CN102509171A - Flow mining method facing to rule execution log - Google Patents

Flow mining method facing to rule execution log Download PDF

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Publication number
CN102509171A
CN102509171A CN2011103255013A CN201110325501A CN102509171A CN 102509171 A CN102509171 A CN 102509171A CN 2011103255013 A CN2011103255013 A CN 2011103255013A CN 201110325501 A CN201110325501 A CN 201110325501A CN 102509171 A CN102509171 A CN 102509171A
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rule
regular
task
relation
flow
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CN102509171B (en
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尹建伟
曹斌
邓水光
李莹
吴健
吴朝晖
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Zhejiang University ZJU
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Zhejiang University ZJU
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Abstract

The invention discloses a flow mining method facing to a rule execution log, which comprises the following steps: 1) business rule engine; 2) XESame; and 3) Prom, wherein ProM is an open-sourcing mining framework and supports the flow mining in a plug-in board mode. A ''.xes'' file generated in step 2) serves as an input source, a plug-in board mode is used for an alpha-r method mining of the mining work, and finally, a flow mining result graph is formed by matching with Petri network modeling.

Description

A kind of digging flow method of rule-oriented execution journal
Technical field
The invention belongs to the data mining field, mainly is to traditional digging flow technology based on event log, proposes the digging flow technology of rule-oriented engine daily record, relates to a kind of digging flow method of rule-oriented execution journal.
Background technology
Workflow technology provides positive effect to its tissue of optimization of enterprises and operation control process; Nowadays should technology be widely used in the various infosystems of enterprise, comprised ERP (ERP) system, Customer Relation Management (CRM) system, supply chain management (SCM) system, B2B system etc.On the one hand, these infosystems have been brought all competitive edges on the informatization road to enterprise really; On the other hand, these infosystems generally all are to be driven by the Work flow model that shows, promptly must design the execution flow process that a Work flow model comes the accurate description workflow in advance.Yet; The design of Work flow model is a complicacy, relate to the engineering of every aspect; Both needed abundant Wokflow Modeling Design experience; Also to have good communication skill (comprise with staff and upper strata decision maker between continuous the interchange), therefore such design is not only consuming time but also effort often, also leads to errors easily.Simultaneously, owing to all be to have the final say by the person of corporate decision to determine to adopt which Work flow model at last, often have certain subjectivity.Moreover the model that the complicacy of service logic possibly cause designing has deviation with actual operational scheme, and during actual motion, operation flow is also very possible to cause Work flow model to lack adaptability along with the change of environment or all factors.
The proposition of workflow mining technology its objective is in order to find potential operation flow and then business events flow path to be improved or rebuilds just in order to remedy above deficiency.Nowadays commonplace based on the digging flow of event log.
In this simultaneously, along with the continuous development of Business Rule Engine, rely on its powerful support; The pattern of the sort of " hard coded " formula before the operating information system of enterprise will be abandoned; Turn to the pattern of " configurable " formula, not only can realize the joining property of height of enterprise operation system runtime, promote the flexible tenability of Business Works; Make enterprise can handle some and complicated service thereof rule flow process simultaneously, for positive effect is played in the lifting of the productive capacity and the market competitiveness.
Summary of the invention
In order to solve the problems of the technologies described above, the present invention proposes a kind of digging flow method of rule-oriented execution journal.
A kind of digging flow method of rule-oriented execution journal comprises the steps:
1) obtains regular flow daily record
Figure 621915DEST_PATH_IMAGE001
and be converted into the ProM input format of standard;
2) to the regular flow daily record after the conversion In each bar rule track
Figure 771847DEST_PATH_IMAGE002
Each regular task tInquire about, if tIt is regular track
Figure 566628DEST_PATH_IMAGE002
Middle article one rule task, then tIt is exactly flow process
Figure 634815DEST_PATH_IMAGE003
Starting point;
3) obtaining should the rule task tThe corresponding related fact collection of LHS FL (r)The fact collection related with the RHS of correspondence FR (r)
4) right FL (r)Judge, if empty, then regular task tIt is flow process
Figure 224060DEST_PATH_IMAGE004
Terminal point; If be not empty, then
For regular task tThe regular task of afterwards each T', acquisition should the rule task T'Middle rule R'The corresponding related fact collection of LHS FL (r')The fact collection related with the RHS of correspondence FR (r')Judge FL (r)With FL (r')Relation, if the true renewal frequency among both is all identical, then tWith T'Exist
Figure 207059DEST_PATH_IMAGE005
Relation; If there is an identical fact at least in both, then tWith T'Exist
Figure 539952DEST_PATH_IMAGE006
Relation; If there is an identical fact at least in both, then tWith T'Exist
Figure 527893DEST_PATH_IMAGE007
Relation; If FR (r)In regular task tNever triggered any rule afterwards, so tIt is exactly flow process
Figure 553617DEST_PATH_IMAGE003
Terminal point;
5) for regular track
Figure 758334DEST_PATH_IMAGE002
In any two regular tasks t, T'Rule r, R', if FL (r)With FL (r')Be empty set perhaps tWith T'All and track
Figure 629338DEST_PATH_IMAGE002
In the Else Rule task do not exist
Figure 734435DEST_PATH_IMAGE006
Relation, then tWith T'Exist
Figure 931061DEST_PATH_IMAGE008
Relation;
6) merge result and discovery
Figure 357494DEST_PATH_IMAGE009
relation of excavating by above-mentioned steps;
7) through Petri net form formula final excavation result is carried out modeling;
Above-mentioned rule be a doublet (LHS, RHS), wherein: LHS is a left-hand component, i.e. the set of one group of limited said conditions in rule; RHS is a right-hand component, i.e. the set of the limited number action of a group in rule; Make that T is the set of regular task; Then
Figure 736916DEST_PATH_IMAGE010
representes a regular trajectory mark;
Figure 197985DEST_PATH_IMAGE011
is a regular flow daily record; Wherein
Figure 299933DEST_PATH_IMAGE012
is the power set of
Figure 479241DEST_PATH_IMAGE013
; Said
Figure 456162DEST_PATH_IMAGE014
expression begins the regular task carried out at first, when promptly move in system in the rule base at first by the regular task of parallel triggering; Said relation
Figure 771737DEST_PATH_IMAGE015
expression parend; Be present under two kinds of different situations; Be do not relate in the regular task any fact or the rule RHS in the involved fact can't trigger other rule again; Between two rules of said
Figure 310166DEST_PATH_IMAGE016
expression direct cause and effect dependence is arranged; Relation has been represented the initial node of each parallel branch; Last relation
Figure 483014DEST_PATH_IMAGE009
is based on two different tracks, so be choice relation between its expression rule.
Further; Said true f is made up of tlv triple
Figure 918675DEST_PATH_IMAGE018
;
Figure 362426DEST_PATH_IMAGE019
representes true type I D;
Figure 952545DEST_PATH_IMAGE020
representes true ID; The true set a regular task of
Figure 772733DEST_PATH_IMAGE021
expression is used in combination and makes with the form of workflow the number of times that is updated in the final decision together.
Further; Make that g is the regular flow daily record on the regular set of tasks T (i.e. ); With
Figure 677552DEST_PATH_IMAGE023
/the involved fact collection of difference pairing LHS/RHS of delegate rules r; And the renewal frequency of the true f of π (f) expression: when there being track
Figure 178514DEST_PATH_IMAGE025
; Wherein
Figure 323188DEST_PATH_IMAGE026
and
Figure 374320DEST_PATH_IMAGE027
, when
Figure 673452DEST_PATH_IMAGE028
:
Figure 835443DEST_PATH_IMAGE029
? iff
Figure 100203DEST_PATH_IMAGE030
the same;
Figure 823702DEST_PATH_IMAGE031
? iff?
Figure 908332DEST_PATH_IMAGE032
;
Figure 811697DEST_PATH_IMAGE033
? iff?
Figure 429498DEST_PATH_IMAGE034
;
Figure 822433DEST_PATH_IMAGE035
? iff?
Figure 659939DEST_PATH_IMAGE036
;
When there being an other regular trajectory mark ; It shares some identical regular task with track
Figure 638970DEST_PATH_IMAGE038
, makes
Figure 202807DEST_PATH_IMAGE039
:
Figure 262029DEST_PATH_IMAGE040
And if only if
Figure 569514DEST_PATH_IMAGE041
Beneficial effect of the present invention is: this technical Analysis is embedded in the business rule log information that Business Rule Engine produced in the enterprise information system; Provide the citation form of regular daily record; The excavation of the conversion through journal format and the digging flow algorithm of rule-based daily record; Find potential flow process between rule, thereby reconstruction provides positive suggestion for the operation flow of enterprise is improved perhaps.
Description of drawings
Fig. 1 is that the rule based on the fact triggers graph of a relation in α-r method;
A regular flow daily record of Fig. 2 sample;
Fig. 3 is based on the process flow diagram that α-the r method is excavated that utilizes of Fig. 2;
The digging flow integrated stand composition of Fig. 4 rule-oriented daily record.
Embodiment
To combine accompanying drawing and specific embodiment that the present invention is done further explanation below.
In the present invention; Consider such situation; Be that Business Rule Engine and workflow engine have been integrated in the operating information system of enterprise, they cooperatively interact and help enterprise to carry out professional efficient circulation and execution, i.e. activity in operation flow circulation drives through workflow engine; And in the flow process execution of the related service logic of each Activity On the Node will by the coupling of business rule whether determine, cause the execution of a series of professional actions after promptly any rule is met.Under such situation, in case operating information system brings into operation, the log information of traditional infosystem that digging flow relied on begins by the flow engine record, and the regular log information that regulation engine produced is also noted simultaneously.From prior art, can learn; The regular daily record that regulation engine produced is the contextual information (regular flow daily record) when carrying out according to time sequencing about rule in the rule base; Because regulation engine and workflow engine merge use each other, so the running of the operation flow of information in the regulation engine daily record and enterprise has getting in touch of countless ties.Yet; The rule log information almost seldom is collected the analytical work that is used for carrying out the digging flow aspect; Therefore, excavate implicit procedure information the regular log information that the invention is intended to produce, and then come the reconstruct flow process from the angle of carrying out flow process between business rule from regulation engine.
One, dependency rule is formulated
At first provide some following definition:
Definition (1) fact: the fact fBy tlv triple
Figure 161907DEST_PATH_IMAGE018
Form, wherein:
1) the true type I D of
Figure 896645DEST_PATH_IMAGE019
expression
2)
Figure 443164DEST_PATH_IMAGE020
representes true ID
3) the true number of times that in same instance (i.e. the set of a regular task, be used in combination together and make final decision), is updated of
Figure 288760DEST_PATH_IMAGE021
expression with the form of workflow
Definition (2) regular Rule: rule be a doublet (LHS, RHS), wherein:
1) LHS is left-hand component (Left-Hand-Side), i.e. the set of one group of limited said conditions in rule;
2) RHS is right-hand component (Right-Hand-Side), i.e. the set of the limited number action of a group in rule.
Definition (3) regular flow track, regular flow daily record: make that T is the set of regular task, then
Figure 750308DEST_PATH_IMAGE010
Represent a regular trajectory mark,
Figure 655947DEST_PATH_IMAGE011
Be a regular flow daily record, wherein Be Power set.
Contain one or more regular flow track in the regular daily record, every corresponding at least one instance of regular trajectory mark.Through analyzing the information such as occurrence frequency that whole regular flow log information can obtain the regular flow track, be the procedure information that is being contained between every regular trajectory mark and the present invention paid close attention to.To the integrity issue of regular log information, suppose that log information recording does not have noise, promptly be complete, this point is consistent with traditional digging flow method based on event log.
Definition (4) triggers relation based on the rule of the fact: make g be regular set of tasks T (promptly
Figure 906035DEST_PATH_IMAGE022
) on the regular flow daily record, with
Figure 920258DEST_PATH_IMAGE023
/
Figure 175790DEST_PATH_IMAGE024
The involved fact collection of the difference pairing LHS/RHS of delegate rules r, and the renewal frequency of the true f of π (f) expression:
Suppose to exist track
Figure 130233DEST_PATH_IMAGE025
; Wherein and ,
Figure 43460DEST_PATH_IMAGE028
:
1.
Figure 533085DEST_PATH_IMAGE029
? iff
Figure 310548DEST_PATH_IMAGE030
same.
2.
Figure 728891DEST_PATH_IMAGE031
? iff?
Figure 224594DEST_PATH_IMAGE032
.
3.
Figure 255260DEST_PATH_IMAGE033
? iff?
Figure 152809DEST_PATH_IMAGE034
.
4.
Figure 742054DEST_PATH_IMAGE035
? iff?
Figure 459474DEST_PATH_IMAGE036
.
Suppose to exist an other regular trajectory mark
Figure 290901DEST_PATH_IMAGE037
, it shares some identical regular task with track .Make
Figure 803102DEST_PATH_IMAGE039
, then:
5.
Figure 7819DEST_PATH_IMAGE040
? iff
Figure 645867DEST_PATH_IMAGE041
.
Need to prove that preceding four relations are based on same regular trajectory mark, last definition then is based on two different rules trajectory marks under the same regular flow daily record.Can find out from above-mentioned definition, just can find most relation through the fact of analyzing in every rule in the single track.To mainly rely on above-mentioned relation in the method.
Two, method realizes
The present invention has realized the digging flow method of rule-oriented execution journal with ProM (a digging flow instrument of the increasing income) form of plug-in unit, below with its called after α-r method when proposing the digging flow technology of rule-oriented execution journal.Its implementation procedure is following:
α-r method implementation procedure
------------------------------------------------------------------------------------------
Input input: regular flow daily record
Output output: with the process flow diagram of Petri net modeling
1, for each the bar rule path
Figure 875488DEST_PATH_IMAGE002
in the regular flow daily record
Figure 183476DEST_PATH_IMAGE042
, do:
1.2, for regular track
Figure 314297DEST_PATH_IMAGE002
Each regular task t, do:
1.2.1, if tBe Middle article one rule task, so tIt is exactly flow process
Figure 877314DEST_PATH_IMAGE004
Starting point
1.2.2, obtain the corresponding related fact collection of LHS of this rule task FL (r)
1.2.3, obtain the corresponding related fact collection of RHS of this rule task FR (r)
If 1.2.4 FL (r)Be sky
1.2.4.1, regular task tIt is flow process
Figure 56623DEST_PATH_IMAGE004
Terminal point.
1.2.5, for regular task tThe regular task of afterwards each T', do:
1.2.5.1, obtain should the rule task in rule R'The corresponding related fact collection of LHS FL (r')
1.2.5.2, obtain should the rule task in rule R'The corresponding related fact collection of RHS FR (r')
1.2.5.3, if FL (r)With FL (r')In true renewal frequency all identical, then tWith T'Exist
Figure 962438DEST_PATH_IMAGE005
Relation;
1.2.5.4, if FR (r)With FL (r')At least there is an identical fact, then tWith T'Exist
Figure 215696DEST_PATH_IMAGE006
Relation;
1.2.5.5, if FL (r)With FL (r')At least there is an identical fact, then tWith T'Exist
Figure 190343DEST_PATH_IMAGE007
Relation;
If 1.2.6 FR (r)In regular task tNever triggered any rule afterwards, so tIt is exactly flow process
Figure 529051DEST_PATH_IMAGE003
Terminal point.
1.3, for regular track
Figure 250276DEST_PATH_IMAGE002
In any two regular tasks t, T'Rule r, R', if FL (r)With FL (r')Be empty set perhaps tWith T'All and track In the Else Rule task do not exist
Figure 503589DEST_PATH_IMAGE006
Relation, then tWith T'Exist
Figure 391910DEST_PATH_IMAGE008
Relation.
2, merge result and discovery
Figure 212099DEST_PATH_IMAGE009
relation of excavating by above-mentioned steps.
3, through Petri net form formula final excavation result is carried out modeling.
------------------------------------------------------------------------------------------
Note the structure of above form, be divided into for three steps, wherein the first step mainly is to trigger the step of relation between mining rule; Second step was in order to find the choice relation between Different Rule trajectory mark; The 3rd step was the demonstration of Petri figure.
The realization flow of whole α-r method has more than been described; Each bar rule track for the regular flow daily record; Excavate and find the cause and effect between its regular task, relation such as parallel,, find the choice relation between the regular task for the analysis of different rules track.At last, after all relations came to light, AND-Split and AND-Join were used to the expression of concurrency relation, and OR-Split and OR-Join then are used to the expression of choice relation, and these provide the rule digging process flow diagram with the form of Petri figure in the lump.
Three, excavate architecture design
Rule-based digging flow finally shows with the form of Petri net through the conversion of regular log collection, daily record, the excavation of algorithm, the modeling several steps of Petri net.The integral body that the present invention provides is excavated framework and is divided into three parts: regular log collection, regular daily record conversion and digging flow.Detailed description will be explained at Fig. 4.
Four, object lesson
Fig. 1 representes that the rule based on the fact solves graph of a relation in α-r method.According to definition 4; But MS system "
Figure 3730DEST_PATH_IMAGE043
" expression begins the regular task carried out at first, when promptly move in system in the rule base at first by the regular task of parallel triggering.Relation " " expression parend; Be present under two kinds of different situations, do not relate in the promptly regular task any fact or the rule RHS in the involved fact can't trigger other rule again.Between two rules of "
Figure 259579DEST_PATH_IMAGE045
" expression direct cause and effect dependence is arranged.From the workflow angle, relation "
Figure 883459DEST_PATH_IMAGE046
" has been represented the initial node of each parallel branch.Last relation " " is based on two different tracks, so be choice relation between its expression rule.
Fig. 2 is a regular daily record matched rule record sheet, specifies the principle of rule-based digging flow algorithm with this diagram data.Every row is represented a rule coupling log record among the figure; Have four row; Be respectively Case ID, LHS (Conditions), Fired Rule ID and RHS (Actions), condition part, the rule of triggering and the action that triggers of representing use-case sign, rule to trigger respectively.Be recorded as example with article one, Case ID is 1, and LHS is f (1,1; 0), f (2,1,0); It is 0 that two facts and their initialized update times are used in expression, and Rule is A, and expression has triggered regular A; RHS is Update f (2,1,1); Expression has been upgraded true f (2,1,0) feasible and has been increased to 1 from 0.
Fig. 3 is based on Fig. 2 data, the regular process flow diagram of analyzing out through rule-based digging flow principle.Fact collection among Fig. 2 is { f 1,f 2, f 3, comprise three kinds of true types, two regular flow path are arranged, be respectively 1-2-3-4-6-7 and 1-2-3-5-6-7.At first, in two Case, start node all is 1, and end node all is 7.In first Case, see preceding two recorded informations, the LHS of second knows that according to definition (8) rule 1 and 2 is a cause-effect relationship corresponding to the Actions of article one, and 1-2.In like manner visible, rule 2 and 4 also is the priority cause-effect relationship.For rule 1 and 3, rule 1 corresponding Actions is the part of the LHS of rule 3 correspondences, and another part is f (3; 1,0), update times is 0; Can know that according to definition (2) (definition of the fact) this fact preexists in true concentrating, therefore rule 1 and 3 also is the priority cause-effect relationship.And rule 4 and 6, similar rule 1 and 3 contains f (2 among the LHS of regular 6 correspondences that different is; 1,1), this fact is f (2; 1,0) fact is once upgraded in triggering rule 1 back, before triggering rule 6, should the fact exist; So also be reasonably, as a result rule 4 and 6 also is the priority cause-effect relationship.Can know that in like manner rule 6 and 7 also is the priority cause-effect relationship.Next the concurrency relation between analysis rule.For rule 2 and rule 3, the triggering fact of rule 2 is f (2,1,1); The triggering fact of rule 3 is f (2,1,1) and f (3,1; 0), both have the true f (2,1,1) of identical triggering; And f (3,1,0) is the true fact of storage in advance of concentrating, and can know that according to the definition of concurrency relation between the middle rule of definition (8) 2 and 3 are concurrency relation.Can know that in like manner rule 3 and rule 6 also are concurrency relations.For second Case, it also is the same analyzing the result who obtains in the same way.And the excavation of choice relation (OR) obtains through analyzing on Case1 and the Case2 integral body.
Fig. 4 representes rule-based digging flow integrated stand composition, and being divided into is three parts: Business Rule Engine, XESame and ProM.1) Business Rule Engine (regular log collection).This is the source of regular record log information, is whole framework and outside mutual part.The enterprise business rule engine is in the regular record information of run duration with all operations of form record of daily record; The file type of record can be " .csv ", " .xls ", " .txt " or the like, and this paper adopts the Data Source form of the file of " .csv " type as experiment.2) XESame (regular daily record conversion).XESame is an auxiliary instrument of increasing income of realizing the journal format translation function.Its major function is the configuration through mapped file, the Rule Information of Business Rule Engine generation is converted to " .xes " file that meets the ProM input of standard from skimble-scamble file layouts such as " .csv ", " .xls ", " .txt ".This step can be regarded as the processing section in regular log information source.3) ProM (digging flow).ProM is the excavation framework of increasing income, and excavates with the form support process of plug-in unit." .xes " file that it generated with second step is as the input source, the excavation of the α-r method through carrying out excacation with card format, and cooperate the modeling of Petri net, finally form digging flow figure as a result.This step is the core of whole framework, and it has constituted whole excavation and display part with second step.
The above only is a preferred implementation of the present invention; Should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the present invention's design; Can also make some improvement and retouching, these improvement and retouching also should be regarded as in the protection domain of the present invention.

Claims (3)

1. the digging flow method of a rule-oriented execution journal is characterized in that, comprises the steps:
1) obtains regular flow daily record and be converted into the ProM input format of standard;
2) to the regular flow daily record after the conversion
Figure 55839DEST_PATH_IMAGE001
In each bar rule track Each regular task tInquire about, if tIt is regular track
Figure 106152DEST_PATH_IMAGE002
Middle article one rule task, then tIt is exactly flow process Starting point;
3) obtaining should the rule task tThe corresponding related fact collection of LHS FL (r)The fact collection related with the RHS of correspondence FR (r)
4) right FL (r)Judge, if empty, then regular task tIt is flow process
Figure 119818DEST_PATH_IMAGE004
Terminal point; If be not empty, then
For regular task tThe regular task of afterwards each T', acquisition should the rule task T'Middle rule R'The corresponding related fact collection of LHS FL (r')The fact collection related with the RHS of correspondence FR (r')Judge FL (r)With FL (r')Relation, if the true renewal frequency among both is all identical, then tWith T'Exist Relation; If there is an identical fact at least in both, then tWith T'Exist Relation; If there is an identical fact at least in both, then tWith T'Exist Relation; If FR (r)In regular task tNever triggered any rule afterwards, so tIt is exactly flow process
Figure 61043DEST_PATH_IMAGE003
Terminal point;
5) for regular track
Figure 251591DEST_PATH_IMAGE002
In any two regular tasks t, T'Rule r, R', if FL (r)With FL (r')Be empty set perhaps tWith T'All and track
Figure 926286DEST_PATH_IMAGE002
In the Else Rule task do not exist
Figure 387354DEST_PATH_IMAGE006
Relation, then tWith T'Exist
Figure 754881DEST_PATH_IMAGE008
Relation;
6) merge result and discovery relation of excavating by above-mentioned steps;
7) through Petri net form formula final excavation result is carried out modeling;
Above-mentioned rule be a doublet (LHS, RHS), wherein: LHS is a left-hand component, i.e. the set of one group of limited said conditions in rule; RHS is a right-hand component, i.e. the set of the limited number action of a group in rule; Make that T is the set of regular task; Then
Figure 710778DEST_PATH_IMAGE010
representes a regular trajectory mark;
Figure 291932DEST_PATH_IMAGE011
is a regular flow daily record; Wherein
Figure 564782DEST_PATH_IMAGE012
is the power set of
Figure 231386DEST_PATH_IMAGE013
; Said
Figure 746419DEST_PATH_IMAGE005
expression begins the regular task carried out at first, when promptly move in system in the rule base at first by the regular task of parallel triggering; Said relation expression parend; Be present under two kinds of different situations; Be do not relate in the regular task any fact or the rule RHS in the involved fact can't trigger other rule again; Between two rules of said expression direct cause and effect dependence is arranged; Relation
Figure 842048DEST_PATH_IMAGE007
has been represented the initial node of each parallel branch; Last relation
Figure 662237DEST_PATH_IMAGE009
is based on two different tracks, so be choice relation between its expression rule.
2. the digging flow method of a kind of rule-oriented execution journal according to claim 1 is characterized in that,
Said true f is made up of tlv triple ;
Figure 322381DEST_PATH_IMAGE015
representes true type I D;
Figure 697999DEST_PATH_IMAGE016
representes true ID; The true set a regular task of
Figure 56299DEST_PATH_IMAGE017
expression is used in combination and makes with the form of workflow the number of times that is updated in the final decision together.
3. the digging flow method of a kind of rule-oriented execution journal according to claim 1; It is characterized in that; Make that g is the regular flow daily record on the regular set of tasks T (i.e.
Figure 965087DEST_PATH_IMAGE018
); With /the involved fact collection of
Figure 941450DEST_PATH_IMAGE020
difference pairing LHS/RHS of delegate rules r; And the renewal frequency of the true f of π (f) expression: when there being track ; Wherein and
Figure 826120DEST_PATH_IMAGE023
, when
Figure 114013DEST_PATH_IMAGE024
:
Figure 79695DEST_PATH_IMAGE025
? iff
Figure 697496DEST_PATH_IMAGE026
the same;
Figure 824852DEST_PATH_IMAGE027
? iff?
Figure 600041DEST_PATH_IMAGE028
;
Figure 605299DEST_PATH_IMAGE029
? iff?
Figure 844651DEST_PATH_IMAGE030
;
Figure 142908DEST_PATH_IMAGE031
? iff?
Figure 467710DEST_PATH_IMAGE032
;
When there being an other regular trajectory mark
Figure 273730DEST_PATH_IMAGE033
; It shares some identical regular task with track
Figure 102009DEST_PATH_IMAGE034
, makes
Figure 836747DEST_PATH_IMAGE035
:
Figure 383266DEST_PATH_IMAGE036
? iff
Figure 995906DEST_PATH_IMAGE037
.
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