Automatic Generation of Minimal and Safe Transactions in Conceptual Database Design

Transcription

1 Automatic Geeratio of Miimal ad Safe Trasactios i Coceptual Database Desig M. A. Pastor, M. Celma-Giméez, L. Mota-Herraz Departameto de Sistemas Iformáticos y Computació; Uiversidad Politécica de Valecia Camio de Vera s/ E Valecia España Telephoe: (+34) Ext Fax: (+34) {mapastor mcelma lmota}@dsic.upv.es Abstract The coceptual desig of iformatio systems usig a Etity-Relatioship Model is geerally thought to be limited to static features. Nevertheless, may dyamic aspects ca be derived from a Etity- Relatioship diagram sice the specificatio of differet costraits etails a determied miimal structure o the trasactios that ca be applied to such a system. May attempts have bee made to combie the Etity-Relatioship Model with other represetatio formalisms i order to model dyamic features. I our work, we propose a algorithm that obtais the set of miimal ad safe trasactios that ca be performed o the system. A update (isert or delete) trasactio o a object is said to be safe if it icludes, besides the update operatio, all other operatios o ay system objects which are required to satisfy the itegrity costraits. A safe trasactio is said to be miimal if there is ot a subset of the trasactio which is safe too. The miimal ad safe trasactios are the basic uits that ca be used to specify the more complex trasactios which model user requiremets. 1. Itroductio The Etity-Relatioship (ER) Model [1] is a vastly exteded coceptual model, ad it seems to cotiue beig frequetly used, sice it is preset i the stadard UML class diagram. This fact justifies the curret iterest for extedig ER with behavioural capabilities, that is, procedures which care for itegrity costrait eforcemet after trasactio executio [8]. Whe the ER Model is used to create a database coceptual schema, a diagram is obtaied [3,7]. This diagram represets the etity types that costitute the iformatio system ad also icludes the relatioship types betwee them. Thus, the diagram models the structural features of the system. Each diagram occurrece represets a sapshot of the system state. The dyamic features that ca be modeled are reduced to a set of itegrit y costraits that limit the valid occurreces of the diagram ad the, the allowed trasitios of states. The most geeral costraits are depicted i the ER Model by meas of differet symbols. The miimal update trasactios o ay diagram object which are safe with respect to these costraits ca be determied from the ER diagram idepedetly of the system state [6]. A update trasactio is a trasactio for isertig or deletig a object (the modificatio of a object is cosidered i this paper as a deletio followed by a isertio). A update trasactio is safe if it icludes, besides the update operatio o the iteded object, all other operatios o ay diagram objects which are required for satisfyig the itegrity costraits. A safe update trasactio is miimal if there is ot a subset of the trasactio which is safe too. The set of costraits that are cosidered i this paper are the followig: - The implicit costrait of the ER Model which determies that a relatioship ca exist oly if the correspodig participat etities also exist. - The implicit costrait of the ER Model which determies that a etity of a - specialized etity type is also a etity of the geeral etity type. - The costraits which force the iclusio of a etity of a geeral etity type ito the specialized etity types (total specializatio). If this costrait is ot required, the specializatio is partial. - The costrait which forbids a geeral etity type to be icluded i more tha oe of the specialized etity types (disjoit specializatio). If this costrait is ot required, the specializatio is said to be overlapped. - The cardiality costraits which defie the miimum ad maximum participatio of etities i relatioships.

2 The implicatios that all these costraits have i the trasactio desig ca be aalysed directly o the diagram. The set of operatios that must costitute a update trasactio ca be derived from that aalysis. I this paper, a algorithm that obtais the set of miimal ad safe trasactios with respect to these costraits is proposed. For each etity type ad each relatioship type of the diagram, ad isert trasactio schema ad a delete trasactio schema are geerated. 2. A Exteded Etity-Relatioship Model The Exteded Etity-Relatioship (EER) Model used i this paper icludes symbols for etity types, relatioship types with cardiality costraits ad weak etity types [5]. It also icludes idetificatio, uiqueess ad o ull value costraits for the attributes. Fially, it icludes geeralizatio/specializatio for the etity types ad the participatio of the relatioship types i other relatioship types by meas of their defiitio as aggregated etity types. All these symbols ca be see i Figure 1: a) Etity type (E) b) Relatioship type (R). Card: R(E(1,),F(0,1)) c) Weak etity type (E) E E 1 R F E R 1 d) Aggregated etity type (R) E R S F e) Geeral (E) ad specialized (F, G, H) etity types X={T P}, Y={D O} E X,Y G F G H f) Attributes a a a a Ordiary Idetifier Uique Not Null Figure 1: EER symbols Some features of the model are: (a) The represetatio of relatioship types icludes the cardiality costraits. The expressio R(E(1,), F(0,1)) i Figure 1 meas that each occurrece of E relates to x occurreces of F (1? x? ) through R ad that each occurrece of F is related to y occurreces of F (0? y? 1). If the miimum cardiality of a etity type is equal to 1, the it is said to have the Existece Costrait (EC) i R. (b) Weak etity types deped o their participatio i oe or more relatioship types for their idetificatio. They take the idetifier attributes from the etities they are related to through those special relatioship types. (c) The specialized etity types are coected to the geeral etity type through a circle by a lie. The specializatio properties (total or partial, ad disjoit or overlapped) are specified i the circle. The EER Model icludes also a trasactioal laguage with operators to update objects. A isertio operator (is) ad a deletio operator (del) are defied for etity types ad for relatioship types. Also two operators for isertig ad deletig specializatios are defied. The sytax of these operators is the followig: - INS_ENT NAME_ENT_TYPE {WHERE CONDITION ATTRIBUTES ATTRIBUTE_ASSIGNMENT_LIST} - INS_REL NAME_REL_TYPE WHERE CONDITION [ATTRIBUTES ATTRIBUTE_ASSIGNMENT_LIST] - INS_SPE NAME_SPE_TYPE WHERE CONDITION [ATTRIBUTES ATTRIBUTE_ASSIGNMENT_LIST]

3 - DEL_ENT NAME_ENT_TYPE [WHERE CONDITION] - DEL_REL NAME_REL_TYPE [WHERE CONDITION] - DEL_SPE NAME_SPE_TYPE [WHERE CONDITION] The coditio i the previous operatios is a formula expressed i a logical laguage which is similar to the relatioal tuple calculus. This formula icludes oly oe free variable which is defied o the type of object which is affected by the operatio. The differet assigmets that make the formula true correspod to the occurreces that must be iserted or deleted by the operatio. I the case of etity isertio, the coditio is optioal ad it would oly make sese for isertios from other etity types. I the relatioship isertio, this coditio is madatory i order to istace the compoets of the relatioship occurrece that is to be iserted, because it is assumed that, to isert a relatioship, the etities that are goig to associate i it already exist. I the same way, the isertio of a occurrece i a subclass requires that the correspodig occurrece exists i the geeral etity type. I the case of deletio operatios, the coditio is optioal; whe it is ot icluded, the deletio is applied to all the occurreces of the object type. 3. Approach to the solutio I order to desig the algorithm to geerate the set of safe trasactios, two kids of EER diagrams ca be cosidered: those without cycles ad the oes with cycles. A cycle exists if a object type depeds, direct or idirectly, o itself for isertio. Iitially, oly the former are aalysed. I sectio 4.2, the latter are take ito accout. Below, the procedure outlie is iformally described; it will be developed later: 1. Isertio. (a) Etity type: if the etity type has the existece costrait i some relatioship type, it is also ecessary to isert a occurrece i this relatioship type. (b) Relatioship type: if the relatioship type participates as aggregated etity with existece costrait i aother relatioship type, it is ecessary to isert a occurrece i this latter relatioship type, also. 2. Deletio. Deletio operatios are defied i two ways: restrictive ad i-cascade. I the restrictive way, as the system cotrols which costraits are fulfilled, if the deletio is goig to leave the database i a icosistet state, the deletio will ot be allowed. I the icascade way, apart from the iitial deletio operatio, those object occurreces which cause a icosistecy are also deleted. The selectio of oe of these choices must be doe with respect to each object type i which the origial deleted object participates. (a) Etity type: i. Restrictive with respect to a relatioship type R: it oly icludes the operatio of etity deletio. ii. I-cascade with respect to a relatioship type R: i additio to the deletio operatio of the etity, the deletio of the occurreces from R where the deleted etity participates is icluded i the trasactio. (b) Relatioship type: the deletio ca be of two types, as i the case of etity types. i. Restrictive with respect to a etity or relatioship type: it oly icludes the operatio of relatioship deletio. ii. I-cascade with respect to a etity type E or to a relatioship type R: if a etity participatig i the relatioship to be deleted has the existece costrait i it, the, besides the relatioship deletio, it is ecessary to iclude the deletio from E for those cases i which the deleted relatioship occurrece is the last oe i which the etity participates. Furthermore, if the relatioship type participates as aggregated etity i aother relatioship type R, besides the previous deletio operatios, the deletio of the occurreces from R i which the aggregate etity takes part is icluded i the trasactio. I the i-cascade deletio, the operatios added to the trasactio ca require propagatio as well. This propagatio must be icluded i the trasactio.

4 I some cases, oly the i-cascade deletio is adequate; for example i the relatioship R(E(1,1), F(0,)) a restrictive deletio for E or R is ot possible. 4. Trasactio geeratio I this sectio, we preset a set of algorithms to achieve automatic geeratio of the miimal ad safe update trasactios for a give diagram. There are two possible approaches for desigig this set of trasactios. These approaches are preseted below usig the example i Figure 2. c0? c a0? a m r1 b0? b C 1 T 1 A R B Figure 2: EER example diagram The modular approach costructs a trasactio for each object type of the diagram (etity type or relatioship type) icludig oly oe operatio (isertio o deletio) ad, if it is ecessary, calls to other trasactios. Therefore, the trasactios oly take ito accout the operatio o their ow objects ad the adjacet objects that are ecessary. Two objects of a diagram are adjacet if they are located at the eds of the same lie (i this case, we will say the distace betwee the objects is 1). Whe the isertio trasactio is desiged for B, a call to the isertio trasactio i R must also be icluded i additio to the isertio i B. Some of the geerated trasactios are hidde. They are oly defied to be called from other trasactios, ad they are ot available to the system users. For example, the isertio trasactio i T is oly used by the isertio trasactio i A. This is because the cardiality costraits of A i T (maximum ad miimum equal to 1) prevet the T isertio trasactio from beig used aloe. The complete approach costructs each trasactio by icludig all the operatios that are ecessary o ay object, regardless of the distace to the iitial object i the diagram. Thus, a basic trasactio does ot iclude calls to other trasactios. I the example, apart from the isertio operatio i B, the isertio trasactio i B cotais the isertio operatio i R. Oly those trasactios that have to be available to the users are geerated. I the example, the isertio trasactio i T is ot geerated. The parameters of the trasactios are obviously the same i both approaches ad they are described as follows: - I the case of isertio ito a etity type, a parameter must appear for each attribute of this etity type. I the case of isertio i a relatioship type it is ecessary to iclude a parameter for each idetifier attribute of each participat etity type ad a parameter for each relatioship type attribute. However, if a isertio trasactio eeds to call other trasactios, the parameters of the latter must also be icluded with the parameters of the former. This problem is solved by the algorithm. - I the case of deletio, a parameter for each idetifier attribute of the object type to delete is eeded if it is a etity type. A parameter for each idetifier attribute of every compoet etity type is eeded if it is a relatioship type. The geerated trasactio for the isertio i A is preseted for both approaches.? TRANSACTION Modular_Is_A (a 0 x,?,a m x,c 0 x); Is_et A attributes a 0? a 0 x,?,a m? a m x; Modular_Is_T(a 0 x,c 0 x); TRANSACTION Complete_Is_A (a 0 x,?,a m x,c 0 x); VAR TX:T; Is_et A attributes a 0? a 0 x,?,a m? a m x; Is_rel T where A(TX.A)?TX.A.a 0 =a 0 x?? C(TX.C)?TX.C.c 0= c 0 x;

5 The i-cascade deletio trasactio of the etity type A with respect to ay object appears below i the modular ad complete approaches TRANSACTION Modular_Del_A (a 0 x); VAR AX:A; Del_et A where AX.a 0 =a 0 x; Modular_Del_T(a 0 x,-); Modular_Del_R(a 0 x,-); TRANSACTION Complete_Del_A (a 0 x); VAR AX:A, TX: T, RX:R, BX:B; Del_et A where AX.a 0 =a 0 x; Del_rel T where??ax(a(ax)?tx.a=ax); Del_rel R where??ax(a(ax)?rx.a=ax); Del_et B where??rx(r(rx)?rx.b=bx); I the example, o the oe had, the deletio of a etity from the etity type A forces the deletio of a occurrece from the relatioship type T; o the other had, sice the i-cascade deletio has bee chose for relatioship type R, the it is ecessary to delete the occurreces i which the deleted etity participates. Fially, due to the miimum cardiality costrait of the etity type B i R (equal to 1), ay deletio from R determies the deletio of the participat etity from B. A call to a trasactio does ot require all its parameters to be istaced. Thus, i the call Modular_Del_R(a 0 x, -), the secod parameter is a script; this symbol deotes ay value for the parameter that correspods to it by locatio i the trasactio defiitio. The trasactios called by the precedig trasactios i the modular approach are the followig: TRANSACTION Modular_Is_T (a 0 x,c 0 x); VAR TX:T; Is_rel T where A(TX.A)?TX.A.a 0 =a 0 x?? C(TX.C)?TX.C.c 0= c 0 x; TRANSACTION Modular_Del_T (a 0 x,c 0 x) VAR AX:A;TX:T;S_AX: Set of occurreces of A; Del_rel T where TX.A.a 0 =a 0 x?tx.c.c 0 =c 0 x; S_AX? {AX??TX(T(TX)?TX.A=AX)}; FOR EACH AX i S_AX DO Modular_Del_A(AX.a 0 ); TRANSACTION Modular_Del_R(a 0 x,b 0 x); VAR BX:B;RX:R;S_BX: Set of occurreces of B; Del_rel R where RX.A.a 0 =a 0 x?rx.b.b 0 =b 0 x; S_BX? {BX??RX(R(RX)?RX.B=BX)}; FOR EACH BX i S_BX DO Modular_Del_B(BX.b 0 ); To be able to use the calls to other trasactios for reachig a cosistet system state, it is ecessary to iclude selectio coditios to determie which occurreces of other objects must be elimiated. Each oe of these coditios is expressed usig a formula i the above metioed logical laguage. This formula cotais a free variable so that all the istaces of the free

6 variable that make the formula true are elimiated. All these istaces are icluded i oe variable of set type. This set is later crossed, callig to the deletio trasactio for each oe of the occurreces that are cotaied i it. The correspodig values of idetifier attributes of these istaces are used as parameters. I the trasactios of T ad R, there are calls to deletio trasactios o other objects of the diagram which have a similar structure. For example, i the trasactio Modular_Del_R, sice etity type B has the existece costrait i R, whe occurreces of R are deleted, those occurreces of B which o loger participate i R must also be deleted. Sice the maximum cardiality of B i R is 1, we kow that for each deleted occurrece of R, oe occurrece of B must be elimiated. Aother importat problem relative to the successive calls to differet trasactios from deletio eeds to be emphasized. Whe a occurrece of T is deleted, there is determied which occurreces of A ca be left icosistet (those that do ot participate i T). This fact prevets fallig ito a ifiite loop of calls, because the deletio of T came from a deletio i A. Thus, there are o occurreces of A that fulfil this coditio. Therefore, o call to the deletio trasactio of A is made, ad the possible loop is avoided Algorithm for the trasactio geeratio from a EER diagram without cycles The modular approach has bee chose for the developmet of the trasactio geerator algorithm so that the obtaied trasactios are simpler. The algorithm starts from a EER diagram. As a result of the algorithm executio, the set of miimal ad safe update trasactios which are ecessary for the evolutio of the system represeted by the diagram is obtaied. Whe a isertio trasactio calls aother isertio trasactio, it must be kow which parameters must be used. Defiig a order i the trasactio geeratio allows that those trasactios that are called from aother trasactio are defied beforehad. I order to determie the required parameters for a isertio trasactio it is ecessary to use the basic operatio parameters plus all the parameters that occur i each oe of the ivoked trasactios. To avoid udesired duplicatio i this set of parameters, some of them have to be elimiated: the idetifier parameters of the callig object, because they always appear i the ewly ivoked trasactio. Cosequetly, it is ecessary to desig a algorithm that determies the order for trasactio geeratio; this arragemet is also based o the miimum cardiality costraits of the relatioship type i which each object participates. The sortig algorithm accepts a EER diagram as a uique parameter ad it returs a ordered list of all the diagram object ames. This algorithm is show i Appedix A. As stated above, the arragemet is oly ecessary to geerate the isertio trasactios, sice i deletio trasactios it is ot ecessary to iclude parameters from other trasactios. The geeratio of the deletio trasactios is doe for each object right after the geeratio of its correspodig isertio trasactio. Oce the arragemet of the objects of the EER diagram is obtaied, the trasactio geerator algorithm is the followig: ALGORITHM Trasactio_Geerator LI: Sorted list of object ames from a EER diagram; OUTPUT T: Text that cosists of the set of safe ad miimal update trasactios for the objects i the iput EER diagram; VAR Trasactio: Text; T? ''; FOR EACH object O i LI i order DO IF O is a etity type Geerate_is_et_trasactio(O,Trasactio); Joi(T,Trasactio);

7 Geerate_del_et_trasactio(O,Trasactio); Joi((T, Trasactio); ELSE /*O is a relatioship type*/ Geerate_is_rel_trasactio(O,Trasactio); Joi(T, Trasactio); Geerate_del_rel_trasactio(O,Trasactio); Joi(T, Trasactio); The algorithms to create safe trasactios for the differet object types are preseted i Appedix B. They are preseted i a abbreviated form cetered i the calls to other trasactios that have to be icluded to eforce cardiality costraits. The cotrols that have to be icluded to avoid icosistece due to other costraits are left out of this simplified versio Algorithm Extesio to iclude EER diagrams with cycles Whe a EER diagram cotais a cycle, that is, a depedecy for isertio, a problem arise whe the geerated trasactios are used. a 0... A R B b 0... a m b S c 0 T C... c p Figure 3: EER diagram with a cycle Effectively, a isertio i A requires a existig etity from B for isertig a relatioship i R; but, to isert a etity i B, a existig etity i C is eeded to isert a relatioship i S, ad this etity also eeds a existig etity i A to isert a relatioship i T. This is a deadlock that must be solved by geeratig, i additio to the ormal trasactios cited above, special trasactios for this situatio. The special trasactios must iclude a isertio operatio o each object type icluded i the cycle, plus calls to the modified isertio trasactios o these objects. The modified trasactios are the ormal oes except for that the isertio operatio o the iteded object type is elimiated. A particular case of cycle is the Total specializatio, because the isertio i the geeral etity type ad i oe of the specialized etity type must be simultaeous; due to this fact, a special trasactio is eeded for each specialized etity type, that jois the isertio trasactio o the geeral etity type ad the isertio trasactio o the correspodig specialized etity type. Therefore, the defied algorithms for isertio trasactio desig are modified to take ito accout the presece of cycles. This extesio is ot icluded i the preset paper. 5. Coclusios ad future work I this work, we preset a ew perspective of the Etity-Relatioship Model, as a coceptual modellig tool. Traditioally, the ER model has bee criticized due to its lack of a dyamic dimesio. I cotrast to this criticism, the authors defed that the itegrity costraits defied i the ER diagram restrict the valid state trasitios i the system, ad they ca therefore determie the miimal trasactios that ca be performed o it. Followig this mai idea, give ay ER diagram we propose a algorithm to obtai the set of safe ad miimal trasactios with respect to a subset of itegrity costraits. These miimal trasactios are the basic uits that should be used to desig the more geeral oes that implemet the user requiremets. The mai features of this work are the followig:

8 1. We propose a extesio of the ER Model which icludes a trasactioal laguage. This laguage icludes a isert ad a delete operator for etity types, for relatioship types ad for specialized etity types. 2. We aalyse differet EER diagram patters i order to develop the algorithm. 3. Fially, we preset the algorithm that automatically geerates the set of miimal ad safe trasactios for a give EER diagram. The mai advatage of the proposal cosists of its possible itegratio ito the existig CASE tools based o the ER model for coceptual modellig. I this way, these tools could offer the desiger a miimal trasactio diagram that is able to perform the safe system evolutio. This work ca be exteded takig ito accout more geeral itegrity costraits. Appedix A: Algorithm for sortig the objects of a ER diagram ALGORITHM SORT OUTPUT L: Sorted list of object ames; VAR Possible: boolea; L? empty list; FOR EACH object O i EERX DO IF O has ot EC i ay relatioship type Add(L,O); REPEAT FOR EACH object O i EERX DO IF O is ot i L Possible? true; FOR EACH relatioship type R where O has EC DO IF R is ot i L Possible? false; IF Possible Add(L,O); UNTIL every O is i L; Appedix B: Algorithms for geeratig the trasactios ALGORITHM Geerate_is_et_trasactio E: Defiitio of the etity type; OUTPUT T: Trasactio text; VAR Tras_Parameters, Operatios: Text; Add to Tras_Parameters a parameter for each attribute of E; Geerate the isertio operatio ito the etity type E; Add this operatio to Operatios; FOR EACH relatioship type R where E has EC DO Add to Tras_Parameters a parameter for each parameter of the isertio trasactio ito R that is ot yet i

9 Tras_Parameters; Geerate a call to the isertio trasactio ito R; Add this call to Operatios; T? 'TRANSACTION'; Joi(T, 'Is_Et_Trasactio_', ame(e), Tras_Parameters, '', Operatios, '';) ALGORITHM Geerate_is_rel_trasactio R: Defiitio of the relatioship type; OUTPUT T: Trasactio text; VAR Variables, Tras_Parameters, Operatios: Text; FOR EACH etity type E that participates i R DO Add to Tras_Parameters a parameter for each idetifier of E; Add to Tras_Parameters a parameter for each attribute of R; Add to Variables a variable defied over R; Geerate the isertio operatio i the relatioship type R; Add the operatio to Operatios; FOR EACH relatioship S where R has EC as aggregated object DO Add to Tras_Parameters a parameter for each parameter of the isertio trasactio ito S that is ot yet i Tras_Parameters; Geerate a call to the isertio trasactio ito S; Add this call to Operatios; T? 'TRANSACTION'; Joi(T, 'Is_Rel_Trasactio_', ame(r), Tras_Parameters, 'Variables', Variables, '', Operatios, ''); ALGORITHM Geerate_del_et_trasactio E: Defiitio of the etity type; OUTPUT T: Trasactio text; VAR Variables, Tras_Parameters, Operatios: Text; Add to Tras_Parameters a parameter for each idetifier of E; Geerate a variable o E; Add this variable to Variables; Geerate the deletio operatio from the etity type E; Add this operatio to Operatios; FOR EACH relatioship type R where E participates DO IF the deletio is i-cascade with respect to R Geerate a call to the deletio trasactio from R; Add this call to Operatios; T? 'TRANSACTION'; Joi(T, 'Del_Et_Trasactio_', ame(e), Tras_Parameters, 'Variables', Variables, '', Operatios, ''); ALGORITHM Geerate_del_rel_trasactio

10 R: Defiitio of the relatioship type; OUTPUT T: Trasactio text; VAR Tras_Parameters, Operatios, Variables: Text; FOR EACH etity type E that participates i R DO Add to Tras_Parameters a parameter for each idetifier of E Geerate a variable o R; Add this variable to Variables; Geerate the deletio operatio for R; Add this operatio to Operatios; FOR EACH relatioship type S where R participates (*as aggregated object*) DO IF the deletio is i-cascade with respect to S Geerate a call to the deletio trasactio for S; Add this call to Operatios; FOR EACH etity type E that participates i R with EC DO Geerate a set variable o E; Add this variable to Variables; Geerate a query o this variable; Geerate a FOR loop o this variable icludig a call to the deletio trasactio of E; Add this loop to Operatios; T? 'TRANSACTION'; Joi(T, 'Del_rel_trasactio', ame(r), Tras_Parameters, 'Variables ', Variables, '', Operatios, '') Refereces [1] P.P. Che. The Etity-Relatioship Model: Towards a Uified View of Data. ACM TODS, Vol. 1, No. 1, pp. 9-36, [2] G. Egels, M. Gogolla, U. Hohestei, K. Hülsma, P. Löhr-Richter, G. Saake, H. D. Ehrich. Coceptual Modelig of Database Applicatios Usig a Exteded ER Model. Data ad Kowledge Egieerig, Vol. 9, No. 2, pp , North Hollad, [3] R. Elmasri, S.B. Navathe. Fudametals of Database Systems. Third Editio. Addiso- Wesley, [4] M. Gogolla. A Exteded Etity-Relatioship Model. Fudametals ad Pragmatics. LNCS 767, Spriger-Verlag, [5] L. Mota-Herraz. M.A. Pastor. Diseño coceptual co el modelo Etidad-Relació. Departameto de Sistemas Iformáticos y Computació, Iteral Report, DSICID/56/97, [6] J.A. Pastor-Collado. Supportig Trasactio Desig i IS Coceptual Modellig through Pre-sythesised Update Trasactio Specificatios. EXSELSI [7] B. Thalheim. Etity-Relatioship Modelig. Foudatio of Database Techology. Spriger- Verlag, [8] Balaba, M. ad Shoval, P. MEER -A EER Model ehaced with structure methods, Iformatio Systems, 27 ( ), 2002.