The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliab...The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliability. Based on the analysis of the characteristics of real-time embedded software, the formal method is introduced into the real-time embedded software testing field and the real-time extended finite state machine (RT-EFSM) model is studied firstly. Then, the time zone division method of real-time embedded system is presented and the definition and description methods of time-constrained transition equivalence class (timeCTEC) are presented. Furthermore, the approaches of the testing sequence and test case generation are put forward. Finally, the proposed method is applied to a typical avionics real- time embedded software testing practice and the examples of the timeCTEC, testing sequences and test cases are given. With the analysis of the testing result, the application verification shows that the proposed method can effectively describe the real-time embedded software state transition characteristics and real-time requirements and play the advantages of the formal methods in accuracy, effectiveness and the automation supporting. Combined with the testing platform, the real-time, closed loop and automated simulation testing for real-time embedded software can be realized effectively.展开更多
Wireless Mesh Networks is vulnerable to attacks due to the open medium, dynamically changing network topology, cooperative algorithms, Lack of centralized monitoring and management point. The traditional way of protec...Wireless Mesh Networks is vulnerable to attacks due to the open medium, dynamically changing network topology, cooperative algorithms, Lack of centralized monitoring and management point. The traditional way of protecting networks with firewalls and encryption software is no longer suffi- cient and effective for those features. In this paper, we propose a distributed intrusion detection ap- proach based on timed automata. A cluster-based detection scheme is presented, where periodically a node is elected as the monitor node for a cluster. These monitor nodes can not only make local intrusion detection decisions, but also cooperatively take part in global intrusion detection. And then we con- struct the Finite State Machine (FSM) by the way of manually abstracting the correct behaviors of the node according to the routing protocol of Dynamic Source Routing (DSR). The monitor nodes can verify every node's behavior by the Finite State Ma- chine (FSM), and validly detect real-time attacks without signatures of intrusion or trained data.Compared with the architecture where each node is its own IDS agent, our approach is much more efficient while maintaining the same level of effectiveness. Finally, we evaluate the intrusion detection method through simulation experiments.展开更多
According to the basic emotional theory, the artificial emotional model based on the finite state machine(FSM) was presented. In finite state machine model of emotion, the emotional space included the basic emotiona...According to the basic emotional theory, the artificial emotional model based on the finite state machine(FSM) was presented. In finite state machine model of emotion, the emotional space included the basic emotional space and the multiple emotional spaces. The emotion-switching diagram was defined and transition fimction was developed using Markov chain and linear interpolation algorithm. The simulation model was built using Stateflow toolbox and Simulink toolbox based on the Matlab platform. And the model included three subsystems: the input one, the emotion one and the behavior one. In the emotional subsystem, the responses of different personalities to the external stimuli were described by defining personal space. This model takes states from an emotional space and updates its state depending on its current state and a state of its input (also a state-emotion). The simulation model realizes the process of switching the emotion from the neutral state to other basic emotions. The simulation result is proved to correspond to emotion-switching law of human beings.展开更多
Using state assignment to minimize power dissipation and area for finite state ma-chines is computationally hard. Most of published results show that the reduction of switchingactivity often trades with area penalty. ...Using state assignment to minimize power dissipation and area for finite state ma-chines is computationally hard. Most of published results show that the reduction of switchingactivity often trades with area penalty. In this paper, a new approach is proposed. Experimentalresults show a significant reduction of switching activity without area penalty compared withprevious publications.展开更多
Finite state machine theory (FSM) is introduced and applied to global control of electric vehicle. Theoretical adaptation for application of FSM in control of electric vehicle is analyzed. Global control logic for par...Finite state machine theory (FSM) is introduced and applied to global control of electric vehicle. Theoretical adaptation for application of FSM in control of electric vehicle is analyzed. Global control logic for parts of electric vehicle is analyzed and built based on FSM. Using Matlab/Simulink, BJD6100-HEV global control algorithm is modeled and prove validity by simulation.展开更多
In this paper, a finite state machine approach is followed in order to find the semantic similarity of two sentences. The approach exploits the concept of bi-directional logic along with a semantic ordering approach. ...In this paper, a finite state machine approach is followed in order to find the semantic similarity of two sentences. The approach exploits the concept of bi-directional logic along with a semantic ordering approach. The core part of this approach is bi-directional logic of artificial intelligence. The bi-directional logic is implemented using Finite State Machine algorithm with slight modification. For finding the semantic similarity, keyword has played climactic importance. With the help of the keyword approach, it can be found easily at the sentence level according to this algorithm. The algorithm is proposed especially for Nepali texts. With the polarity of the individual keywords, the finite state machine is made and its final state determines its polarity. If two sentences are negatively polarized, they are said to be coherent, otherwise not. Similarly, if two sentences are of a positive nature, they are said to be coherence. For measuring the coherence (similarity), contextual concept is taken into consideration. The semantic approach, in this research, is a totally contextual based method. Two sentences are said to be semantically similar if they bear the same context. The total accuracy obtained in this algorithm is 90.16%.展开更多
Building high confidence regression test suites to validate new system versions is a challenging problem. A modelbased approach to build a regression test suite from a given test suite is described. The generated test...Building high confidence regression test suites to validate new system versions is a challenging problem. A modelbased approach to build a regression test suite from a given test suite is described. The generated test suite includes every test that will traverse a change performed to produce the new version, and consists of only such tests to reduce the testing costs. Finite state machines extended with typed variables (EFSMs) are used to model systems and system changes are mapped to EFSM transition changes adding/deleting/replacing EFSM transitions and states. Tests are a sequence of input and expected output messages with concrete parameter values over the supported data types. An invariant is formulated to characterize tests whose runtime behavior can be accurately predicted by analyzing their descriptions along with the model. Incremental procedures to efficiently evaluate the invariant and to select tests for regression are developed. Overlaps among the test descriptions are exploited to extend the approach to simultaneously select multiple tests to reduce the test selection costs. Effectiveness of the approach is demonstrated by applying it to several protocols, Web services, and model programs extracted from a popular testing benchmark. Our experimental results show that the proposed approach is economical for regression test selection in all these examples. For all these examples, the proposed approach is able to identify all tests exercising changes more efficiently than brute-force symbolic evaluation.展开更多
This study aims to propose a decision-making method based on artificial potential fields(APFs)and finite state machines(FSMs)in emergency conditions.This study presents a decision-making method based on APFs and FSMs ...This study aims to propose a decision-making method based on artificial potential fields(APFs)and finite state machines(FSMs)in emergency conditions.This study presents a decision-making method based on APFs and FSMs for emergency conditions.By modeling the longitudinal and lateral potential energy fields of the vehicle,the driving state is identified,and the trigger conditions are provided for path planning during lane changing.In addition,this study also designed the state transition rules based on the longitudinal and lateral virtual forces.It established the vehicle decision-making model based on the finite state machine to ensure driving safety in emergency situations.To illustrate the performance of the decision-making model by considering APFs and finite state machines.The version of the model in the co-simulation platform of MATLAB and CarSim shows that the developed decision model in this study accurately generates driving behaviors of the vehicle at different time intervals.The contributions of this study are two-fold.A hierarchical vehicle state machine decision model is proposed to enhance driving safety in emergency scenarios.Mathematical models for determining the transition thresholds of lateral and longitudinal vehicle states are established based on the vehicle potential field model,leading to the formulation of transition rules between different states of autonomous vehicles(AVs).展开更多
To ensure the quality of Web applications, Web testing is one of the effective methods. The testing is a process of revealing errors that is used to give confidence that the implementation of a Web application meets i...To ensure the quality of Web applications, Web testing is one of the effective methods. The testing is a process of revealing errors that is used to give confidence that the implementation of a Web application meets its original specification. This work proposes a Web testing framework based on Stream X-Machines (SXMs), which provides a way to derive test cases for a Web application. It starts from constructing the SXM model, from which a test translator is employed to extract the test paths and then translates them into an XML-style test specification, which is the input of test engine. The test engine generates test cases and then executes them, and finally produces test report. This testing method is a significant contribution to informed research.展开更多
Nonlinear dynamic analysis of rotating machinery system has always been the hot spot of the rotational dynamics re-search. This article sets up a rotating machinery condition monitoring system to realize the measureme...Nonlinear dynamic analysis of rotating machinery system has always been the hot spot of the rotational dynamics re-search. This article sets up a rotating machinery condition monitoring system to realize the measurement of system dynamic charac-teristic parameters based on NI(National Instruments) virtual instruments technology. The measurement of vibration signal of rotating machinery system is achieved by using NI company general data acquisition module of NI Company. Meanwhile, by analyzing and processing the acquired data using LabVIEW 2012, the dynamic characteristics, such as .the speed of the rotating machinery system, the axis trajectory, spectrum parameters, are attained. The measurement results show that the rotating machinery condition monitor-ing system based on LabVIEW is easy to operate, easy to realize the function extension and maintenance, and that it can be used in the industrial engineering projects with rotation characteristics. LabVIEW as the development tools used by virtual instrument func-tion is very powerful data acquisition software products support is one of the features of it, so using LabVIEW programming and data acquisition is simple and convenient.展开更多
This paper presents the application of finite state machine (FSM) theory to the programming of nonlinear hysteretic model simulation for both known and newly created rules. The complicated reversed internal paths invo...This paper presents the application of finite state machine (FSM) theory to the programming of nonlinear hysteretic model simulation for both known and newly created rules. The complicated reversed internal paths involved in the nonlinear relationship which not only depend on material properties, but also on load history, often confuse rule creators and scholars. In this paper, we first describe the development of past hysteretic models. Then we introduce the FSM theory conceptually, and explain how it is applied to reversed and diverse routes. Next, state definitions and procedures are explained with a specific data example using the bilinear model. Finally, the successful application to UC-win/FRAME (3D) is described and several characteristics are summarized. By using FSM’s states and the linkages to represent a hysteresis model, we can quickly realize the programming of the defined complex model rules, and the nonlinear modeling becomes more efficient and feasible.展开更多
Traditional matrix-based approaches in the field of finite state machines construct state transition matrices,and then use the powers of the state transition matrices to represent corresponding dynamic transition proc...Traditional matrix-based approaches in the field of finite state machines construct state transition matrices,and then use the powers of the state transition matrices to represent corresponding dynamic transition processes,which are cornerstones of system analysis.In this study,we propose a static matrix-based approach that revisits a finite state machine from its structure rather than its dynamic transition process,thus avoiding the“explosion of complexity”problem inherent in the existing approaches.Based on the static approach,we reexamine the issues of closed-loop detection and controllability for deterministic finite state machines.In addition,we propose controllable equivalent form and minimal controllable equivalent form concepts and give corresponding algorithms.展开更多
Aspect-oriented programming modularizes crosscutting concerns into aspects with the advice invoked at the specified points of program execution. Aspects can be used in a harmful way that invalidates desired properties...Aspect-oriented programming modularizes crosscutting concerns into aspects with the advice invoked at the specified points of program execution. Aspects can be used in a harmful way that invalidates desired properties and even destroys the conceptual integrity of programs. To assure the quality of an aspect-oriented system, rigorous analysis and design of aspects are highly desirable. In this paper, we present an approach to aspect-oriented modeling and verification with finite state machines. Our approach provides explicit notations (e.g., pointcut, advice and aspect) for capturing crosscutting concerns and incremental modification requirements with respect to class state models. For verification purposes, we compose the aspect models and class models in an aspect-oriented model through a weaving mechanism. Then we transform the woven models and the class models not affected by the aspects into FSP (Finite State Processes), which are to be checked by the LTSA (Labeled Transition System Analyzer) model checker against the desired system properties. We have applied our approach to the modeling and verification of three aspect-oriented systems. To further evaluate the effectiveness of verification, we created a large number of flawed aspect models and verified them against the system requirements. The results show that the verification has revealed all flawed models. This indicates that our approach is effective in quality assurance of aspect-oriented state models. As such, our approach can be used for model-checking state-based specification of aspect-oriented design and can uncover some system design problems before the system is implemented.展开更多
Motivated by the inconvenience or even inability to explain the mathematics of the state space optimization of finite state machines(FSMs)in most existing results,we consider the problem by viewing FSMs as logical dyn...Motivated by the inconvenience or even inability to explain the mathematics of the state space optimization of finite state machines(FSMs)in most existing results,we consider the problem by viewing FSMs as logical dynamic systems.Borrowing ideas from the concept of equilibrium points of dynamic systems in control theory,the concepts of t-equivalent states and t-source equivalent states are introduced.Based on the state transition dynamic equations of FSMs proposed in recent years,several mathematical formulations of t-equivalent states and t-source equivalent states are proposed.These can be analogized to the necessary and sufficient conditions of equilibrium points of dynamic systems in control theory and thus give a mathematical explanation of the optimization problem.Using these mathematical formulations,two methods are designed to find all the t-equivalent states and t-source equivalent states of FSMs.Further,two ways of reducing the state space of FSMs are found.These can be implemented without computers but with only pen and paper in a mathematical manner.In addition,an open question is raised which can further improve these methods into unattended ones.Finally,the correctness and effectiveness of the proposed methods are verified by a practical language model.展开更多
基金supported by the Aviation Science Foundation of China
文摘The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliability. Based on the analysis of the characteristics of real-time embedded software, the formal method is introduced into the real-time embedded software testing field and the real-time extended finite state machine (RT-EFSM) model is studied firstly. Then, the time zone division method of real-time embedded system is presented and the definition and description methods of time-constrained transition equivalence class (timeCTEC) are presented. Furthermore, the approaches of the testing sequence and test case generation are put forward. Finally, the proposed method is applied to a typical avionics real- time embedded software testing practice and the examples of the timeCTEC, testing sequences and test cases are given. With the analysis of the testing result, the application verification shows that the proposed method can effectively describe the real-time embedded software state transition characteristics and real-time requirements and play the advantages of the formal methods in accuracy, effectiveness and the automation supporting. Combined with the testing platform, the real-time, closed loop and automated simulation testing for real-time embedded software can be realized effectively.
基金Acknowledgements Project supported by the National Natural Science Foundation of China (Grant No.60932003), the National High Technology Development 863 Program of China (Grant No.2007AA01Z452, No. 2009AA01 Z118 ), Project supported by Shanghai Municipal Natural Science Foundation (Grant No.09ZRI414900), National Undergraduate Innovative Test Program (091024812).
文摘Wireless Mesh Networks is vulnerable to attacks due to the open medium, dynamically changing network topology, cooperative algorithms, Lack of centralized monitoring and management point. The traditional way of protecting networks with firewalls and encryption software is no longer suffi- cient and effective for those features. In this paper, we propose a distributed intrusion detection ap- proach based on timed automata. A cluster-based detection scheme is presented, where periodically a node is elected as the monitor node for a cluster. These monitor nodes can not only make local intrusion detection decisions, but also cooperatively take part in global intrusion detection. And then we con- struct the Finite State Machine (FSM) by the way of manually abstracting the correct behaviors of the node according to the routing protocol of Dynamic Source Routing (DSR). The monitor nodes can verify every node's behavior by the Finite State Ma- chine (FSM), and validly detect real-time attacks without signatures of intrusion or trained data.Compared with the architecture where each node is its own IDS agent, our approach is much more efficient while maintaining the same level of effectiveness. Finally, we evaluate the intrusion detection method through simulation experiments.
基金Project(2006AA04Z201) supported by the National High-Tech Research and Development Program of China
文摘According to the basic emotional theory, the artificial emotional model based on the finite state machine(FSM) was presented. In finite state machine model of emotion, the emotional space included the basic emotional space and the multiple emotional spaces. The emotion-switching diagram was defined and transition fimction was developed using Markov chain and linear interpolation algorithm. The simulation model was built using Stateflow toolbox and Simulink toolbox based on the Matlab platform. And the model included three subsystems: the input one, the emotion one and the behavior one. In the emotional subsystem, the responses of different personalities to the external stimuli were described by defining personal space. This model takes states from an emotional space and updates its state depending on its current state and a state of its input (also a state-emotion). The simulation model realizes the process of switching the emotion from the neutral state to other basic emotions. The simulation result is proved to correspond to emotion-switching law of human beings.
基金Supported by NNSF of China(Key International Cooperative Project No.60010121219)
文摘Using state assignment to minimize power dissipation and area for finite state ma-chines is computationally hard. Most of published results show that the reduction of switchingactivity often trades with area penalty. In this paper, a new approach is proposed. Experimentalresults show a significant reduction of switching activity without area penalty compared withprevious publications.
文摘Finite state machine theory (FSM) is introduced and applied to global control of electric vehicle. Theoretical adaptation for application of FSM in control of electric vehicle is analyzed. Global control logic for parts of electric vehicle is analyzed and built based on FSM. Using Matlab/Simulink, BJD6100-HEV global control algorithm is modeled and prove validity by simulation.
文摘In this paper, a finite state machine approach is followed in order to find the semantic similarity of two sentences. The approach exploits the concept of bi-directional logic along with a semantic ordering approach. The core part of this approach is bi-directional logic of artificial intelligence. The bi-directional logic is implemented using Finite State Machine algorithm with slight modification. For finding the semantic similarity, keyword has played climactic importance. With the help of the keyword approach, it can be found easily at the sentence level according to this algorithm. The algorithm is proposed especially for Nepali texts. With the polarity of the individual keywords, the finite state machine is made and its final state determines its polarity. If two sentences are negatively polarized, they are said to be coherent, otherwise not. Similarly, if two sentences are of a positive nature, they are said to be coherence. For measuring the coherence (similarity), contextual concept is taken into consideration. The semantic approach, in this research, is a totally contextual based method. Two sentences are said to be semantically similar if they bear the same context. The total accuracy obtained in this algorithm is 90.16%.
文摘Building high confidence regression test suites to validate new system versions is a challenging problem. A modelbased approach to build a regression test suite from a given test suite is described. The generated test suite includes every test that will traverse a change performed to produce the new version, and consists of only such tests to reduce the testing costs. Finite state machines extended with typed variables (EFSMs) are used to model systems and system changes are mapped to EFSM transition changes adding/deleting/replacing EFSM transitions and states. Tests are a sequence of input and expected output messages with concrete parameter values over the supported data types. An invariant is formulated to characterize tests whose runtime behavior can be accurately predicted by analyzing their descriptions along with the model. Incremental procedures to efficiently evaluate the invariant and to select tests for regression are developed. Overlaps among the test descriptions are exploited to extend the approach to simultaneously select multiple tests to reduce the test selection costs. Effectiveness of the approach is demonstrated by applying it to several protocols, Web services, and model programs extracted from a popular testing benchmark. Our experimental results show that the proposed approach is economical for regression test selection in all these examples. For all these examples, the proposed approach is able to identify all tests exercising changes more efficiently than brute-force symbolic evaluation.
基金supported by the National Natural Science Foundation of China(Grant No.52102454)the Postdoctoral Science Foundation of China(Grant No.2021M700169)+4 种基金in part by the Natural Science Foundation of Chongqing(Grant No.cstc2021jcyj-msxmX0395)the Special Funding for Postdoctoral Research Projects in Chongqing(Grant No.2021XM3069)the Youth Project of Science and Technology Research Program of Chongqing Education Commission of China(Grant Nos.KJQN202001302 and KJQN202203909)the Natural Science Foundation of Yongchuan District(Grant No.2023yc-jckx20089)the Opening Project of Intelligent Policing Key Laboratory of Sichuan Province(Grant No.ZNJW2023KFQN002).
文摘This study aims to propose a decision-making method based on artificial potential fields(APFs)and finite state machines(FSMs)in emergency conditions.This study presents a decision-making method based on APFs and FSMs for emergency conditions.By modeling the longitudinal and lateral potential energy fields of the vehicle,the driving state is identified,and the trigger conditions are provided for path planning during lane changing.In addition,this study also designed the state transition rules based on the longitudinal and lateral virtual forces.It established the vehicle decision-making model based on the finite state machine to ensure driving safety in emergency situations.To illustrate the performance of the decision-making model by considering APFs and finite state machines.The version of the model in the co-simulation platform of MATLAB and CarSim shows that the developed decision model in this study accurately generates driving behaviors of the vehicle at different time intervals.The contributions of this study are two-fold.A hierarchical vehicle state machine decision model is proposed to enhance driving safety in emergency scenarios.Mathematical models for determining the transition thresholds of lateral and longitudinal vehicle states are established based on the vehicle potential field model,leading to the formulation of transition rules between different states of autonomous vehicles(AVs).
文摘To ensure the quality of Web applications, Web testing is one of the effective methods. The testing is a process of revealing errors that is used to give confidence that the implementation of a Web application meets its original specification. This work proposes a Web testing framework based on Stream X-Machines (SXMs), which provides a way to derive test cases for a Web application. It starts from constructing the SXM model, from which a test translator is employed to extract the test paths and then translates them into an XML-style test specification, which is the input of test engine. The test engine generates test cases and then executes them, and finally produces test report. This testing method is a significant contribution to informed research.
文摘Nonlinear dynamic analysis of rotating machinery system has always been the hot spot of the rotational dynamics re-search. This article sets up a rotating machinery condition monitoring system to realize the measurement of system dynamic charac-teristic parameters based on NI(National Instruments) virtual instruments technology. The measurement of vibration signal of rotating machinery system is achieved by using NI company general data acquisition module of NI Company. Meanwhile, by analyzing and processing the acquired data using LabVIEW 2012, the dynamic characteristics, such as .the speed of the rotating machinery system, the axis trajectory, spectrum parameters, are attained. The measurement results show that the rotating machinery condition monitor-ing system based on LabVIEW is easy to operate, easy to realize the function extension and maintenance, and that it can be used in the industrial engineering projects with rotation characteristics. LabVIEW as the development tools used by virtual instrument func-tion is very powerful data acquisition software products support is one of the features of it, so using LabVIEW programming and data acquisition is simple and convenient.
文摘This paper presents the application of finite state machine (FSM) theory to the programming of nonlinear hysteretic model simulation for both known and newly created rules. The complicated reversed internal paths involved in the nonlinear relationship which not only depend on material properties, but also on load history, often confuse rule creators and scholars. In this paper, we first describe the development of past hysteretic models. Then we introduce the FSM theory conceptually, and explain how it is applied to reversed and diverse routes. Next, state definitions and procedures are explained with a specific data example using the bilinear model. Finally, the successful application to UC-win/FRAME (3D) is described and several characteristics are summarized. By using FSM’s states and the linkages to represent a hysteresis model, we can quickly realize the programming of the defined complex model rules, and the nonlinear modeling becomes more efficient and feasible.
基金supported by the National Natural Science Foundation of China(Nos.U1804150,62073124,and 61973175)。
文摘Traditional matrix-based approaches in the field of finite state machines construct state transition matrices,and then use the powers of the state transition matrices to represent corresponding dynamic transition processes,which are cornerstones of system analysis.In this study,we propose a static matrix-based approach that revisits a finite state machine from its structure rather than its dynamic transition process,thus avoiding the“explosion of complexity”problem inherent in the existing approaches.Based on the static approach,we reexamine the issues of closed-loop detection and controllability for deterministic finite state machines.In addition,we propose controllable equivalent form and minimal controllable equivalent form concepts and give corresponding algorithms.
基金supported in part by the ND EPSCoR IIP-SG via NSF of USA under Grant No.EPS-047679The fourth author was supported in part by the National Natural Science Foundation of China under Grant No.60603036+1 种基金the National Basic Research 973 Program of China under Grant No.2009CB320702the National High-Tech Research and Development 863 Program of China under Grant No.2009AA01Z148
文摘Aspect-oriented programming modularizes crosscutting concerns into aspects with the advice invoked at the specified points of program execution. Aspects can be used in a harmful way that invalidates desired properties and even destroys the conceptual integrity of programs. To assure the quality of an aspect-oriented system, rigorous analysis and design of aspects are highly desirable. In this paper, we present an approach to aspect-oriented modeling and verification with finite state machines. Our approach provides explicit notations (e.g., pointcut, advice and aspect) for capturing crosscutting concerns and incremental modification requirements with respect to class state models. For verification purposes, we compose the aspect models and class models in an aspect-oriented model through a weaving mechanism. Then we transform the woven models and the class models not affected by the aspects into FSP (Finite State Processes), which are to be checked by the LTSA (Labeled Transition System Analyzer) model checker against the desired system properties. We have applied our approach to the modeling and verification of three aspect-oriented systems. To further evaluate the effectiveness of verification, we created a large number of flawed aspect models and verified them against the system requirements. The results show that the verification has revealed all flawed models. This indicates that our approach is effective in quality assurance of aspect-oriented state models. As such, our approach can be used for model-checking state-based specification of aspect-oriented design and can uncover some system design problems before the system is implemented.
基金Project supported by the National Natural Science Foundation of China(Nos.U1804150,62073124,and 61973175)。
文摘Motivated by the inconvenience or even inability to explain the mathematics of the state space optimization of finite state machines(FSMs)in most existing results,we consider the problem by viewing FSMs as logical dynamic systems.Borrowing ideas from the concept of equilibrium points of dynamic systems in control theory,the concepts of t-equivalent states and t-source equivalent states are introduced.Based on the state transition dynamic equations of FSMs proposed in recent years,several mathematical formulations of t-equivalent states and t-source equivalent states are proposed.These can be analogized to the necessary and sufficient conditions of equilibrium points of dynamic systems in control theory and thus give a mathematical explanation of the optimization problem.Using these mathematical formulations,two methods are designed to find all the t-equivalent states and t-source equivalent states of FSMs.Further,two ways of reducing the state space of FSMs are found.These can be implemented without computers but with only pen and paper in a mathematical manner.In addition,an open question is raised which can further improve these methods into unattended ones.Finally,the correctness and effectiveness of the proposed methods are verified by a practical language model.