealed no statistically significant difference,with values greater than 0.9 for the parent and nested domains.In addition,the relative RMSE(RRMSE%)reached 46.60%.The experiment on WRF-Solar and WRF-Dudhia revealed a negative bias for global radiation,but WRF-Solar attained a slightly lower RMSE and higher correlation coefficient than WRF-Dudhia.The WRF-Solar-simulated results on diffuse radiation under clear sky conditions were slightly poorer,with RMSE,RRMSE,mean percentage error and MAE of 181.93 W m^(−2),170.52%,93.04%and 138 W m^(−2),respectively.Based on Himawari-8 cloud data,statistical results on cloud optical thickness(COT)for cloudy days revealed that WRF-Solar overestimated diffuse radiation at COTs greater than 20.Moreover,when the aerosol optical depth was greater than or equal to 0.8,WRF-Solar also overestimated the diffuse radiation,with a mean difference of 58.57 W m^(−2).The errors of WRF-Solar simulations in global and diffuse radiation exhibited a significant dependence on the SZA.The dispersion degree of deviation increased gradually with the decrease in the SZA.Thus,WRF-Solar serves as an improved numerical tool that can provide high temporal and high-spatial-resolution solar radiation data for the prediction of photovoltaic power.Studies should explore the improvement of cumulus parameterisation schemes to enhance the accuracy of solar radiation component estimation and prediction under cloudy conditions.展开更多
Program slicing is an effective technique for an- alyzing concurrent programs. However, when a conventional closure-based slicing algorithm for sequential programs is ap- plied to a concurrent interprocedural program,...Program slicing is an effective technique for an- alyzing concurrent programs. However, when a conventional closure-based slicing algorithm for sequential programs is ap- plied to a concurrent interprocedural program, the slice is usually imprecise owing to the intransitivity of interference dependence. Interference dependence arises when a state- ment uses a variable defined in another statement executed concurrently. In this study, we propose a global dependence analysis approach based on a program reachability graph, and construct a novel dependence graph called marking-statement dependence graph (MSDG), in which each vertex is a 2-tuple of program state and statement. In contrast to the conven- tional program dependence graph where the vertex is a state- ment, the dependence relation in MSDG is transitive. When traversing MSDG, a precise slice will be obtained. To en- hance the slicing efficiency without loss of precision, our slic- ing algorithm adopts a hybrid strategy. The procedures con- taining interaction statements between threads are inlined and sliced by the slicing algorithm based on program reachability graphs while allowing other procedures to be sliced as se- quential programs. We have implemented our algorithm and three other representative slicing algorithms, and conducted an empirical study on concurrent Java programs. The exper- imental results show that our algorithm computes more pre- cise slices than the other algorithms. Using partial-order re- duction techniques, which are effective for reducing the size of a program reachability graph without loss of precision, ouralgorithm is optimized, thereby improving its performance to some extent.展开更多
文摘Though Unified Modeling Language (UML) has been widely used in software development, the major problems confronted lie in comprehension and testing. Dependence analysis is an important approach to analyze, understand, test and maintain programs. A new kind of dependence analysis method for UML class diagrams is developed. A set of dependence relations is definedcorresponding to the relations among classes. Thus, the dependence graph of UML class diagram can be constructed from these dependence relations. Based on this model, both slicing and measurement coupling are further given as its two applications.
基金Supported in part by the National Natural Science F oundation of China(6 0 0 730 12 )
文摘Extracting objects from legacy systems is a basic step in system's object orientation to improve the maintainability and understandability of the systems. A new object extraction model using association rules and dependence analysis is proposed. In this model data are classified by association rules and the corresponding operations are partitioned by dependence analysis.
基金supported by the National Natural Science Foundation of China(Nos.51875015,51620105010)。
文摘The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.
文摘Classes are the basic modules in object-oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about the tightness of the attributes and methods of classes. This paper discusses the relationships between attributes and attributes, attributes and methods, methods and methods of a class based on dependence analysis. Then the paper presents methods to compute these dependencies. Based on these, the paper proposes a method to measure the class cohesion, which satisfies the properties that a good measurement should have. The approach overcomes the limitations of previous class cohesion measures, which consider only one or two of the three relationships in a class. Keywords cohesion - object-orientation - class - program complexity - dependence analysis Supported by the National Natural Science Foundation of China under Grant No.60073012; the National Basic Research 973 Program of China under Grant No.2002CB312000; the Program for Cross-Century Outstanding Teachers of the Ministry of Education; the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No.20020286004; the Natural Science Foundation of Jiangsu, China, under Grant No.BK2001004; the Jiangsu Key Science and Technology Project under Grant No.BE2001025; the Opening Foundation of State Key Laboratory of Software Engineering in Wuhan University; the Opening Foundation of Jiangsu Key Laboratory of Computer Information Processing Technology in Soochow University.Zheng-Qiang Chen was born in 1976. He received the M.S. and Ph.D. degrees in computer science in 2000 and 2003, respectively. His current research interests include program analysis, understanding and testing as well as other topics related to reverse engineering. He has published more than 30 technical papers.Bao-Wen Xu was born in 1961. He received the M.S. and Ph.D. degrees in computer science in 1984 and 2002, respectively. He is a professor in the Computer Science & Engineering Department of Southeast University, Nanjing, China. His current research interests include programming language, program analysis, understanding, metrics and testing, Web search engine, and other topics related to reverse engineering. He has published more than 200 technical papers and 10 books. He is General Chairs of IEEE FTDCS'2004 and ICYCS'99, PC Chairs of WISA'2004 and WEBSA'2003, PC Members of IEEE COMPSAC'2003,'2002 and '2001, IEEE ICTAI'2003 and IEEE IRI'2003, and Session Chairs of IEEE ICTAI'2003 and COMPSAC'2002.Yu-Ming Zhou was born in 1974. He received the M.S. and Ph.D. degrees in computer science in 1999 and 2003, respectively. His current research interests include program analysis and metrics. He has published more than 20 technical papers.
基金Supported by the National High Technology Research and Development Program of China (863 Program) (2009AA01Z147)the National Natural Science Foundation of China (90818027, 60633010, 60803008)the National Science Foun for Distinguished Young Scholars (60425206)
文摘To avoid the precision loss caused by combining data- flow facts impossible to occur in the same execution path in dependence analysis for C programs, this paper first proposes a flow-sensitive and context-insensitive points-to analysis algorithm and then presents a new dependence analysis approach based on it. The approach makes more sufficient consideration on the executa- ble path problem and can avoid invalid combination between points-to relations and between points-to relations and reaching definitions. The results of which are therefore more precise than those of the ordinary dependence analysis approaches.
基金supported by the Nature Conservancy[grant number NA/KUNMING/YU030112]Yunnan Provincial Fund of Social Science[grant number YB2013024]
文摘Conflict between conservation and community livelihood is a significant issue in China.Based on Sustainable Livelihood Framework(SLA),this study systematically analyzed livelihoods assets of a community in a Yunnan snub-nosed monkey conservation area and found that the livelihood pentagon of the community was shaped by multiple but frail and unstable income sources,abundant natural resources with restricted use right,underutilized labors,inadequate financial resources,inconvenient physical capital and weak social capital.Villagers'income heavily depended on forest,and grazing and nontimber forest products(NTFP)collection are common and major income sources for villagers.However,differentiation of income dependence on forest among villagers'groups showed that there is no close correlation between the level of income and the level of income dependence on forest.Households'daily life also heavily depended on the forest due to heating and pig-feed cooking;hence,fuelwood cannot be easily replaced by any other energy resource for a long period.
基金Supported in part by the National Natural Science Foundation of China(NSFC)(No.60073012),Natural Science Foundation of Jiangsu (BK2001004).
文摘Classes are the basic modules in Object-Oriented (OO) software, which consist of attributes and methods. Thus, in OO environment, the cohesion is mainly about how tightly the attributes and methods of classes cohere with each other. This letter discusses the relationships between attributes and attributes, attributes and methods, methods and methods of a class,and the properties of these relationships. Based on these properties, the letter proposes a new framework to measure the cohesion of a class. The approach overcomes the limitations of previous class cohesion measures, which consider only one or two of the three relationships in a class.
基金co-supported by the National Natural Science Foundation of China (51875015,51620105010,51675019)Natural Science Foundation of Beijing Municipality(L171003)。
文摘With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit.
基金Supported by the National Natural Science Foundation of China(71731002,71971190)。
文摘The goal of sentiment analysis is to detect the opinion polarities of people towards specific targets.For finegrained analysis aspect-based sentiment analysis(ABSA)is a challenging subtask of sentiment analysis The goals of most literature are to judge sentiment orientation for a single aspect,but the entities aspects belong to are ignored.Sequence-based methods,such as LSTM,or tagging schemas,such as BIO,always rely on relative distances to target words or accurate positions of targets in sentences It will require more detailed annotations if the target words do not appear in sentences.In this paper,we discuss a scenario where there are multiple entities and shared aspects in multiple sentences.The task is to predict the sentiment polarities of different pairs,ie,(entity,aspect)in each sample and the target entities or aspects are not guaranteed to exist in texts.After converting the long sequences to dependency relation-connected graphs,the dependency distances are embedded automatically to generate contextual representations during iterations We adopt partly densely connected graph convolutional networks with multi-head attention mechanisms to judgethe sentiment polarities for pairs of entities and aspects.The experiments conducted onaChinesedataset demonstrate the effectiveness of the method.Wealso explore the influences of different attention mechanisms and the connection manners of sentences on the tasks.
基金supported by the National Natural Science Foundation of China(41975044,41925007,42371354,42375129,and 41801021)Fundamental Research Funds for National University,China University of Geosciences,Wuhan(CUGDCJJ202201).
文摘Compared with physical models,WRF-Solar,as an excellent numerical forecasting model,includes abundant novel cloud physical and dynamical processes,which enablesenable the high-frequency output of radiation components which are urgently needed by the solar energy industry.However,the popularisation of WRF-Solar in a wide range of applications,such as the estimation of diffuse radiation,suffers from unpredictable influences of cloud and aerosol optical property parameters.This study assessed the accuracy of the improved numerical weather prediction(WRF-Solar)model in simulating global and diffuse radiation.Aerosol optical properties at 550 nm,which were provided by a moderate resolution imaging spectroradiometer,were used as input to analyse the differences in accuracies obtained by the model with/without aerosol input.The sensitivity of WRF-Solar to aerosol and cloud optical properties and solar zenith angle(SZA)was analysed.The results show the superiority of WRF-Solar to WRF-Dudhia in terms of their root mean square error(RMSE)and mean absolute error(MAE).The coefficients of determination between WRF-Solar and WRF-Dudhia revealed no statistically significant difference,with values greater than 0.9 for the parent and nested domains.In addition,the relative RMSE(RRMSE%)reached 46.60%.The experiment on WRF-Solar and WRF-Dudhia revealed a negative bias for global radiation,but WRF-Solar attained a slightly lower RMSE and higher correlation coefficient than WRF-Dudhia.The WRF-Solar-simulated results on diffuse radiation under clear sky conditions were slightly poorer,with RMSE,RRMSE,mean percentage error and MAE of 181.93 W m^(−2),170.52%,93.04%and 138 W m^(−2),respectively.Based on Himawari-8 cloud data,statistical results on cloud optical thickness(COT)for cloudy days revealed that WRF-Solar overestimated diffuse radiation at COTs greater than 20.Moreover,when the aerosol optical depth was greater than or equal to 0.8,WRF-Solar also overestimated the diffuse radiation,with a mean difference of 58.57 W m^(−2).The errors of WRF-Solar simulations in global and diffuse radiation exhibited a significant dependence on the SZA.The dispersion degree of deviation increased gradually with the decrease in the SZA.Thus,WRF-Solar serves as an improved numerical tool that can provide high temporal and high-spatial-resolution solar radiation data for the prediction of photovoltaic power.Studies should explore the improvement of cumulus parameterisation schemes to enhance the accuracy of solar radiation component estimation and prediction under cloudy conditions.
文摘Program slicing is an effective technique for an- alyzing concurrent programs. However, when a conventional closure-based slicing algorithm for sequential programs is ap- plied to a concurrent interprocedural program, the slice is usually imprecise owing to the intransitivity of interference dependence. Interference dependence arises when a state- ment uses a variable defined in another statement executed concurrently. In this study, we propose a global dependence analysis approach based on a program reachability graph, and construct a novel dependence graph called marking-statement dependence graph (MSDG), in which each vertex is a 2-tuple of program state and statement. In contrast to the conven- tional program dependence graph where the vertex is a state- ment, the dependence relation in MSDG is transitive. When traversing MSDG, a precise slice will be obtained. To en- hance the slicing efficiency without loss of precision, our slic- ing algorithm adopts a hybrid strategy. The procedures con- taining interaction statements between threads are inlined and sliced by the slicing algorithm based on program reachability graphs while allowing other procedures to be sliced as se- quential programs. We have implemented our algorithm and three other representative slicing algorithms, and conducted an empirical study on concurrent Java programs. The exper- imental results show that our algorithm computes more pre- cise slices than the other algorithms. Using partial-order re- duction techniques, which are effective for reducing the size of a program reachability graph without loss of precision, ouralgorithm is optimized, thereby improving its performance to some extent.