Source: http://www.google.com/patents/USRE36602?dq=6016038
Timestamp: 2015-05-24 10:40:48
Document Index: 488476892

Matched Legal Cases: ['art. 15', 'art.\n16', 'art.\n17', 'art.\n28', 'art.\n36', 'art.\n40']

Patent USRE36602 - Concurrent engineering design tool and method - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inAdvanced Patent SearchPatentsA computer-based engineering design system to design a part, a tool to make the part, and the process to make the part. The design system has a processor and a memory. The memory stores feature templates, each feature template being a representation of a primitive object having a form and a function....http://www.google.com/patents/USRE36602?utm_source=gb-gplus-sharePatent USRE36602 - Concurrent engineering design tool and methodAdvanced Patent SearchPublication numberUSRE36602 EPublication typeGrantApplication numberUS 08/882,838Publication dateMar 7, 2000Filing dateJun 26, 1997Priority dateNov 24, 1993Fee statusPaidAlso published asUS5552995, US5822206Publication number08882838, 882838, US RE36602 E, US RE36602E, US-E-RE36602, USRE36602 E, USRE36602EInventorsDonald H. Sebastian, Steven Pratt, Sivakumar Muthuswamy, David Kniep, Souran Manoochehri, Scott KolodzieskiOriginal AssigneeThe Trustees Of The Stevens Institute Of TechnologyExport CitationBiBTeX, EndNote, RefManPatent Citations (9), Non-Patent Citations (197), Referenced by (47), Classifications (13), Legal Events (4) External Links: USPTO, USPTO Assignment, EspacenetConcurrent engineering design tool and method
US RE36602 EAbstract
1. A computer-based engineering design system to design a part, a tool to make the part, and the process to make the part, comprising: a processor,a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a representation of a primitive geometric entity having the form of the primitive object, each feature template including information relating to a tool to make the primitive object and a process to make the primitive object; an input device coupled to the processor receiving a request to design the part, the request including one or more predetermined functions that the part performs; and a core design module executable by the processor, the core design module designing the part, the tool to make the part and process to make the part by accessing the plurality of feature templates in the memory to locate one or more primitive objects that perform the one or more predetermined functions. 2. The engineering design system of claim 1 further comprising an output device coupled to the processor, the output device displaying a graphical representation of the primitive geometric entity corresponding to each one or more primitive objects located by the processor.
3. The engineering design system of claim 2 wherein at least one primitive geometric entity is displayed on the output device at a location on the output device specified by a user.
4. The engineering design system of claim 2 wherein at least one primitive geometric entity is displayed on the output device at a location on the output device specified by the core design module.
5. The engineering design system of claim 2 wherein at least one primitive geometric entity is displayed on the output device at a location on the output device specified by the core design module and a user.
6. The engineering design system of claim 2 wherein at least one primitive geometric entity is displayed on the output device at a location on the output device specified in the feature template that includes the primitive geometric entity.
7. The engineering design system of claim 1 wherein a set of dimensions for each primitive geometric entity corresponding to each one or more primitive objects located by the processor is specified by a user.
8. The engineering design system of claim 1 wherein a set of dimensions for each primitive geometric entity corresponding to each one or more primitive objects located by the processor is determined by the core design module.
9. The engineering design system of claim 1 further comprising an interface to a computer-aided drafting system, the interface coupled to the processor and transmitting to the computer-aided drafting system a set of instructions defining the primitive geometric entity corresponding to each one or more primitive objects located by the processor.
10. The engineering design system of claim 1 wherein each feature template is indexed by the form of the primitive object represented in the template.
11. The engineering design system of claim 1 wherein each feature template represents a primitive object having more than one function.
12. The engineering design system of claim 1 wherein each feature template represents a primitive object having one or more functions.
14. A computer-based design system to design a part, a tool to make the part, and the process to make the part, the part comprising a plurality of sub-parts, the design system comprising:a processor; a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a representation of a primitive geometric entity having the form of the primitive object, each feature template including information relating to a tool to make the primitive object and a process to make the primitive object; an input device coupled to the processor receiving a set of instructions, each instruction in the set of instructions referring to a sub-part and specifying the function that the sub-part performs; and a core design module executable by the processor, the core design module designing the part, the tool to make the part and process to make the part by accessing the plurality of feature templates in the memory to locate for each instruction a primitive object that performs the function specified for the sub-part. 15. The engineering design system of claim 14 wherein the core design module further comprises means for combining the sub-parts to create the part.
16. The engineering design system of claim 14 wherein the core design module simultaneously designs the part, the tool to make the part and the process to make the part.
17. A computer-based engineering design system to assist in designing a part and a tool to make the part, the system comprising:a processor, a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a representation of a primitive geometric entity having the form of the primitive object, each feature template including information relating to a tool to make the primitive object; an input device coupled to the processor receiving a request to design the part, the request including a predetermined function that the part performs; and a core design module executable by the processor, the core design module designing the part and the tool to make the part by accessing the plurality of feature templates in the memory to locate the primitive object that best performs the predetermined function. 18. The engineering design system of claim 17 further comprising an output device coupled to the processor, the output device displaying a graphical representation of the primitive geometric entity corresponding to the primitive object located by the processor.
19. The engineering design system of claim 18 wherein the graphical representation of the primitive geometric entity is displayed on the output device at a location on the output device specified by a user.
20. The engineering design system of claim 18 wherein the graphical representation of the primitive geometric entity is displayed on the output device at a location on the output device specified by the core design module.
21. The engineering design system of claim 18 wherein the graphical representation of the primitive geometric entity is displayed on the output device at a location on the output device specified by the core design module and a user.
22. The engineering design system of claim 18 wherein the graphical representation of the primitive geometric entity is displayed on the output device at a location on the output device specified in the feature template.
23. The engineering design system of claim 18 wherein a set of dimensions for the primitive geometric entity corresponding to the primitive object located by the processor is specified by a user.
24. The engineering design system of claim 18 wherein a set of dimensions for the primitive geometric entity corresponding to the primitive object located by the processor is determined by the core design module.
25. The engineering design system of claim 17 further comprising an interface to a computer-aided drafting system, the interface coupled to the processor and transmitting to the computer-aided drafting system a set of instructions defining the primitive geometric entity corresponding to the primitive object located by the processor.
26. The engineering design system of claim 17 wherein each feature template is indexed by the form of the primitive object represented in the template.
27. The engineering design system of claim 17 wherein the core design module simultaneously designs the part and the tool to make the part.
28. A computer-based engineering design system to assist in designing a product and a tool to make the product, the system comprising:a processor, a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a representation of a primitive geometric entity having the form of the primitive object, each feature template including information relating to the tool to make the primitive object; an input device coupled to the processor receiving a request to design the product, the request including a predetermined function that the product performs; and means for simultaneously designing the product and the tool to make the product by accessing the plurality of feature templates in the memory to locate the primitive object that best performs the predetermined function. 29. A computer-based design system to assist in the simultaneous design of a part, a tool to make the part, and a process to make the part, the design system comprising:a processor, a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a form information relating to the primitive object, tool information relating to a tool to make the primitive object and process information relating to a process to make the primitive object; an input device coupled to the processor receiving a request to design the part, the request including a predetermined function that the part performs; and a core design module executable by the processor, the core design module simultaneously designing the part, the tool to make the part and the process to make the part by accessing the plurality of feature templates in the memory to locate one or more feature templates representing primitive objects that perform the predetermined function. 30. The design system of claim 29 wherein each feature template further comprises material information relating to a material with which to make the primitive object that the feature template represents.
31. A computer-based design system to assist in the simultaneous design of a complex object, a tool to make the complex object, and a process to make the complex object, the design system comprising:a processor, a memory coupled to the processor, the memory storing a plurality of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including a form information relating to the primitive object, tool information relating to a tool to make the primitive object and process information relating to a process to make the primitive object; an input device coupled to the processor receiving a request to design the complex object, the request including a predetermined function that the complex object should perform; and a core design module executable by the processor, the core design module simultaneously designing the complex object, the tool to make the complex object and the process to make the complex object by accessing the plurality of feature templates in the memory to locate one or more feature templates representing primitive objects that perform the predetermined function. 32. A method to design a part, a tool to make the part and a process to make the part, comprising the steps of:receiving a set of constraint relationships that specify the desired function of the part; selecting a material with which to make the part; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including part information including at least one representation of a primitive geometric entity having the form of the primitive object, each feature template further including tool information and process information relating to the primitive object; accessing the set of feature templates to obtain a selected feature template being a representation of a primitive is object having the desired function and capable of being made from the selected material; and concurrently designing a part drawing, a tool drawing and a process specification to make the part by utilizing the part information, the tool information and the process information in the selected feature template. 33. The method of claim 32 further comprising the step of displaying a representation of the part drawing on an output device by plotting a representation of the primitive geometric entity corresponding to the selected feature template.
34. The method of claim 32 further comprising the step of outputting the part specification to a tooling generator to produce a prototype tool.
35. The method of claim 32 further comprising the step of utilizing the part drawing, the tool drawing and the process specification to make the part.
36. The method of claim 32 further comprising the step of utilizing the part drawing, the tool drawing and the process specification to make a part specification.
37. The method of claim 36 further comprising the step of inputting the part specification as a set of constraints to an automated design system.
38. A method to concurrently design a part, a tool to make the part and a process to make the part, comprising the steps of:receiving a set of constraint relationships that specify the desired function of the part, the part having a plurality of sub-parts; for each sub-part, receiving a set of constraint parameters that specify the desired function of the sub-part; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including form information, tool information and process information relating to the primitive object; for each sub-part of the part, accessing the set of feature templates to retrieve a selected feature template for each sub-part being a representation of a primitive object having the desired function of the sub-part; combining the form information in the selected feature templates for each sub-part to create a part drawing; and concurrently with the previous step, designing a tool drawing and a process specification by utilizing the tool information and the process information in the selected feature templates. 39. The method of claim 38 wherein the step of combining further comprises the step of providing connectivity information for all sub-parts in the part.
40. The method of claim 38 wherein the step of combining further comprises the step of providing parametric relationships between sub-parts.
41. A method to design a part, a tool to make the part and a process to make the part comprising the steps of:receiving a set of constraint relationships that specify the desired function of the part; selecting a material with which to make the part; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including form information, tool information and process information relating to the primitive object; accessing the set of feature templates to obtain a selected feature template being a representation of a primitive object having the desired function and capable of being made from the selected material; and concurrently designing a part drawing, a tool drawing and a process specification to make the part by utilizing the form information, the tool information and the process information in the selected feature template. 42. A method to concurrently design a part having a plurality of sub-parts, a tool to make the part and a process to make the part, comprising the steps of:for each sub-part, receiving a set of constraint parameters that specify the desired function of the sub-part; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including form information, tool information and process information relating to the primitive object; for each sub-part of the part, accessing the set of feature templates to retrieve a selected feature template for each sub-part being a representation of a primitive object having the desired function of the sub-part; combining the form information in the selected feature templates for each sub-part to create a part drawing; and concurrently with the previous step, designing a tool drawing and a process specification by utilizing the tool information and the process information in the selected feature templates. 43. In a computer-based design system, a method for designing a part, comprising the steps of:providing a set of part templates each representing an object that has a form and a function, each part template including form information; providing a set of tool templates each representing a tool to make an object, each tool template including tool information; providing a set of process templates each representing a process to make an object, each process template including process information; providing a set of feature templates, each feature template associated with a part template, a tool template and a process template; receiving a set of constraint relationships, the constraint relationships including a desired function for an object under design; accessing the set of feature templates to retrieve a selected part template representing an object having the desired function, an associated tool template and an associated process template; and utilizing the form information in the selected part template, the tool information in the associated tool template and the process information in the associated process template to concurrently design a part drawing, a tool drawing and a process specification. 44. A method to design a product, a tool to make the product and a process to make the product comprising the steps of:receiving a set of constraint relationships that specify the desired function of the product; selecting a material with which to make the product; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including form information, tool information and process information relating to the primitive object; accessing the set of feature templates to obtain a selected feature template being a representation of a primitive object having the desired function and capable of being made from the selected material; and concurrently designing a product drawing, a tool drawing and a process specification to make the product by utilizing the form information, the tool information and the process information in the selected feature template. 45. A method to concurrently design a product having a plurality of sub-parts, a tool to make the product and a process to make the product, comprising the steps of:for each sub-part, receiving a set of constraint parameters that specify the desired function of the sub-part; providing a set of feature templates, each feature template being a representation of a primitive object having a form and a function, each feature template indexed by the function of the primitive object and including form information, tool information and process information relating to the primitive object; for each sub-part of the product, accessing the set of feature templates to retrieve a selected feature template for each sub-part being a representation of a primitive object having the desired function of the sub-part; combining the form information in the selected feature templates for each sub-part to create a product drawing; and concurrently with the previous step, designing a tool drawing and a process specification by utilizing the tool information and the process information in the selected feature templates. Description
Automated processes are known for certain elements of the design process, but these are of limited application. For example, Flexible Computer Integrated Manufacturing (FCIM) is a known automated approach to produce a variety of parts for a given automated system. Quality Functional Deployment (QFD) is a known process that is used to help determine functional requirements from customer needs. Many attempts have been made to develop intelligent design systems using different implementations strategies. One implementation method is to integrate a commercial CAD system with an expert system inference engine. Some have attempted to integrate an expert system shell with a solid modeler. Another known approach is to use an existing knowledge-based engineering tool which already provides geometric modeling capabilities and mechanisms for embedding heuristic knowledge in the form of rules and methods. Systems developed using the above mentioned approaches have shortcomings due to the limitations of the commercial software packages which they are built around. None of these known tools or processes fully integrate part tool and process design. Further, no known system represents all the knowledge for part, tool and process design in a systematic way so that this knowledge can be used in all stages of the design process.
The method of the present invention initially begins at the start of the manufacturing "food chain", piece part design. Without good part design, subassemblies cannot be reliably designed, and without reliable sub-assemblies, defective product designs will abound.
The representative embodiment of the present invention comprises five modules, namely, a material selector module, an engineering economics estimator module, a core design module (that performs the integrated design phase), a tooling generator and a tool fabrication process planner module. Once the customer requirements for the new product are ascertained and a preliminary design concept has been determined, the present invention is first used to help decide appropriate materials and production economics criteria.
The knowledge representation scheme of the present invention enables engineering economics to be given to a user. For example, once the part, tool and process design have been established, the system can access on-line data-bases or stored information to determine the cost producing the part in different geographic areas, the cost of producing two parts per mould compared with three parts per mould, and which machines are needed to produce the part and the cost of such machines. Thus, it can be determined if it is feasible to produce the part within budget. The system can inform the user of breakdown of its estimated production cost (e.g., inform the user that the material cost is the greatest cost) to enable the user to redesign the part, tool or process so that budgets are met.
TABLE 1______________________________________          FormFeature        (primitive(primitive object)          geometric entity)                         Function______________________________________Feature class-wallUniform thickness          Rectangular Prism                         Support                         Shield/                         AccessTapered        Trapezoidal Prism                         Support                         Shield/                         AccessStepped        Assembly of Walls                         SupportTriangular     Triangular Prism                         Support                         Shield/                         AccessCurved         Segment of     Support          Cylindrical Shell                         Shield/                         AccessFlat Disk      Circular Plate Support                         Shield/                         AccessHousingBox            5-Sided Rectangular                         Support          Box            Shield                         AccessRound          Cylinder closed one                         Support          end            Shield/                         AccessDome           Hemisphere     Support                         Shield/                         AccessProjectionRib            Rectangular Prism                         Support                         Flow-                         LeaderGusset         Triangular Prism                         Support                         Flow-                         LeaderPost           Cylinder       Support                         LocateBoss           Hollow Cylinder                         Fasten                         SupportDepressionHole           Cylinder       Locate                         Support                         Shield/                         AccessGroove         Rectangular Slot                         Locate                         Support                         Shield/                         AccessAssemblySnap           Clip           FastenHinge          Flexible Connection                         Support                         LocateHole for molded-          Cylinder       Fastenin-InsertRectangular    Rectangular Frame                         LocateFlange                        Support                         Shield/                         AccessCircular Flange          Circular Ring  Locate                         Support                         Shield/                         AccessDog-Ear-Flange Dog-Ear        Locate                         Support                         Shield/                         AccessHelical thread Helix          FastenJoinFillet         Concave Bead   Flow-                         Leader______________________________________
The present invention supports design at various design levels. For example, a feature template may, in the design process, represent a sub-part (such as a boss), a part (such as a gear), or an assembly or subsystem (comprising a number of parts), or a product or system. For conveniences the term "part" is used, but this term is not limited to part, and includes sub-part, assembly, subsystem and product. Accordingly, a feature template may represent any object in the design process, for example, from a screw to a completed product.
The next step is that of economies estimation (step 46). In the representative embodiment, this step is carried out by an engineering economics estimator module (74 of FIG. 4). At the economics estimation step 46, various design approaches are presented to the user to enable the user to determine production requirements that economically feasible. The economics estimator module can work with minimal information about a part (typically, less than is usually contained in a preliminary design sketch) to arrive at optimal choices. In the field of injection molded plastics, examples of decisions made at step 46 include mold and machine configuration, manufacturing locale, vendor of raw materials, production rate etc. It is noted that if, at a later design phase, revisions to a design are made, then new economic estimations can be presented to the user. At any stage, the user can change the parameters decided at this step, and the present invention will automatically update cost estimates etc. that are effected by such changes.
The representation system 76a of the present invention can be regarded as the hub of the concurrent design process. As such, it can freely interchange data with existing commercial software from a variety of environments. This eliminates the need to create a wide variety of system functionalities that are presently available. For example, the present invention can export data to spreadsheet and scientific graphics packages, and export graphics and reports to word processing and. desktop publishing programs.
The representative embodiment supports, amongst others, the following interfaces: to CAD systems--IGES, Pro-Engineer and IDEAS; for FEM structural analysis--PATRAN/NASTRAN and IDEAS; for FEM molding filling, cooling and shrinkage analysis--C-FLOW, IDEAS, Mold-flow and TMC; and for tool design--IDEAS, Pro-Engineer and DME Moldbase Catalog.
In the representative embodiment the Pro-Engineer CAD system, available from Parametric Technology Inc, is used as the rendering engine 104. The representation system 76a interfaces with Pro-Engineer to create drawings of the part and tool design, as discussed below. The rendering engine 104 can display a graphical representation of the surfaces generated by the geometry engine 102. The rending is sufficiently rapid to allow realtime interaction with the part (e.g., scaling, translation, rotation, zooming of views).
______________________________________Restore("BasicObjects")Loads basic wall and boss templates andmaterial properties into the system.ListT()Lists available templatesListI()Lists available instances of templatesListG()Lists other objects in the systemCreate1(:WallTemplate, BaseWall)creates a base wall; the system will queryfor three size dimensions and placementinformation.Create1(:WallTemplate, SideWall1)Create1(:WallTemplate, SideWall2)Create1(:WallTemplate, SideWall3)Create1(:WallTemplate, SideWall4)creates four side walls; the system willquery for the three side dimensions andplacement information for each wall.Create1(:BossTemplate, Boss1)creates a boss; the system will query forheight and diameter dimensions and placementinformation for the boss.ModifyAttr(:Boss1, X, :BaseWall.Width/2)ModifyAttr(:Boss1, Y, :BaseWall.Length/2)used to move the boss to the center of theplate if not placed correctly. These twostatements define a parametric relationshipwhich constrains the boss to the center of thebase wall.ModifyAttr(:Boss1, X, 1.0 + :Basewall.Width/2)ModifyAttr(:Boss1, Y, 1.0 + :BaseWall.Length/2)Constrains the boss to be offset one inch inthe X and Y directions form the centre of thebase wall.CreateO(PartData)AddAttr(:PartData, Material, :Nylon)AddAttr(:PartData, MaxCost, :1.00)AddAttr(:PartData, PartCost,Cost(Material.PricePerPound))AddAttr(:BaseWall, Pressure, 5.0)ModifyAttr(:Boss1, Diameter,1.2*:BaseWall.Thickness)modifies the diamter attribute of the bossModifyAttr(:BassWall, Thickness, 0.125)modifies the thickness of the base wall.ModifyAttr(:PartData, Material, :PolyCarbonate)change the material to polycarbonateSave("work")saves the modelRestore("work")retrieves the modelAddAttr(:WallTemplate, WallVolume,Length*Width*Thickness)AddAttr(:WallTemplate, VolumeConstraint,WallVolume &gt; 25.0)adds a volume constraint; these twoinstructions an attribute and compute thevolume. The computed volume is used toevaluate the volume constraint.CreateT(SeparationWallTemplate, `GenCost`, `Wall`)creates a new template named"SeparationWallTemplate"AddAttr(:SeparationWallTemplate, Thickness,0.75 * AttachedWall().Thickness)adds a constraint that the separation wall'sthickness is always 0.75 times the attachedwall's thicknessCreate1(:SeparationWallTemplate, SeparationWall)creates a new insuance of a wall; the systemwill query for the size dimensions andplacement information.______________________________________
The present invention supports the grouping of sub-parts into new sub-parts or parts. Accordingly, a macro-feature template can be created, as discussed above, being an assembly of feature templates and/or other macro-feature templates. A macro-feature is therefore an instance of an assembly of objects created according to a macro-feature template.
The present invention provides a group of external objects that characterize interactions between the part under design and the part's environment. Typical interactions in this category include structural thermal and EMI constraints. Additionally, parts which have been previously designed can be introduced to the design of a new part as an external object.
The following is an a description of a high level pseudo-code describing the functions performed by the core design module 76 when adding a new instance of a template. This pseudo-code is representative only, and in this example, is limited to creating a housing for an electrical component:
Successful design or injection molded plastic parts requires extensive knowledge of material properties and behavior, tooling, injection conditions and other processing parameters. This complex relationship between plastic product design and the cost and quality of the product demands design experts with many years of experience who understand the interaction of these variables.
v Maintains the current value of f(value(cval(A)))
Given some universe of "symbols" Σ. ##EQU6##
Σ contains a special symbol .di-elect cons. which is equivalent to "no symbol" or the "empty symbol", and has the following properties:
a,b .di-elect cons.&#931;&#923;(a&#8802;&#949;&#923;b&#8802;&#949;).fwdarw.a.tbd.b v a&#8802;b a,b .di-elect cons.&#931;&#923;(a.tbd.&#949;v b.tbd..di-elect cons.)&#8594;a&#8802;b
R Represents a set of"actual" references that a given dependent object depends on.
The function resolves is a predicate that defines when a "symbolic" reference "resolves" or "identifies" a dependent object. ##EQU7##
The function independent is a predicate that defines when a given dependent object is "independent", i.e. it has no symbolic references ##EQU8##
The function add-- references adds an "actual" reference to a dependent object provided that the actual reference is resolved by some "symbolic" reference in the dependent object. ##EQU9##
The function remove-- reference removes an "actual" reference from a given dependent object. ##EQU10##
The function unresolved-- references computes all of the "symbolic" references that do not have a corresponding "actual" reference. ##EQU11##
The function satisfied is a predicate that defines when a dependent object is satisfied, i.e. there exists an "actual" reference for each of the "symbolic" references in a given dependent object. ##EQU12##
The function resolve-- references resolves all possible "symbolic" references given a universe of dependent objects. ##EQU13##
The function resolved-- references returns the set of "actual" references already resolved against some universe of dependent objects. ##EQU14##
The set of unsatisfied objects USO is the subset of dependent objects that are unsatisfied, I.E.: ##EQU15##
The function satisfies computes the subset of unsatisfied objects that would be partially satisfied if the given dependent object was added to the set of dependent objects. ##EQU16##
The function resolve adds on "actual" reference to all unsatisfied objects that contain a "symbolic" reference to the given dependent object, resolve returns the set of fully satisfied objects that results from resolving references. ##EQU17##
The dependancy module is a triple: ##EQU18##
7.4.1 Functions on a dependency module ##EQU19##
Functions of Dependency Graph ##EQU20## Algorithm for detecting cycles in a directed graph Input: a digraph G.
Performance: Proportional to |E(G)|+|IV(G)|. ##EQU21##
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