CN103713997B - A kind of transformation relation form description and decomposition method - Google Patents

Abstract

The invention discloses a kind of transformation relation form description and decomposition method, comprise the steps: that (1), according to target tested software, the transformation relation that extraction and design software must are fulfilled for, creates transformation relation；(2) based on symbolic logic, the transformation relation obtained carried out Formal Modeling: first determine the constraints that transformation relation is set up, and carry out formalized description；It is then based on symbolic logic and describes the input and output parameter of transformation relation, set up transformation relation form descriptive model；(3) based on formalized model, extract subrelation and the set description form of transformation relation composition model constituting transformation relation respectively, set up transformation relation decomposition model.The present invention is simple and clear, is described by symbolic logic, it is ensured that the descriptive power of formalized model and the scope of application, provides accurately for transformation relationship description, specification, effective method, and the automation being more conducive to follow-up metamorphic testing is implemented.

Description

A kind of transformation relation form description and decomposition method

Technical field

The present invention relates to a kind of transformation relation form description and decomposition method, belong to software metamorphic testing technical field.

Background technology

Software test is currently to find and determine the Main Means whether software exists fault, is also maximally efficient method One of.And the biggest problem that software test faces is how that the output judging test case is the most correct.This basis for estimation Referred to as test judgement (Test Oracle).Often the most not exclusively, this is also that software test faces the most to this test judgement One of main difficult problem, i.e. a test judgement difficult problem.

Such as processing complicated numerical computations, calculation procedure and the software such as scientific algorithm, such as solving of partial differential equation, Test man is difficult to judge that the output that calculation procedure provides is the most correct.In encryption system, calculate public key algorithm and relate to surpass The calculating of big integer, is the most also very difficult to verify the correctness of result of calculation.When testing Web search engine, how to sentence Disconnected Search Results is the most also extremely difficult.In OO software test, it is judged that two observe to as if No equivalence is also almost to be difficult to.In GIS software is tested, how tester judges the figure that software provides Shape length, area isometry information the most also lack certain foundation.

But, although preferable test judgement can not be directly obtained, it is not intended that software test can not be carried out.Its Metamorphic testing (Metamorphic Testing) technology that middle T.Y.Chen etc. propose provides one for solving a test judgement difficult problem Plant effective ways.It carrys out decision procedure output by the meeting property of necessary relation between output of repeatedly testing checking tested program Whether there is mistake, and these necessary relations are referred to as changed in quality relation (Metamorphic Relation).Transformation relation be into The foundation of row metamorphic testing, the validity of metamorphic testing directly depends on the quality of transformation relation.Therefore, the most more efficiently Construct, describe and measure transformation relation, just have very important significance.

By the summary analysis to existing metamorphic testing pertinent literature, find that each document all can provide corresponding transformation Relation, wherein in 81 main literature, altogether gives 686 transformation relations, and description form is different, as mathematical formulae, Natural language, also some complex relationship use the description form of both mixing.For these different types of transformation relations Description form, although combine different literature research backgrounds, the concrete meaning of transformation relation can be further to define.But entering During row transformation relation multiplexing, will there is problems in that

On the one hand, there is ambiguity in the description of transformation relation.Either mathematical relationship or denotational description, or natural Language describes, and all there is certain ambiguity；

On the other hand, multiple description form indigestion.Generally for these transformation relations, particularly lack and determine mathematics The relation of description form, or when test input occurs with matrix or other complex forms, do not understanding research background On the basis of, transformation relation meaning is not directly perceived, its meaning indigestion.

The two factor greatly constrains application and the multiplexing of transformation relation.

Summary of the invention

Goal of the invention: for problems of the prior art with not enough, the present invention provides a kind of based on logistic Unified transformation relationship description and decomposition method, use a kind of formal description model based on metamorphic testing constraints, and Establish transformation relation decomposition model on this basis.

Technical scheme: a kind of transformation relation form description and decomposition method, comprises the steps:

(1) for tested software, transformation relation is created；

In step (1), it is necessary first to according to target tested software, the transformation that extraction and design software must are fulfilled for is closed System.And the design considerations of these transformation relations is software requirement specification or algorithm.At this moment transformation relation can pass through nature Language describes, it is also possible to be described by mathematical formulae.When transformation relation comes from software requirement specification, owing to specification is led to Being often natural language or half formalized description, the most at this moment tester is typically only capable to obtain the transformation of natural language description Relation.When transformation relation is from program function, owing to program function generally can be described by suitable mathematical relationship, The most at this moment transformation relation is also just generally expressed by mathematical form.This step is mainly follow-up formalized description and divides Solve and basis is provided.

(2) based on symbolic logic, the transformation relation obtained is carried out Formal Modeling, set up transformation relation form model Mainly comprise the steps:

The transformation relation obtained by step (1) is typically natural language description or mathematical relationship describes, and these shapes All there is ambiguity in various degree in the description of formula.And symbolic logic can describe these relations more accurately, intuitively.

(2-1) determine the constraints that transformation relation is set up, and carry out formalized description；

Transformation relation is by the basis of metamorphic testing.And the establishment of relation of changing in quality also is to there is certain constraints. The constraints that transformation relation is set up relates generally to three main bodys, i.e. requirement specification, program function and program.These three main body can With formalization representation respectively it is: [S], [P] and P.

These three main body the most just can form three relations:

A. requirement specification and the uniformity of program function；

B. requirement specification and the uniformity of program；

C. program function and the uniformity of program.

Three relations can be with formalization representation: A. [S]=[P], B. [S]=P, C. [P]=P.

For metamorphic testing, the main target of test is tested software, and requirement specification and program function Consistency checking generally falls into testing requirement checking content.Therefore, the constraints that transformation relation is set up just includes B and C two kinds.

(2-2) the input parameter of transformation relation is described based on symbolic logic；

Transformation relation input parameter is described the main number needed in view of input.Typically, transformation relation is originally Body can't be extremely complex, and otherwise, the checking of the correctness of transformation relation own is also difficult to judge.It is therefore contemplated that The input parameter of transformation relation meets limited countability.Based on this, transformation relation input parameter can be expressed as:

(x₁,x₂,…,x_n)

x_iRepresent a test input；i=1,2,…,n；N is natural number, represents the number of input parameter.

(2-3) output parameter of transformation relation is described based on symbolic logic；

For general software, one can consider that when the input of software determines, its output determines that, i.e. tests input It is one to one with test output.Therefore, the output parameter of transformation relation can be expressed as:

(P(x₁),P(x₂),…,P(x_n))

P(x_i) represent corresponding to test one input x_i, tested program actual output accordingly.

(2-4) transformation relation form descriptive model is set up；

After completing above step, it is possible to constraints based on transformation relation and input, output parameter, set up formalization Descriptive model.

1) when constraints is [S]=P, i.e. the constraints that transformation relation is set up is for assuming software metrics and program one Cause, say, that the indispensable attributes obtaining Main Basis software metrics of transformation relation.At this moment, as input parameter (x₁,x₂,…, x_n) when meeting relation r, output parameter (P (x₁),P(x₂),…,P(x_n)) meet relation r_f.Therefore, transformation relation can describe For:

$\frac{\left[S\right]\left(x_i\right)=P\left(x_i\right)}{r(x_1,x_2,...,x_n)\→r_f(P\left(x_1\right),P\left(x_2\right),...,P\left(x_n\right))},i=\mathrm{1,2},...,n,$ Can also be expressed as:

$\frac{\left[S\right]\left(x_i\right)=P\left(x_i\right)}{r(x_1,x_2,...,x_n)\→r_f\left(\right[S]\left(x_1\right),[S]\left(x_2\right),...,[S\left]\left(x_n\right)\right)},i=\mathrm{1,2},...,n$

[S](x_i) represent for test input x_iThe program output that software metrics determines.

2) when constraints is [P]=P, i.e. the constraints that transformation relation is set up is for assuming program function and program one Cause, say, that the indispensable attributes obtaining Main Basis program function of transformation relation.At this moment, as input parameter (x₁,x₂,…, x_n) when meeting relation r, output parameter (P (x₁),P(x₂),…,P(x_n)) meet relation r_f.Therefore, at this moment transformation relation can be retouched State for:

$\frac{\left[S\right]\left(x_i\right)=P\left(x_i\right)}{r(x_1,x_2,...,x_n)\→r_f(P\left(x_1\right),P\left(x_2\right),...,P\left(x_n\right))},i=\mathrm{1,2},...,n,$ Can also be expressed as:

$\frac{P\left(x_i\right)=P\left(x_i\right)}{r(x_1,x_2,...,x_n)\→r_f\left(\right[P]\left(x_1\right),[P]\left(x_2\right),...,[P\left]\left(x_n\right)\right)},i=\mathrm{1,2},...,n$

[P](x_i) represent for test input x_iThe program output that software metrics determines.

Generally go through other method of testings, select and structure meets relation r (x₁, x₂..., x_n) test input be not stranded Difficulty, if at this moment program output can not meet relation r_f(P(x₁),P(x₂),…,P(x_n)) time, it is believed that assumed condition is false, That is:

Or (P (x_i)≠[S](x_i)), wherein i=1,2 ..., n.At this moment just claim to be surveyed by transformation Examination is found that mistake or fault present in program.

(3) transformation relation decomposition model is set up based on formalized model:

We say mainly there is following reason to decompose transformation relation:

First, transformation is related to that the variable itself comprised is many.Definition according to transformation relation is it will be seen that transformation relation bag The variable contained is the most single, and quantity is also the most many.Basic transformation relation comprises input variable, output variable, also has journey Order function variable etc..

Secondly, transformation is related to that the relation itself comprised is many.By the formal definitions formula of transformation relation it can clearly be seen that There is multiple relatively independent relation in transformation relation, such as program input variables relation r (x₁,x₂,…,x_n), program output variable is closed It is r_f(P(x₁),P(x₂),…,P(x_n)), and program function relation [P] (x_i) and program output and program function output between Relation allow r (P (x_i),[P](x_i)) etc..

Finally, it is complicated that transformation relation calculates type.By Part I it will be seen that grind in existing transformation relationship example The relation of different types is occurred in that in studying carefully, such as trigonometric function form, such as integral function relation, also just like vector form, or Matrix form, there is also part can not describe simply by formula, and by the relation of natural language description.

It is extremely complex that these three reason has been doomed directly transformation relation to be carried out tolerance, and measurement metric is also to be difficult to obtain Take.For this reason, it may be necessary to transformation relation is decomposed.Firstly, it is necessary to determine the subrelation related in transformation relation respectively.

(3-1) determine and describe input parameters relationship；

Two kind transformation relations shown for (2-4), it inputs parameter (x₁,x₂,…,x_n) meeting relation r, therefore can lead to The form crossing set is described as: MR_IR={ (x₁,x₂,…,x_n)|r(x₁,x₂,…,x_n)}。

(3-2) determine and describe output parameter relation；

Two kind transformation relations shown for (2-4), its output parameter meets relation r_f, in like manner can be by the form of set It is described as:

MR_OR={(P(x₁),P(x₂),…,P(x_n))|r_f(P(x₁),P(x₂),…,P(x_n))}。

(3-3) determine and describe from relation；

Two kind transformation relations shown for (2-4), it is probably, from relation, the relation that requirement specification determines, it is also possible to journey The relation that order function determines.Therefore, can being described as from relation of transformation relation:

MR_SR={(x_i,y_i)|y_i=[S](x_i) i=1,2 ..., n, or

MR_SR={(x_i,y_i)|y_i=[P](x_i)}。

Therefore, for the first transformation relation, can be described as by the form of set:

$\left\{(r,[S],r_f)\right|r(x_1,x_2,..,x_n)\stackrel{P\left(x_i\right)=\left[S\right]\left(x_i\right)}{\→}{r}_f(P\left(x_1\right),P\left(x_2\right),...,P\left(x_n\right))\},i=\mathrm{1,2},...,n$

For the second transformation relation, in like manner can be described as by the form of set:

$\left\{(r,[P],r_f)\right|r(x_1,x_2,..,x_n)\stackrel{P\left(x_i\right)=\left[P\right]\left(x_i\right)}{\→}{r}_f(P\left(x_1\right),P\left(x_2\right),...,P\left(x_n\right))\},i=\mathrm{1,2},...,n$

These three subrelation constitutes transformation relation decomposition model, as shown in Figure 1.

Beneficial effect: compared with prior art, what the present invention provided describes based on logistic transformation relation formization With decomposition method, transformation relation is described for accurate, unambiguity and provides effective means.First to transformation relation and survey of changing in quality The constraints of examination is analyzed, it is determined that two kinds of constraintss that transformation relation formization describes, the most respectively with two kinds the most about Based on bundle condition, establish transformation relation form descriptive model, be finally based on the formalized model of transformation relation, carry respectively Take out subrelation and the set description form of transformation relation composition model constituting transformation relation.The formalization that the present invention provides Description method is simple and clear, is described by symbolic logic, it is ensured that the descriptive power of formalized model and the scope of application, for changing in quality Relationship description provides accurately, specification, effective method, and the automation being more conducive to follow-up metamorphic testing is implemented.

Accompanying drawing explanation

Fig. 1 is that the transformation relation of the present invention decomposes illustraton of model；

Fig. 2 is the method flow diagram of the present invention.

Detailed description of the invention

Below in conjunction with specific embodiment, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate the present invention Rather than restriction the scope of the present invention, after having read the present invention, the those skilled in the art's various equivalences to the present invention The amendment of form all falls within the application claims limited range.

As in figure 2 it is shown, flow chart based on logistic transformation relation form description Yu decomposition method, in order in detail The Formal Modeling of the present invention, description and decomposable process carefully, are clearly described, this example is with realization [P (x)]=sin (x) function Program P as a example by carry out related description.This program is used for calculating y=sin (x).

The first step: for tested software, creates transformation relation；

Create transformation relation: owing to for tested program P, its program function is clear and definite, and the requirement specification of program is also Uncertain, therefore this example is only with program function for according to extracting transformation relation.And for program function [P (x)]=sin (x), by Its basic character can obtain following 10 transformation relations, and the proof of these fundamental propertys is the most highly developed.In this example I Select 1st therein, the 6th and the 10th transformation relation as a example by illustrate.

MR_sin1:sin(x)=sin(x+2π)

MR_sin2:sin(x)=-sin(x+π)

MR_sin3:-sin(-x)=sin(x)

MR_sin4:sin(x)=sin(π-x)

MR_sin5:sin(x)=-sin(2π-x)

MR_sin6:sin(x)+sin(y)+sin(z)-sin(x+y+z)=4*sin((x+y)/2)*sin((x+z/2))*sin ((y+z)/2)

${\mathrm{MR}}_{\sin 7}:{\sin }^2\left(x\right)+{\sin }^2(\frac{\mathrm{\π}}{2}-x)=1$

MR_sin8:sin(3*x)=3*sin(x)-4*sin³(x)

MR_sin9:sin²(x)-sin²(y)=sin(x+y)*sin(x-y)

MR_sin10:sin(5*x)=16*sin⁵(x)+5*sin(3*x)-10*sin(x)

Second step: the transformation relation obtained is carried out Formal Modeling based on symbolic logic

This step mainly includes that transformation relation constraint conditional formsization describes, inputs parametric form description and output parameter Formalized description three part.

Transformation relation constraint conditional formsization describes: in this example transformation Relation acquisition according to being program function [P (x)]=sin (x), the constraints of above transformation relation is that program function is consistent with program, can be expressed as: P (x)=[P (x)]。

MR_sin1:sin(x)=sin(x+2π)

MR_sin6:sin(x)+sin(y)+sin(z)-sin(x+y+z)=4*sin((x+y)/2)*sin((x+z/2))*sin ((y+z)/2)

MR_sin10:sin(5*x)=16*sin⁵(x)+5*sin(3*x)-10*sin(x)

Input parametric formization describes:

(1) MR_sin1Its input parameter only has two, and therefore input parameter can be expressed as two tuples: (x₁,x₂)；

(2) MR_sin6Its input parameter has seven, and its input parameter can be expressed as seven tuples: (x₁,x₂,x₃,x₄,x₅,x₆, x₇)；

(3) MR_sin10Its input parameter has three, and therefore input parameter can be expressed as triple: (x₁,x₂,x₃)。

Output parameter formalized description:

Due to program the determining that property program in this example, therefore input, with output, there is corresponding relation.

(1) MR_sin1Its input parameter only has two, and therefore output parameter the most only two can be expressed as two tuples: (P(x₁),P(x₂))；

(2) MR_sin6Its input parameter has seven, therefore output parameter the most only seven, and can be expressed as is seven tuples: (P(x₁),P(x₂),P(x₃),P(x₄),P(x₅),P(x₆),P(x₇))；

(3) MR_sin10Its input parameter has three, and therefore output parameter the most only three can be expressed as triple: (P(x₁),P(x₂),P(x₃))。

These three transformation relation can be with formalized description:

$\begin{array}{c}\left(1\right){\mathrm{MR}}_{\sin 1}:\\ \frac{P\left(x_i\right)=\left[P\right]\left(x_i\right)}{r(x_1,x_2)\→r_f(P\left(x_1\right),P\left(x_2\right))}\⇒\frac{P\left(x_i\right)=\sin \left(x_i\right)}{x_2-x_1=2\mathrm{\π}\→P\left(x_2\right)-P\left(x_1\right)=0}i=\mathrm{1,2}\end{array}$

3rd step: set up transformation relation decomposition model based on formalized model

For the transformation relation in example, after setting up transformation relation form model, based on this, it can be carried out point Solve, thus obtain the subrelation of transformation relation, final structure transformation relation decomposition model.

$\left\{(r,[P],r_f)\right|r(x_1,x_2,..,x_n)\stackrel{P\left(x_i\right)=\left[P\right]\left(x_i\right)}{\→}{r}_f(P\left(x_1\right),P\left(x_2\right),...,P\left(x_n\right))\},i=\mathrm{1,2},...,n$

Determine input parameters relationship: input parameters relationship is the precondition of transformation relation.Above three is changed in quality and closes System, can respectively obtain its input parameters relationship is:

(1) MR_sin1_IR={(x₁,x₂)|r(x₁,x₂)=(x₂-x₁=2π)}

Determine output parameter relation: output parameter relation is the postcondition of transformation relation.Above three is changed in quality and closes System, can respectively obtain its output parameter relation is:

(1) MR_sin1_OR={(y₁,y₂)|r_f(y₁,y₂)=(y₂-y₁=0) }

(2) MR_sin6_OR={(y₁,y₂,...,y₇)|r(y₁,y₂,...,y₇)

=(4*y₇*y₆*y₅-y₄-y₃-y₂-y₁=0) }

(3) MR_sin10_OR={(y₁,y₂,y₃)|r(y₁,y₂,y₃)=(y₃-16*y⁵ ₁+5*y₂-10*y₁=0) }

Determine from relation: for identical tested program, different transformation relations is identical from relation, can table It is shown as:

MR_sin_SR={(x,y)|y=sin(x)}。

Claims (1)

1. a transformation relation form description and decomposition method, it is characterised in that comprise the steps:

(1) according to target tested software, the transformation relation that extraction and design software must are fulfilled for, create transformation relation；Described slough off The design considerations of change relation is software requirement specification or algorithm；

(2) based on symbolic logic, the transformation relation obtained is carried out Formal Modeling；First the constraint that transformation relation is set up is determined Condition, and carry out formalized description；Being then based on symbolic logic and describe the input and output parameter of transformation relation, foundation is sloughed off Become relation form descriptive model；

(3) based on formalized model, subrelation and the collection of transformation relation composition model constituting transformation relation is extracted respectively Close description form, set up transformation relation decomposition model；

In described step (1), when transformation relation comes from software requirement specification, changed in quality relation by natural language description；When When transformation relation is from program function, it is described transformation relation by mathematical formulae；

In described step (2), set up transformation relation form model and mainly comprise the steps:

(2-1) determine the constraints that transformation relation is set up, and carry out formalized description；

The constraints that transformation relation is set up relates generally to three main bodys, i.e. requirement specification, program function and program, these three master Body can distinguish formalization representation: [S], [P] and P；

These three main body the most just can form three relations:

A. requirement specification and the uniformity of program function；

B. requirement specification and the uniformity of program；

C. program function and the uniformity of program；

Three relations can be with formalization representation: A. [S]=[P], B. [S]=P, C. [P]=P；

For metamorphic testing, the main target of test is tested software, and the uniformity of requirement specification and program function is tested Card generally falls into testing requirement checking content；Therefore, the constraints that transformation relation is set up just includes B and C two kinds；

(2-2) the input parameter of transformation relation is described based on symbolic logic；

Transformation relation input parameter is expressed as:

(x₁,x₂,…,x_n)

x_iRepresent a test input；I=1,2 ..., n；N is natural number, represents the number of input parameter；

(2-3) output parameter of transformation relation is described based on symbolic logic；

The output parameter of transformation relation is expressed as:

(P(x₁),P(x₂),…,P(x_n))

P(x_i) represent corresponding to test one input x_i, tested program actual output accordingly；

(2-4) transformation relation form descriptive model is set up；

Constraints based on transformation relation and input, output parameter, set up formal description model；

1) when constraints is [S]=P, i.e. the constraints that transformation relation is set up is consistent with program for hypothesis software metrics, The indispensable attributes obtaining Main Basis software metrics of that is transformation relation；At this moment, as input parameter (x₁,x₂,…,x_n) When meeting relation r, output parameter (P (x₁),P(x₂),…,P(x_n)) meet relation r_f；Therefore, transformation relation can be described as:

Can also be expressed as:

$\frac{\left[S\right]\left(x_i\right)=P\left(x_i\right)}{r(x_1,x_2,..,x_n)\→r_f\left(\right[S]\left(x_1\right),[S]\left(x_2\right),...,[S\left]\left(x_n\right)\right)},i=\mathrm{1,2},...,n$

[S](x_i) represent for test input x_iThe program output that software metrics determines；

2) when constraints is [P]=P, i.e. the constraints that transformation relation is set up is consistent with program for assuming program function, The indispensable attributes obtaining Main Basis program function of that is transformation relation；At this moment, as input parameter (x₁,x₂,…,x_n) When meeting relation r, output parameter (P (x₁),P(x₂),…,P(x_n)) meet relation r_f；Therefore, at this moment transformation relation can describe For:

Can also be expressed as:

$\frac{P\left(x_i\right)=\left[P\right]\left(x_i\right)}{r(x_1,x_2,..,x_n)\→r_f\left(\right[P]\left(x_1\right),[P]\left(x_2\right),...,[P\left]\left(x_n\right)\right)},i=\mathrm{1,2},...,n$

[P](x_i) represent for test input x_iThe program output that software metrics determines；

If program output can not meet relation r_f(P(x₁),P(x₂),…,P(x_n)) time, it is believed that assumed condition is false, it may be assumed that

Or (P (x_i)≠[S](x_i)), wherein i=1,2 ..., n；At this moment just claim to be sent out by metamorphic testing Show mistake or fault present in program；

Described step (3) comprises the steps:

(3-1) determine and describe input parameters relationship；

Two kind transformation relations shown for (2-4), it inputs parameter (x₁,x₂,…,x_n) meet relation r, therefore can be by collection The form closed is described as: MR_IR={ (x₁,x₂,…,x_n)|r(x₁,x₂,…,x_n)}；

(3-2) determine and describe output parameter relation；

Two kind transformation relations shown for (2-4), its output parameter meets relation r_f, in like manner can be described by the form of set For:

MR_OR={ (P (x₁),P(x₂),…,P(x_n))|r_f(P(x₁),P(x₂),…,P(x_n))}；

(3-3) determine and describe from relation；

Two kind transformation relations shown for (2-4), it is probably, from relation, the relation that requirement specification determines, it is also possible to program letter The relation that number determines；Therefore, can being described as from relation of transformation relation:

MR_SR={ (x_i,y_i)|y_i=[S] (x_i) i=1,2 ..., n, or

MR_SR={ (x_i,y_i)|y_i=[P] (x_i)}；

Therefore, for the first transformation relation, can be described as by the form of set:

For the second transformation relation, in like manner can be described as by the form of set: