Aspects of Formal and Graphical Design of a Bus System

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1 Apect of Formal and Graphical Deign of a Bu Sytem Tiberiu Seceleanu Univerity of Turku, Dpt. of Information Technology Turku, Finland tiberiu.eceleanu@utu.fi Tomi Weterlund Turku Centre for Computer Science Turku, Finland tomi.weterlund@utu.fi Abtract Thi tudy how the derivation of a local egmented bu arbiter from an original ingle egment bu arbiter. The operation are performed in the formal framework of action ytem and illutrated in a graphical manner uing the correponding action ytem UML profile notation. The derivation i ueful both to demontrate the capability of preerving correctne when conidering an important hardware deign deciion and alo to identify mean through which thi kind of deciion can be performed in a graphical environment. 1 Introduction The complexity of modern day digital ytem, timulated by the latet advance in technology, lead often to problem concerning the correctne of the development flow. On one hand, modular deign i one of the olution toward partially reducing the tak of the deigner of complex ytem, while on the other hand, the employment of formal method in ytem deign trie to olve the apect related to correctne. However, the preure impoed by time-to-market apect uually doe not leave enough time for thorough analyi of deign, before they are hipped. Additionally, the often heavy mathematical apparatu behind formal method framework till forbid the expected wide uage of uch approache in ytem deign. In thi ituation, the Unified Modeling Language (UML) [11] emerged lately a one poible candidate deign environment which provide a fat learning curve combined with certain capabilitie for formal analyi. UML provide a et of intuitive graphical and textual decription technique that are uppoed to be eaily undertandable for both ytem developer and expert uer working in the application domain. Mot attractive for u i the graphical notation and the poibility to adapt it to an already developed deign tyle. The latter feature come in extremely handy, becaue UML i, in fact, groly imprecie [10]. Action Sytem [1] i a tate-baed formalim, relying on an extended verion of Dijktra language of guarded command [4]. Thi tudy i a continuation of previou work preented in [9], which define a UML profile for Action Sytem. We ue a a cae tudy the egmented bu arbiter, alo decribed previouly in [5]. In the following ection, we how how an exitent (ingle egment) bu arbiter decription can be correctly tranformed into a local egment bu arbiter. For thi, we apply both the UML profile and action ytem technique. 2 The Segmented Bu Platform The growing diverity of ytem-on-a-chip (SOC) device bring up an immene number of poible interface. In many ituation, both the ytem deign and performance are limited by the complexity of the interconnection between the different module and block that are integrated into thoe chip. Furthermore, different data tranfer peed are required a well a parallel tranmiion. A uual bu, where only one module can tranmit at a time, i low, due to large capacitive load caued by the interface of the module that are attached to it and the long phyical length. A olution to the above mentioned problem i a egmented bu deign combined with a globally aynchronou locally ynchronou (GALS) [3] ytem architecture. In thi approach, each ditinct module of a SOC ytem i ynchronized to a local clock, wherea interaction between thoe module are arranged aynchronouly. A egmented bu i a bu which i partitioned into two or more egment. Each egment act a a normal bu between module that are connected to it and operate in parallel with other egment. Segment can be connected / diconnected dynamically to each other in order to etablih connection between module located in different egment. Therefore, thi tructure i more flexible than the uual one (AMBA-like, for intance), where bridge may be interpreted a egment. All dynamically connected egment act a one ingle bu. Due to the egmentation of thi reource, parallel tranaction can take place, thu increaing the performance. Detail about the /04 $20.00 (c) 2004 IEEE 1

2 egmented bu principle and implementation can be found in [5]. Segmented Bu Architecture. The egmented bu tructure i imply illutrated in Figure 1. Every egment i compoed of a group of mater, a group of lave, a egment arbiter (SA), the phyical line (addre, data, requet, acknowledge and read / write line) and an inter-egment bridge controller. The egment with their component act a a tand-alone bue operating in parallel, mater motly aking ervice from the group of lave placed within the confine of one egment. Occaionally, one mater may require ervice from a lave connected to another bu egment. In thi ituation, the local arbitration unit forward the requet to a central arbitration module, in order to etablih an inter-egment connection. The central arbiter (CA) tore the information regarding the current ituation of the egment: what egment are participating in an inter-egment tranaction, what new requet are pending for an inter-egment acce. Baed on thi information, the CA decide if there i a change in the ownerhip of certain egment and deliver the appropriate control ignal to the involved module. 0 j 0 j n-1 Figure 1. Segmented bu tructure. Operation on a Segmented Bu. There are three mode in which operation on a pecific egment may proceed, from the point of view of local arbitration. Thee mode depend on the localization of the mater requeting the bu and the lave. Thu, we have (i) a local mater local lave ituation, (ii) a local mater external lave ituation and (iii) a external mater local or external lave. In all the ituation, the mater that i granted the acce to the bu connect to the lave following a four-phae ignaling protocol. The requet part i alo viible to the SA reiding in the ame egment a the mater. Thu, the SA upervie the acce of the mater to the bu by counting the number of tranfer, in cae (i) and (ii) above. A more detailed block decription of egment component and ignal i given in figure 2. 3 Action Sytem Back and Kurki-Suonio [1] introduced the action ytem formalim, providing a framework for pecifying and refining concurrent program. An action ytem (AS, henceforward) i in general a collection of action or guarded command, which are executed one at a time. The j n-1 Figure 2. The Segment Control Element. Action Sytem i ued for pecification and correctne preerving development of reactive ytem. An action A i defined (for example) by A ::= x := x.r (nondeterminitic aignment) A 1 A 2 (nondeterminitic choice) A 1 ; A 2 (equential compoition) A 1 A 2 (prioritized compoition) where R i a predicate, x i a variable or a lit of variable, and A 1 and A 2 are action. Semantically, an action A i defined by the weaket precondition for A to etablih ome pot-condition Q, denoted wp(a, Q). In thi paper, we regard an action A a being of the form g S, where g i the guard of the action, given by ga = wp(a, fale), and S i the action body. An action i aid to be enabled, if it guard i true, diabled otherwie. Action are conidered atomic, meaning that whenever one i elected for execution, it will be completed without interference. Atomic action may be part of non-atomic action compoition, in which cae, the execution of the whole compoition i interrupted after the execution of one of it enabled component. Additionally, the quantified compoition of action i defined by [ i = 0... n : A i] = A 0 A 1... A n, where can be any of the allowed operator. An action ytem i a compoition of (non-atomic) action, decribing a certain behavior. A long a the ytem contain enabled action, one of them may be elected for execution, after which action in other ytem may be executed. Refinement. Action ytem are meant to be deigned in a tepwie manner within the refinement calculu framework [2]. The refinement calculu preerve the correctne of the action during refinement procedure. The (atomic) action A i aid to be (correctly) refined by action C, denoted A C, if q.(wp(a, q) wp(c, q)) hold. Thi i equivalent to the condition p, q.((p A q) (p C q)), which mean that the concrete action C preerve every total correctne property of the abtract action A. In the next ection we will make ue of ome rule baed on refinement relation, which we introduce in the following paragraph. Rule 1 Data Refinement. Aume two action A and C with variable a, u and c, u, repectively. Let R(a, c) be a 2

3 boolean relation between the variable a and c. The abtract action A i data-refined by the concrete action C uing the abtraction relation R(a, c), denoted A R C, if q.(r wp(a, q) wp(c, a.r q)) (1) hold. The predicate a.r q i a boolean condition on the program variable a and c. Thi rule formalize a very common practice in HW deign. For intance, it i uual to change data type during deign tep that change the view of the ytem from abtract to more concrete level. Hence, integer could be repreented a bit-vector, or imple data tructure can be tranformed into more complex one, a we illutrate in forthcoming ection. Rule 2 Prioritized compoition. The prioritized compoition defined in [7] offer u the poibility to conciely impoe precedence of ome action / action ytem over other. It i clearly a natural olution for ituation encountered in a bu baed deign, where at leat in the arbitration proce granting the next owner of the bu follow certain priority cheme. Briefly, the prioritized compoition of two action i expreed in term of the non-determinitic choice a: A B = A ga B. The reult of interet to u i the fact that alway, a nonprioritized compoition A B can be turned into a prioritized one, for intance A B, by merely trengthening the guard of the le important action. Hence, alway: A B A B (2) Rule 3 Ditributivity of equence over the choice. Conidering the tatement preent in our deign a conjunctive, monotonic predicate tranformer [2], we benefit in our reaoning of the following rule, decribing the ditributivity of the equence over the choice operator: (A B); C = (A; C) (B; C) (3) There are everal other rule that we will conider in the forthcoming ection, uch a the introduction of a local variable, the introduction or the removal of an empty tatement, for which we do not offer detailed exemplification. They may be found elewhere [2, 8]. 4 UML Profile for Action Sytem The UML profile for Action Sytem i a graphical notation intended to eae the deigner burden by offering a viual repreentation of the ytem under development. With thi graphical repreentation the deigner can compoe the ytem and manage large complex ytem eaier. The operator connecting the action and the action ytem are clearly viible in the graphical repreentation and thu the overall functionality become apparent. The profile cutomize and extend pecific UML type for every action ytem operator and define a notation for them. A Graphical Notation. Table 1 how part of the graphical notation pecified in the profile. Table 1. Notation of action Name Notation AS Meaning Atomic Action Atomic Sequence Non-Atomic Sequence Non-Determinitic Choice Prioritied Compoition A A; B A; B A B A B The notation preented in table 1 i conitent with the action characteritic decribed in ection 3: the full dot and arrow-head correpond to atomic compoition, while the other line termination correpond to non-atomic contruct. Notice that the graphical repreentation for the choice and prioritized compoition correpond to nonatomic ituation. Within a ytem, the next action to be elected for execution i given by the operator emantic. Graphical refinement. One of the intention behind electing UML a a partner language when developing action ytem deign wa the exitence of a graphical environment. However, image by themelve can not enure the correctne of neceary tranformation from high level of abtraction to implementation and therefore, a textual notation of the ytem hould be available at any time. Change that are made in the graphical notation mut be checked under refinement calculu rule, o that the target ytem will be a correct implementation of the original one. On the other hand, during the ytem deign flow, there i a relatively reduced et of tranformation that help the deigner reaon about operation to be performed in order to elect among different level of repreentation. Hence, in the following, we intend to map ome cae of refinement rule into equivalent graphical tranformation rule. Rule G1. Choice to prioritized compoition. Thi rule illutrate the change of a nondeterminitic choice compoition into a prioritized compoition, a hown in figure 3. Figure 3. Prioritizing action. Rule G2. Ditribution of equence over choice. The relation 3 i viualized a hown in figure 4. 3

4 by Figure 6. Thi i alo the tarting point in tranforming the ingle bu arbiter into a SA. Figure 4. Atomic equence ditribution. Rule G3. Non-atomic equence and choice. We give a an example here a rule that i eaily uggeted by the graphical notation, and which can be proven within the action ytem framework. Hence, we can extend the above illutrated Rule 3 to non-atomic action, in the way preented in figure 5. Figure 5. Non-atomic equence ditribution. Figure 6. Single bu arbiter. The Grant Action. We tart by conidering that there i a ingle mater in the ytem. Replicating the action in a proper manner will eventually decribe the granting activity for a larger number of mater. Hence, our derivation begin with the Grant action (Fig. 7). Thu, whenever a mater requet the bu (req) and no other mater i granted (gr = F ), then the arbiter may give acce to reource (gr := T ) or not (kip which mean that leave gr = F ). After thi, the ack line i et to true. It i et back to fale whenever the mater alo reet the req ignal. Following thi, a new granting cycle may tart. 5 Derivation We intend to tart our deign tarting from a ingle egment bu, where we have the decription of mater, the lave and the bu arbiter. The tranformation toward a egmented bu i tranparent except for the arbiter, which become a egment arbiter. The SA ha to take into conideration now a higher priority mater, repreented by the CA. It will alo have to conider idling for the period of time when the egment i jut a tranmiion line between a winning mater and it elected lave, both ituated outide the boundarie of the pecific SAegment. In thi ection we concentrate on the granting activity only. The notation T and F tand for the boolean value of true and fale, repectively. The egment arbiter. The operation of the arbiter on a ingle bu ytem conit of two job. One i to grant the requeting mater the acce to the bu, whenever the previou owner finihed the tranfer. Thi i ignaled by raiing the line gr (gr := T ). The econd one i to upervie the current owner o that the number of tranfer doe not go over a pecified limit. When thi limit i reached, the mater i informed that it ha lot the control. Hence, the variable gr i reet (gr := F ). With the help of the boolean variable ack the arbiter alo inform the mater that the deciion on the next owner of the bu i taken. If requeting mater did not yet receive acce to the bu, they are uppoed to keep on requeting. While a granted mater operate tranfer on the bu, the arbiter mut not grant any other requeting mater. Hence, the uperviion activity mut have a higher priority than granting. Thu, we have the graphical decription offered Figure 7. The initial Grant action. We apply Rule G2 to the Grant action and we obtain the refined verion, Grant 1, a illutrated in Fig. 8 Grant 1 = ( req gr = F (gr := T; ack := T kip; ack := T) ) Figure 8. The action Grant 1. Next, conider the relation R(gr, grant) = ( gr = F (grant = F grant = Hold)) (gr = T grant = T ) The relation R pecifie how we can replace the original two-valued variable gr, with the new, three-valued, variable grant. Thi i required becaue, when a local mater requet an external egment acce, the SA cannot grant it without aking the CA. Hence, it will firt place the correponding grant line to a new value, Hold and will forward the requet to the CA. When the CA grant the acce, it inform the correponding SA, which now forward the grant to the pecific mater. Uing R, we data refine the granting action (Grant 1 R Grant 1 ) a hown in Fig. 9. We continue by introducing the variable which implement the communication with the CA, namely req C and 4

5 Figure 9. The action Grant 1. Grant 4 = ( ( req grant = Hold ackc grant := T; ack := T req local grant = F grant := Hold; req C := T; ack := T ) ) ( req local grant = F grant := T; ack := T ) Figure 12. The action Grant 4. ack C. The firt one i updated by the SA, while the econd i only read by the SA and written by the CA. We obtain the action Grant 2 (Fig. 10). Grant 2 = ( req (grant = F (grant = Hold ack C)) grant := T; ack := T req grant = F grant := Hold; ack := T; req C := T ) Figure 10. The action Grant 2. The arbiter differentiate a local egment requet from an external one by reading the lave addre line (SAddr) provided by the requeting mater. The own addre (legnr) i coded inide the SA. For implicity, we denote local = SAddr = legnr. A new verion of the Grant action i then obtained Fig. 11. Grant 3 = ( req ((local grant = F) (grant = Hold ack C)) grant := T; ack := T req local grant = F grant := Hold; ack := T; req C := T ) Figure 11. The action Grant 3. A mater that need to tranfer data to / from a lave placed in an external egment will wait coniderably more than a mater requeting a local reource. In order to balance thi apect, we decide to give higher prioritie to uch requet. In the ame tep, we apply Rule 3. The reult i repreented by action Grant 4. Here i the point where we take into conideration the exitence of everal mater within the egment. They are numbered from 0 to. Each mater j communicate with the SA by mean of a requet ignal, req[j] and lave addre line SAddr[j]. The SA update for each mater a grant ignal, grant[j]. Moreover, every mater ha acce to the unique ack line ued by the SA to ignal termination of a granting eion. Thu, we replicate the granting activity following a data refinement tep which relate the initial variable req and grant to their vectorized verion, req[0... ] and grant[0... ]. We ue the abtraction relation: R 1 = (req = T j {0,..., }.req[j] = T ) (req = F j {0,..., }.req[j] = F ) and we have Grant 4 R1 Grant 5 Fig. 13. ( ( [ Grant 5 = j := 0... : req[j] grant[j] = Hold ackc ] grant[j] := T; ack := T [ j := 0... : req[j] local grant[j] = F ] ) grant[j] := Hold; ack := T; reqc := T ) ; req[j] ack ack := F ( [ j := 0... : req[j] local grant[j] = F grant[j] := T; ack := T ] ) ; req[j] ack ack := F +1 Figure 13. The action Grant 5. Oberve that there i one ituation which i not yet exactly reflected in the above decription. It correpond to the requet coming from the CA to the SA, aking acce right for another egment mater, either to pa through the egment, or to acce a local reource. The channel devoted to thi communication i imilar with the one conidered by Grant 5 : the CA i jut another local mater from the point of view of the SA. However, we jut want to eparately identify thi pecific mater, a we intend to place it higher in the priority lit. We identify it a the mater[0]. We aign to thi mater the highet priority. Notice further that, actually, the CA doe not provide requeted egment addree. Hence, we may aume that it alway requet local acce, therefore, the correponding grant line can not be placed on Hold. At the ame time, we decide to replace the variable req[0] and grant[0] by req O and ack O, repectively (Fig. 14). Grant 7 = ( [ j := 1... : req[j] grant[j] = Hold ackc grant[j] := T; ack := T req[j] local grant[j] = F grant[j] := Hold; ack := T; reqc := T ] ) ; req[j] ack ack := F ( reqo acko = F acko := T; ack := T ) ; reqo ack ack := F [ j := 1... : req[j] local grant[j] = F grant[j] := T; ack := T ] ; req[j] ack ack := F Figure 14. The action Grant

6 The egment arbiter. An analyi imilar to the one preented above (for the Grant action) i performed for the Supervie action. The full repreentation of the SA i illutrated in figure 15, where we alo named the ubcomponent of the Grant 7 action. The action ytem decription i given in [6]. LAckF = req[j] ack ack := F LAckF O = req O ack ack := F RoAckC = req[j] grant[j] = Hold ack C grant[j] := T ; ack := T RoGr = req[j] local grant[j] = F grant[j] := Hold; ack := T ; req C := T EGr = req O ack O = F ack O := T ; ack := T LGr = req[j] local grant[j] = F grant[j], ack := T 6 Concluion Figure 15. The egment arbiter. In thi tudy we have hown how the action ytem formalim i applied to correctly derive a egment arbiter pecification from a ingle egment arbiter. The work i part of a larger project that analyze the realization of a egmented bu, tarting from high level of abtraction down to implementation. On the way, we alo applied the graphical notation of the action ytem profile for UML. We decribed how the precie rule of refinement can be tranlated into the graphical environment provided by thi profile. However, we may not ay that one can directly ue the viual environment to fulfill all the requirement of a given deign project. The action ytem repreentation hould alway be aide and conulted at every tep. A mall tep toward the relaxation of thi ituation i illutrated by the tranlation of everal refinement tep into their graphical equivalent. Neverthele, for the poible neceary data refinement tep we found yet no olution a to their UML repreentation. In thi direction, further work concentrate on analyzing poibilitie to adapt the technique of the action ytem framework to the environment provided by the Object Contraint Language [11]. Provided the change in ytem repreentation are correctly performed, the graphical decription tranformation, a the one preented in the previou ection (Fig. 7 to Fig. 14) can be eaily automated by uing OCL pecification. Thu, one could think of building a deign methodology that would take advantage of the feature offered by the AS UML profile. Acknowledgement. The work preented in thi tudy wa partly funded by the ITEA Prompt to Implementation project. Reference [1] R. J. R. Back and R. Kurki-Suonio. Ditributed Cooperation with Action Sytem. In ACM Tranaction on Programming Language and Sytem, Vol. 10, No , pp [2] R. J. R. Back and J. von Wright. Refinement Calculu: A Sytematic Introduction. Springer Verlag, [3] D. M. Chapiro. Globally-Aynchronou Locally- Synchronou Sytem. PhD thei, Standford Univerity, [4] E. W. Dijktra. A Dicipline of Programming. Prentice-Hall International, [5] T. Seceleanu, J. Ploila, P. Liljeberg. On-Chip Segmented Bu: A Self Timed Approach. Proceeding of the 15 t h IEEE ASIC/SOC Conference, 2002, page [6] T. Seceleanu, T.Weterlund. Segment Arbiter A Action Sytem. Proceeding of SCS International Sympoium, 2003, pp [7] E. Sekerinki, K. Sere. A Theory of Prioritizing Compoition. The Computer Journal, VOL. 39, No 8, pp The Britih Computer Society. Oxford Univerity Pre. [8] K. Sere. Stepwie Derivation of Parallel Algorithm. Ph.D. Thei, Abo Akademi, Turku, Finland, [9] T.Weterlund, T. Seceleanu. UML Profile for Action Sytem. To appear a a TUCS technical report, [10] J. Whittle. Formal Approache to Sytem Analyi Uing UML: An Overview. In Advanced Topic in Databae Reearch, ed. Keng Siau, pp [11] OMG Unified Modeling Language Specification, ver. 1.4, September,