CN112069059A - Test case generation method and system based on maximum likelihood estimation - Google Patents

Abstract

The invention discloses a method and system for generating a test case based on maximum likelihood estimation and maximum expectation. The area is regarded as the sub-area with the highest priority; latent variables are introduced and combined with the EM algorithm to estimate the probability that the sub-area in the inner area may contain a failure area, and the sub-areas of the inner area are sorted based on the probability; generated according to the priority order of the sub-areas Test cases until software errors are found; if the number of test cases reaches the preset condition and no software errors are found, continue to generate test cases in the sub-region with the highest priority until software errors are found. The method of the present invention can well solve the huge computational cost problem existing in the existing ART method, and to a certain extent, solves the boundary effect problem of the previous ART method, and simultaneously improves the operation efficiency.

Description

Test case generation method and system based on maximum likelihood estimation

technical field

The invention relates to the field of computer technology, in particular to a method and system for generating a test case based on maximum likelihood estimation of maximum expectation.

Background technique

Software testing is an important link in the software development process. It can run the entire system or some modules by manual or automated means, and judge whether the overall or partial functions of the software meet the specified requirements according to whether the expected results are consistent with the actual results. . At present, there are many types of technologies in the field of software testing, among which the most common software testing technologies are white-box testing, gray-box testing, and black-box testing. However, no matter which testing method the tester chooses to use, it is nearly impossible to fully test the input domain of the software, so it is more common to select from some representative subset of the software input domain Test cases to test.

Random tests are the test cases needed to randomly generate experiments in the input domain. However, due to the randomness of the test cases it generates, the ability of this method to detect errors is not high.

Aiming at the disadvantage of poor ability of random testing to find errors, the random testing is improved. The prior art proposes the ART method (adaptive random testing), among which the classic ART method is an adaptive random testing method with a fixed candidate set size. The FSCS-ART method (Adaptive Random Testing with Fixed Candidate Sets) greatly improves the ability to detect errors by ensuring that test cases are more evenly distributed in the software input domain.

However, because the FSCS-ART method introduces a large number of distance calculations, the system computing resource overhead of the method is very huge. Moreover, due to the characteristics of FSCS-ART's selection of test cases, the test cases it chooses to test software tend to accumulate on the boundary of the software input domain, thereby affecting the effect of detecting software errors, which is the boundary effect.

Patent application 201811501282.8 proposes an adaptive random testing method based on iterative region averaging and localization.

Patent application 201911030817.2 proposes an adaptive random test case generation method based on the center point compensation strategy.

The adaptive random test case generation method based on the center point compensation strategy and the adaptive random test method based on iterative area averaging and localization, both of which divide the input domain, but for the division used for test case generation The selection of sub-regions is random, which reduces the computational cost of the traditional ART method to a certain extent, but the blindness of the random selection of sub-regions cannot improve the test efficiency. Therefore, new technical solutions with practical application significance are urgently needed in the technical field.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method based on the maximum likelihood based on the problem of boundary effect that the method in the prior art has a large number of distance calculations, resulting in a huge computational cost and easy accumulation of test cases on the boundary of the software input domain. Estimate the maximum expected test case generation scenario.

The technical solution of the present invention provides a test case generation method based on maximum likelihood estimation and maximum expectation, comprising the following steps:

In step S1, the input domain of the software is divided into multiple sub-regions, and the boundary region of the input domain is distinguished from the internal region, and the boundary region is regarded as the sub-region with the highest priority;

In step S2, latent variables are introduced and combined with the EM algorithm to estimate the probability that the sub-regions in the inner region may contain failure regions, and the sub-regions in the inner region are sorted based on the size of the probability;

Step S3, generate test cases according to the priority order of the sub-areas until software errors are found; if the number of test cases reaches the preset condition and no software errors are found, continue to generate test cases in the sub-areas with the highest priority until software errors are found .

Moreover, step S1 includes the following sub-steps,

Step S1.1, set the boundary length of the inner area according to the failure rate of the input domain, and obtain the boundary area outside the inner area, denoted as D1;

In step S1.2, the priority of the boundary area D1 is ranked first, and the inner area is divided into two parts of the same size, which are denoted as sub-areas D2 and D3.

Moreover, when the input domain is a two-dimensional square, set the boundary length of the inner area as follows,

Among them, b is the edge length of the inner region, a is the edge length of the overall input region, and θ is the failure rate.

Moreover, step S2 includes the following sub-steps,

Step S2.1, randomly generate 1000 test cases in each of the two internal sub-areas D2 and D3, and count the number of test cases in which software errors are found respectively;

Step S2.2, replace the probability that the sub-region can find the software error with the probability that the test case finds the error and falls in the sub-region;

Step S2.3, introduce latent variables, use the EM algorithm to iterate the probability parameters of the previous step until the parameters converge, and use the parameter values when convergence is reached as its maximum likelihood estimator;

Step S2.4, sorting the priorities of the two internal sub-regions D2 and D3 by comparing the probabilities;

In step S2.5, the two internal sub-regions are further divided into two parts of the same size, and the sub-region D2 is divided into D4 and D5, D3 is divided into D6 and D7, and the above step S2.1 is repeated for D4 and D5. Go to step S2.4, repeat the above steps S2.1 to S2.4 for D6 and D7;

Step S2.6, sort the priorities of all the divided sub-regions, and determine the priority order of the sub-regions D1, D4, D5, D6 and D7.

Moreover, the implementation of step S3 is as follows:

1) First, continuously generate test cases from the boundary area with the highest priority, and execute the test. If software errors are found, stop; if no software errors are found, and the total number of test cases generated reaches the preset threshold, then Generate test cases in the sub-area with the second priority, and execute the test. If software errors are found, stop; if no software errors are found, and the total number of test cases generated reaches the preset threshold, it will be executed at the priority level. Generate test cases in the third sub-area, and execute the test. If software errors are found, stop; and so on, after continuously lowering the priority level, if no software errors are found in the sub-area with the lowest priority, and the total test After the number of use cases generated reaches the preset threshold, go to step 2);

2) If step 1) has been executed once, return to execute step 1), if step 1) has been repeatedly executed twice, instead, continue to generate test cases only in the boundary area with the highest priority, and execute the test, Stop until a software error is found or the preset upper limit of the number of tests is reached.

Also, the preferred value for the threshold setting is 10.

The present invention also correspondingly provides a test case generation system based on maximum likelihood estimation for maximum expectation, which is used for realizing the above-mentioned method for generating test case based on maximum likelihood estimation for maximum expectation.

Also, the following modules are included,

The first module is used to divide the input domain of the software into a plurality of sub-regions, distinguish the boundary region of the input domain from the internal region, and use the boundary region as the sub-region with the highest priority;

The second module is used to introduce the maximum likelihood estimation method, estimate the probability that the sub-regions in the inner region may contain failure regions, and sort the sub-regions in the inner region based on the probability;

The third module is used to generate test cases according to the priority order of the sub-areas until software errors are found; if the number of test cases reaches the preset condition and no software errors are found, continue to generate test cases in the sub-area with the highest priority until A software bug was found.

Or, it includes a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the processor to execute the above-mentioned method for generating a test case based on maximum likelihood estimation and maximum expectation.

Alternatively, it includes a readable storage medium on which a computer program is stored, and when the computer program is executed, implements the above-mentioned method for generating a test case based on maximum likelihood estimation and maximum expectation.

The invention discloses a test case generation scheme based on maximum likelihood estimation and maximum expectation. First, the input domain is divided into a plurality of sub-regions of different sizes, latent variables are introduced and combined with the EM method to estimate that the sub-regions may contain The probability of failure areas is finally sorted according to the probability size, and test cases are generated in the sub-areas that are ranked first. The method of the present invention can well solve the huge computational cost problem of the previous ART method, and to a certain extent, solve the boundary effect problem of the previous ART method, and at the same time improve the operation efficiency.

Description of drawings

1 is a flowchart of a test case generation method based on maximum likelihood estimation and maximum expectation provided by an embodiment of the present invention;

FIG. 2 is a diagram showing the iterative process of the first step of the EM-ART method according to an embodiment of the present invention, wherein part (a) is a schematic diagram of the division of D1, D2, and D3, and part (b) is D2.1, D2.2, D3.1, D3.2 Schematic diagram of virtual division;

3 is a diagram showing the iterative process of the second step of the EM-ART method according to an embodiment of the present invention, wherein part (a) is a schematic diagram of the division of D4 and D5, and part (b) is D4.1, D4.2, D5.1, and D5. 2 The schematic diagram of virtual division;

4 is a display diagram of the iterative process of the third step of the EM-ART method and the final division result according to the embodiment of the present invention, wherein part (a) is a schematic diagram of the virtual division of D6.1, D6.2, D7.1, and D7.2; ( Part b) is a schematic diagram of the division of D6 and D7.

Detailed ways

The present invention provides a test case generation method based on maximum likelihood estimation of maximum expectation, which includes: by dividing the input domain into a plurality of sub-regions of different sizes, introducing latent variables and combining EM method to estimate the possibility in these sub-regions Including the probability of failure regions, these sub-regions are finally sorted based on the probability size, and test cases are generated in the top-ranked sub-regions first, thereby reducing computational overhead and mitigating boundary effects. In order to conform to the custom in the technical field, the test case generation method based on maximum likelihood estimation and maximum expectation proposed by the present invention is now abbreviated as EM-ART method.

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

This embodiment provides a method for generating a test case based on maximum likelihood estimation of maximum expectation, see FIG. 1 , and the method includes:

Step S1: Divide the input domain of the software into a plurality of sub-regions, distinguish the boundary region of the input domain from the inner region, and take the boundary region as the sub-region with the highest priority. The inner area can be divided into two or more sub-areas. The present invention proposes to divide the input domain into a plurality of sub-regions of different sizes, and to distinguish the boundary region from the inner region of the software input domain, aiming at the problem of the boundary effect existing in the ART method in the prior art. Taking the two-dimensional square input domain as an example, the specific idea of EM-ART method to divide the software input domain is shown in Figure 2.

In one embodiment, step S1 specifically includes:

Step S1.1: Set the boundary length of the inner region according to the failure rate of the input domain.

Step S1.2: Rank the priority of the boundary area first, and divide the inner area into two parts of the same size to obtain two inner sub-areas.

这里 b为内部正方形区域边长，a为总体输入域边长，θ为失效率。然后，对三个区域D1、 D2、D3进行优先级序号排列，将边界区域D1排在第一位，内部两个大小相等的子区域D2和D3暂时不能确定优先级排列顺序。The inner square area is set in the center of the overall input domain, and the annular area after subtracting the middle square area from the overall input domain is the boundary area. Specifically, in FIG. 2 , the boundary area is set as D1, and as shown in part (a) of FIG. 2 , the inner area is divided into two parts with the same size, which are set as D2 and D3 respectively. That is, the merged area of D2 and D3 is the inner square area in the center of the overall input domain. In order to make the boundary area D1 closer to the true "boundary", the side length of the inner square area also needs to be considered here. The border length of the square area is set to

Here b is the side length of the inner square area, a is the side length of the overall input area, and θ is the failure rate. Then, the three regions D1, D2, and D3 are arranged with priority numbers, and the boundary region D1 is arranged first, and the priority arrangement order of the two inner sub-regions D2 and D3 of equal size cannot be determined temporarily.

During the specific implementation, the user can set the value of θ corresponding to the specific problem according to the application scenario. Usually, the value of θ is small, such as 0.01, 0.005, 0.002, 0.001, 0.0005, 0.0002, and 0.0001.

Step S2: Aiming at the huge computational overhead problem of the previous ART method, introduce latent variables and combine the EM method to estimate the probability that the sub-regions in the inner region may contain failure regions, and finally rank the sub-regions in the inner region based on the probability size. (Boundary regions still have priority over all inner regions neutron subregions);

The present invention proposes that, in view of the huge computational overhead problem of the ART method in the prior art, latent variables are introduced and combined with the EM algorithm to estimate the probability that these sub-regions may contain failure regions, and finally these sub-regions are sorted based on the probability size. .

In order to distribute the test cases more evenly, the embodiment proposes to divide the sub-regions D2 and D3 into two equal parts. Therefore, the priority order of D2 and D3 is first determined based on the maximum likelihood estimation and maximum expectation, and then the sub-regions are divided into two equal parts. The secondary sub-regions within D2 and D3 are sorted in the same way.

In one embodiment, step S2 specifically includes:

Step S2.1: Randomly generate 1000 test cases in each of the two internal sub-areas, and count the number of test cases in which software errors are found respectively.

Specifically, 1000 test cases are randomly generated in the D2 and D3 areas, and the number of test cases in which software errors are found are counted, which are recorded as y1 and y2 respectively.

Step S2.2: Replace the probability that the sub-region can find the software error with the probability that the test case finds the error and falls in the sub-region.

和

来替换原先的概率值进行估计(这里

)，用

和

来替换原先的概率值进行估计，使得结果更加直观，易于比较。y1/1000近似等于α₁，当实验次数越大，计算得到的值就越接近真实的概率值。Specifically, it is assumed that the probability that software errors can be found in sub-region D2 is β ₁ , and the probability that software errors can be found in sub-region D3 is θ-β ₁ . Because the value of θ is small, the result of the trial probability iteration is small. For example, the probability of being able to find errors in two regions is treated specially. If the event under study is described as a test case finding errors and falling in sub-regions D2 or D3, the conditional probability can be used.

and

to replace the original probability value for estimation (here

),use

and

to replace the original probability value for estimation, which makes the result more intuitive and easy to compare. y1/1000 is approximately equal to α ₁ . When the number of experiments is larger, the calculated value is closer to the real probability value.

Step S2.3: Introduce latent variables, use the EM method to iterate the probability parameters of the previous step until the parameters converge, and use the parameter values when convergence is reached as its maximum likelihood estimator.

和

D3可以假设分为D3.1和D3.2，假设的划分方式不限；并假设D3.1和D3.2中发现软件错误的概率分别为

和

然后引入潜变量z₁和z₂，假设D2.1和D2.2中发现软件错误的测试用例分别为z₁和y₁-z₁，同样的，假设D3.1和D3.2中发现软件错误的测试用例分别为z₂和y₂-z₂。Specifically, as shown in part (b) of Figure 2, it is assumed that there are also two sub-regions in D2 and D3, in which D2 can be assumed to be divided into D2.1 and D2.2, and the assumed division method is not limited; and it is assumed that The probabilities of finding software bugs in D2.1 and D2.2, respectively, are

and

D3 can be assumed to be divided into D3.1 and D3.2, and the assumptions are not limited in the way of division; and the probability of software errors found in D3.1 and D3.2 is assumed to be

and

Then introduce latent variables z ₁ and z ₂ , assuming that the test cases where software bugs are found in D2.1 and D2.2 are z ₁ and y ₁ -z ₁ , respectively. Similarly, suppose that software errors are found in D3.1 and D3.2 The wrong test cases are z ₂ and y ₂ -z ₂ respectively.

After the latent variables z ₁ and z ₂ are introduced, the conditional expectation is calculated for the latent variables respectively, and the expression of step E can be obtained:

in,

Taking the derivative of the above formula and setting it to zero, the M-step iterative formula is obtained:

where Q() refers to the mathematical expectation, i refers to the number of iterations,

表示在第i次迭代时

的估计值，

means at the ith iteration

the estimated value of ,

表示测试用例发现错误且落在子区域D2中的条件概率。y ₁ and y ₂ represent the number of software error cases found in the D2 and D3 regions,

Represents the conditional probability that the test case finds an error and falls in subregion D2.

进行迭代直到参数收敛，并将达到收敛的参数值

作为参数

的极大似然估计量，并比较

与

的数值的大小，如果

则将区域D2排在优先级的第二位，反之，则将D3排在优先级的第二位。Using the EM method for unknown parameters

Iterate until the parameters converge and will reach the converged parameter value

as parameter

the maximum likelihood estimator of , and compare

and

the size of the numerical value, if

Then the area D2 is ranked second in priority, otherwise, D3 is ranked second in priority.

Step S2.4: Sort the priorities of the two inner sub-regions D2 or D3 by comparing the probabilities.

Step S2.5: The two inner sub-regions D2 and D3 are further divided into two parts of the same size, and the above steps S2.1 to S2.4 are repeated.

Step S2.6: Sort the priorities of all divided sub-regions.

Specifically, after determining the priority order of the three sub-regions D1, D2 and D3, as shown in part (a) of Figure 3, the D2 region is divided into two identical sub-regions in the same way as before. D4 and D5. As shown in part (b) of Fig. 3, it is assumed that there are two sub-regions in D4 and D5, D4 can be assumed to be divided into D4.1 and D4.2, D5 can be assumed to be divided into D5.1 and D5.2, There is no limit to how the assumption is divided.

子区域D5中能够发现软件错误的概率为

然后统计其中发现软件错误的测试用例的个数，分别记为y₃和y₄，然后再引入潜变量z₃和z₄，假设D4.1和D4.2中发现软件错误的测试用例分别为z₃和y₃-z₃，发现软件错误的概率分别为

和

同样的，假设D5.1和D5.2中发现软件错误的测试用例分别为z₄和y₄-z₄，发现错误的概率分别为

和

然后引入EM方法来对未知参数

进行迭代直到参数收敛，并将达到收敛的参数值

作为参数

的极大似然估计量，最后比较

与

的数值的大小，并依据两者之间的大小关系来对区域D4和D5进行排序。Assume that the probability that software bugs can be found in sub-region D4 is

The probability that a software bug can be found in sub-region D5 is

Then count the number of test cases in which software errors are found, denoted as y ₃ and y ₄ respectively, and then introduce latent variables z ₃ and z ₄ , assuming that the test cases in which software errors are found in D4.1 and D4.2 are respectively z ₃ and y ₃ -z ₃ , the probability of finding a software bug is

and

Similarly, assuming that the test cases for finding software bugs in D5.1 and D5.2 are z ₄ and y ₄ -z ₄ , respectively, the probability of finding bugs is

and

Then the EM method is introduced to measure the unknown parameters

Iterate until the parameters converge and will reach the converged parameter value

as parameter

The maximum likelihood estimator of , and finally compare

and

and sort the regions D4 and D5 according to the size relationship between the two.

子区域D7中能够发现软件错误的概率为

然后统计其中发现软件错误的测试用例的个数，分别记为y₅和y₆，然后再引入潜变量z₅和z₆，假设D6.1和D6.2中发现软件错误的测试用例分别为y₅和y₅-z₅，发现软件错误的概率分别为

和

然后假设 D7.1和D7.2中发现软件错误的测试用例分别为y₆和y₆-z₆，发现错误的概率分别为

和

然后引入EM方法来对未知参数ψ₃进行迭代直到参数收敛，并将达到收敛的参数值

作为参数

的极大似然估计量，最后比较

与

的大小，并依据两者之间的大小关系来对区域D6和D7进行排序。After the priority ordering between D4 and D5 is determined, the sub-region D3 is processed with similar region division and parameter iteration as the sub-region D2, and the region D3 is first divided into two equal sub-regions D6 and D7. As shown in part (a) of Figure 4, it is assumed that there are also two sub-regions in D6 and D7, in which D6 can be divided into D6.1 and D6.2, and D7 can be divided into D7.1 and D7.2. The probability that a software bug can be found in region D6 is

The probability that a software bug can be found in sub-region D7 is

Then count the number of test cases in which software errors are found, denoted as y ₅ and y ₆ respectively, and then introduce latent variables z ₅ and z ₆ , assuming that the test cases in which software errors are found in D6.1 and D6.2 are respectively y ₅ and y ₅ -z ₅ , the probability of finding a software bug is

and

Then suppose that the test cases in D7.1 and D7.2 where software bugs are found are y ₆ and y ₆ -z ₆ , respectively, and the probability of finding bugs is

and

Then the EM method is introduced to iterate _over the unknown parameter ψ3 until the parameters converge, and will reach the converged parameter value

as parameter

The maximum likelihood estimator of , and finally compare

and

and sort the regions D6 and D7 according to the size relationship between them.

To sum up, as shown in part (b) of Figure 4, after three parameter iterations, the input domain is finally divided into five sub-regions D1, D4, D5, D6 and D7, and the five sub-regions are prioritized. , which determines the order in which subsequent experiments generate test cases in these subregions.

Step S3: Use the EM-ART method to test the software, and generate test cases in the sub-regions ranked first.

In the embodiment, the test cases are generated according to the priority order of the sub-areas until software errors are found. If the number of test cases reaches a certain level and no software errors are found, continue to generate test cases in the sub-region with the highest priority until software errors are found.

Specifically, step S3 of the embodiment is implemented as follows:

1) First, continuously generate test cases from the boundary area with the highest priority, and execute the test, and stop if a software error is found. If no software errors are found, and the total number of generated test cases reaches the preset threshold, test cases are generated in the sub-area with the second priority, and the tests are executed. If software errors are found, it will stop. If no software errors are found, and the total number of test cases generated reaches the preset threshold, test cases are generated in the sub-area with the third priority, and the tests are executed. If software errors are found, it will stop. After continuously lowering the priority level, if no software error is found in the sub-region with the lowest priority, and the total number of test cases generated reaches the preset threshold, then go to step 2);

During specific implementation, the threshold can be preset by those skilled in the art as required. In the embodiment, a preferred value of 10 is adopted, that is, 10 test cases are sequentially generated in each area in the order of priority.

2) If step 1) has been executed once, return to execute step 1), if step 1) has been repeatedly executed twice, instead, continue to generate test cases only in the boundary area with the highest priority, and execute the test, Stop until a software error is found or the preset upper limit of the number of tests is reached.

During specific implementation, the method proposed by the technical solution of the present invention can be realized by those skilled in the art using computer software technology to realize the automatic running process. The system device for implementing the method is, for example, a computer-readable storage medium storing a computer program corresponding to the technical solution of the present invention, and a computer that runs the corresponding computer program. The computer equipment of the program should also be within the protection scope of the present invention.

In some possible embodiments, a test case generation system based on maximum likelihood estimation of maximum expectation is provided, including the following modules,

The first module is used to divide the input domain of the software into a plurality of sub-regions, distinguish the boundary region of the input domain from the internal region, and use the boundary region as the sub-region with the highest priority;

The second module is used to introduce the maximum likelihood estimation method, estimate the probability that the sub-regions in the inner region may contain failure regions, and sort the sub-regions in the inner region based on the probability;

The third module is used to generate test cases according to the priority order of the sub-areas until software errors are found; if the number of test cases reaches the preset condition and no software errors are found, continue to generate test cases in the sub-area with the highest priority until A software bug was found.

In some possible embodiments, a test case generation system based on maximum likelihood estimation is provided, comprising a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the processor to execute the above A test case generation method based on maximum likelihood estimation is described.

In some possible embodiments, a test case generation system based on maximum likelihood estimation is provided, including a readable storage medium, on which a computer program is stored, and when the computer program is executed, A test case generation method based on maximum likelihood estimation of maximum expectation as described above is realized.

Although the preferred embodiments of the present invention have been described, additional changes and modifications to these embodiments may occur to those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be construed to include the preferred embodiment and all changes and modifications that fall within the scope of the present invention.

Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, provided that these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A test case generation method based on maximum likelihood estimation maximum expectation is characterized by comprising the following steps,

step S1, dividing the input domain of the software into a plurality of sub-regions, distinguishing the boundary region of the input domain from the internal region, and taking the boundary region as the sub-region with the highest priority;

step S2, introducing latent variables, estimating the probability that the sub-regions in the internal region possibly contain failure regions by combining an EM algorithm, and sequencing the sub-regions in the internal region based on the probability;

step S3, generating test cases according to the priority order of the sub-regions until a software error is found; and if the number of the test cases reaches the preset condition and no software error is found yet, continuing to generate the test cases in the sub-area with the highest priority until the software error is found.

2. The maximum likelihood estimation-based test case generation method of the maximum expectation according to claim 1, wherein: step S1 includes the following sub-steps,

s1.1, setting the boundary length of the internal area according to the failure rate of the input area to obtain a boundary area outside the internal area, and recording the boundary area as D1;

step S1.2, the priority of the bounding region D1 is ranked first, and the inner region is divided into two parts of the same size, denoted as sub-regions D2 and D3.

3. The maximum likelihood estimation-based test case generation method of the maximum expectation according to claim 2, wherein: when the input field is a two-dimensional square, the boundary length of the inner region is set as follows,

wherein b is the side length of the internal region, a is the side length of the input domain of the whole body, and theta is failure rate.

4. The maximum likelihood estimation-based test case generation method of the maximum expectation according to claim 2, wherein: step S2 includes the following sub-steps,

s2.1, randomly generating 1000 test cases in the two inner sub-areas D2 and D3 respectively, and counting the number of the test cases in which the software errors are found respectively;

s2.2, replacing the probability that the sub-region can find the software error by the probability that the test case finds the error and falls in the sub-region;

s2.3, introducing latent variables, iterating the probability parameters of the previous step by using an EM algorithm until the parameters are converged, and taking the parameter values reaching the convergence as maximum likelihood estimators of the parameters;

s2.4, sorting the priorities of the two inner subregions D2 and D3 by comparing the probability;

step S2.5, further dividing the two internal sub-regions into two parts with the same size, respectively, assuming that the sub-region D2 is divided into D4 and D5, D3 is divided into D6 and D7, repeating the above steps S2.1 to S2.4 for D4 and D5, and repeating the above steps S2.1 to S2.4 for D6 and D7;

step S2.6, the priorities of all the divided sub-regions are sorted, and the priority order of the sub-regions D1, D4, D5, D6 and D7 is determined.

5. The method for generating test cases based on maximum likelihood estimation maximum expectation according to claim 1, 2, 3 or 4, wherein: the step S3 is implemented as follows,

1) firstly, continuously generating a test case from a boundary region with the highest priority, executing a test, and stopping if a software error is found; if no software error is found and the total test case generation number reaches a preset threshold value, generating a test case in a sub-area with the second priority and executing the test, and if the software error is found, stopping the test; if no software error is found and the total test case generation number reaches a preset threshold value, generating a test case in a third priority subregion, executing the test, and stopping if the software error is found; by analogy, after the priority level is continuously reduced, if no software error is found in the sub-region with the lowest priority level and the total test case generation number reaches a preset threshold value, entering the step 2);

2) if the step 1) has been executed once currently, returning to execute the step 1), if the step 1) has been executed twice repeatedly currently, continuing to generate the test case only in the boundary area with the highest priority, and executing the test until a software error is found or a preset upper limit of test times is reached.

6. The maximum likelihood estimation-based test case generation method of the maximum expectation according to claim 5, wherein: the threshold setting preferably takes a value of 10.

7. A test case generation system based on maximum likelihood estimation maximum expectation is characterized in that: the method for generating the test case based on the maximum likelihood estimation maximum expectation according to any one of claims 1 to 6.

8. The maximum likelihood estimation based test case generation system of claim 7, wherein: comprises the following modules which are used for realizing the functions of the system,

the first module is used for dividing an input domain of the software into a plurality of sub-regions, distinguishing a boundary region of the input domain from an internal region, and taking the boundary region as the sub-region with the highest priority;

the second module is used for introducing a maximum likelihood estimation expectation mode, estimating the probability that the sub-region in the internal region possibly contains a failure region, and sequencing the sub-regions in the internal region based on the probability;

the third module is used for generating test cases according to the priority order of the sub-regions until a software error is found; and if the number of the test cases reaches the preset condition and no software error is found yet, continuing to generate the test cases in the sub-area with the highest priority until the software error is found.

9. The maximum likelihood estimation based test case generation system of claim 7, wherein: comprising a processor and a memory for storing program instructions, the processor being configured to invoke the stored instructions in the processor to perform a test case generation method based on maximum likelihood estimation maximum expectation as claimed in any one of claims 1 to 6.

10. The maximum likelihood estimation based test case generation system of claim 7, wherein: comprising a readable storage medium having stored thereon a computer program which, when executed, implements a method for maximum likelihood estimation based maximum expectation test case generation as claimed in any one of claims 1-6.

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