Charles T. Davies Jr. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and optionally a checksum of the value are logged. When corruption is detected rather than prevented, techniques for corruption recovery must be employed to restore the database to an uncorrupted state. A high level approach to recovering from indirect logical corruption was described by Davies [20]. Many problems exist in trying to implement this approach in a modern transaction processing system, but one major contribution of this thesis is the development of concrete models and algorithms which can be used in certain cases to automate some or all of the task of recovery from ....

....a large register set, such as the Intel x86 architecture. By contrast, our techniques are language and instruction set independent. 2.3. 7 Logical Corruption Recovery from logical corruption which extends beyond the transaction boundary appears to have been originally discussed by Davies in [20], using the concept of spheres of control, precursors to the concept of a transaction (see [34] pages 174 180) Davies gives four steps which are taken for recovery of a logical error (a post process recovery ) 1. A symptom of the error is detected. 2. The data suspected of being the sources ....

[Article contains additional citation context not shown here]

C. Davies, Jr. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

....effects of corruption from the database image, and present an algorithm which implements this model as a modification of the Dal i recovery algorithm. Recovery from errors when the error is not immediately detected (for example, not detected until after the transaction commits) is discussed in [Dav78] but the delete transaction model algorithm presented in this paper is the first concrete proposal we are aware of for defining and implementing corruption recovery in a transaction processing system. We describe how techniques based on Read Logging can be extended in certain cases to logical ....

....to dealing with external actions associated with transactions. We have presented an initial algorithm for efficient recovery of a database from logical corruption. We are convinced that 1) automatic tools like these can be a significant aid in logical corruption recovery, following the outline of [Dav78] and 2) as with the implementation of read logging for the delete transaction model, such tools can benefit significantly from support within the DBMS. Acknowledgments We would like to thank Dennis Leinbaugh for insightful discussions on codeword maintenance. 9 Authors Biographical ....

Charles T. Davies, Jr. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

.... Atomicity Model After having defined the atomicity taxonomy and three dimensional model for transactions, we can how define infrastructure and execution spheres (see Figure 3) Similar to ACID properties, the notion of (atomic) spheres stems from the domain of traditional database transactions [Davies1978] Atomic spheres basically constitute a collection of actions that can be represented at various levels of granularity, but always looks from an external perspective. Spheres are atomic in the sense that a sphere (including all sub spheres) either totally commits or aborts. This mechanism is ....

Davies, C.T., "Data Processing Spheres of Control", IBM Systems Journal, 17(2):179-198, 1978

....focus on an implementation of advanced transaction models in a particular programming language. 3. 2 Early developed advanced transaction models One of the early attempts to extend the conventional model of ACID transactions (the Flat Transaction model) was the concept of Spheres of Control (SoC, [20]) Each SoC bounds a set of operations that are executed atomically they are all either aborted or committed. Each computation can involve many SoCs. To make the whole computation atomic, the commitment controls of the participating SoCs have to be related each to other; if an SoC sees the ....

Davies, C. T.: Data Processing Spheres of Control, IBM Systems Journal, vol. 17, no. 2, pp. 179-198, 1978

.... restaurant and hotel, it is decided to book tickets at the cinema) Obviously other forms of transaction composition are possible (e.g. t5 could execute in parallel to tc1) Much research on structuring applications out of transactions has been influenced by the ideas of spheres of control [2]. There are several ways in which some or all of the application requirements outlined above could be met. However, it is unrealistic to believe that the one size fits all paradigm will suffice, i.e. a single high level model approach to extended transactions is unlikely to be sufficient for ....

C. T. Davies, "Data processing spheres of control", IBM Systems Journal, Vol. 17, No. 2, 1978, pp. 179-198.

.... and Robinson s method [Lausen 1983, Herlihy 1986] studied alternative validation methods [Harder 1984] and compared optimistic and pessimistic techniques [Agrawal 1983, Badal 1981, Carey 1983, Franaszek Robinson 1985, Menasce Nakanishi 1982, Tay et al. 1984] Nested actions are proposed in [Davies 1978, Reed 1978] Several approaches to us ing pessimistic concurrency control for nested actions have been studied. Read write locking for nested actions is described in [Moss 1981] and has been implemented by systems such as Argus [Liskov 1984, Liskov et al. 1987a] and Camelot [Spector et al. 1987, ....

C. T. Davies. Data processing spheres of control. IBM ystems Jounal, 17(2):179-198, 1978.

....being done) something that cannot be readily achieved by the use of conventional transaction based systems. 1.4 Related work The traditional domain for transaction processing is database systems [Gray 1978] C.T. Davies pioneered the development of the atomic transaction concept [Davies 1973] [Davies 1978]. He addressed many concepts concerned with concurrent systems, recovery and integrity within an overall scheme that he called data processing pheres of control. Spheres of control are intended to deal with various problems including coordinating multiple processes within recovery regions, sharing ....

C.T. Davies, "Data Processing Spheres of Control," IBM System Journal, vol. 17, no.2, pp.179-198, 1978.

....an order between these activities (control flow) and an additional oder specifying alternative orders in case of failures. With this notion of processes we extend classical transaction models by providing a more general concept of both atomicity and isolation based on the notion of spheres [6] and by allowing a greater degree of flexibility by partial compensation and alternatives [11, 8] Local operation: Change design of part X (at R D Dept. a. Research Development Production Business Engineering PDMOperation 1: Change BOM of X in PDM PPCOperation 1: Change BOM ....

C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

....of transactions, then during run time, the entire activity representing the application in execution is frequently required to relax some of the ACID properties of the individual transactions. The entire activity can then be viewed as a non ACID extended transaction . The spheres of control model [4] describes the underlying concepts of recovery and commitment for extended transactions. Much research work has been done on developing specific extended transaction models [e.g. 5 8] Nevertheless, most of the proposed techniques have not found any widespread usage; indeed, most commercial ....

C. T. Davies, "Data processing spheres of control", IBM Systems Journal, Vol. 17, No. 2, 1978, pp. 179-198.

....is a crucial but complicated issue for concurrently accessed data systems. Increasingly sophisticated techniques are being developed to improve performance and functionality of recovery protocols. To better understand and analyze recovery schemes, we reexamine the concept of spheres of control [Dav78] using it as a unifying framework for specifying diverse recovery models simply and precisely. We constrain sphere of control formulations appropriately to capture transaction oriented recovery in both centralized and distributed environments and with different types of schedules, as well as ....

....which we believe is a more important and difficult issue. Specifications using ACTA are necessarily on a high level of abstraction, and the gap between specification and implementation appears difficult to bridge. We feel that the work of Bjork and Davies on spheres of control [Bjo73, Dav73, Dav78] can play a useful role in this regard. We see two benefits to using spheres of control in this way. First, the simplicity of spheres of control descriptions make them a useful tool for design and learning. Second, the concepts of the spheres of control framework are readily formalized, allowing ....

Charles Davies. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

....are released upon termination means that the transactions must terminate and may not exchange results with other transactions. Spheres of control release their results early, but may undo and redo the consuming computations if the results prove to be invalid thus, the consumers have no autonomy [2]. Extended transactions release results liberally, but restrict the autonomy of their components by requiring compensating subtransactions to undo the effects of data that are invalidated [3] Workflows ignore the integrity aspects, but capture the data flow required by specific applications [4] ....

Davies, C.T. Data processing spheres of control. IBM Systems Journal 17, 2 (1978), 179--198.

....We use the term superior (inferior) for the nonreflexive version of the ancestor (descendant) The set of descendants of a transaction 2. The Moss CC method for NTs [13] allows only for upward inheritance of locks. 3. The ideas underlying the concept of NTs stem from Davies spheres of control [5, 6]. 3 together with their parent child relationships is called the transaction s hierarchy. In the following, unless otherwise noted, we use the term transaction to denote both TL transactions and subtransactions. The properties defined for flat transactions are atomicity, consistency, isolation, ....

Davies, C.T.: Data Processing Spheres of Control. IBM Systems Journal, 17 (2), 1978.

....the most important sources of the whole subject of database transactions and integrity controls derive in a large part from this work, which was carried out by C. T. Davies, first for the US Air Force, and later at IBM, and led to the creation of the very influential spheres of control concept [15]. The notion I am using here of failure is very general so failures can usefully be classified in a number of ways, the most important of which are summarized in Figure 2 (also taken from [13] The wording that has been in use for some time as a definition of computer system dependability per ....

Davies, C. T. (1978) Data processing spheres of control. IBM Syst. J., 17, 179--198.

....but they need supplementary restrictions on transaction structure to ensure consistent execution at the global level. 26 10.2 Open Nested Models Open nested transactions differ from standard nested transactions [19] in that the children of a parent operate under different spheres of control [4]. Unlike multilevel transactions [26] open nested transactions are not restricted to conform to a consistent number of levels. Because Interactions are defined for a multidatabase environment, we restrict our nesting to two levels, although the model does not preclude extension to deeper levels ....

Jr. C. T. Davies. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

....can be nontrivial. ETMs thus focus on data integrity issues, albeit relaxed in some way. They are better applicable within a multidatabase system, not across an open organization of autonomous resources. 2. 2 Spheres of Control Spheres of control (SoCs) capture some of the same intuitions as ETMs [Davies (1978)] Gray and Reuter (1993) pp. 174 180] The ConTract model is inspired by SoCs [Wachter and Reuter (1992) p. 220] Intuitively, SoCs attempt to contain the effects of an action as long as it might need to be undone. Ordinarily, a result is released only when it is established that it is correct ....

Davies, Jr., C. T., 1978, "Data Processing Spheres of Control, " IBM Systems Journal, Vol. 17, pp. 179--198.

....mechanisms. Many of the ideas implemented in the mechanisms we survey in the rest of the paper have 21 actually been discussed earlier in other contexts. For instance, some of the ideas related to multilevel transactions, long transactions and cooperative transactions were discussed by Davies in 1978 [Davies 78] 6 SUPPORTING LONG TRANSACTIONS Many of the operations performed on data in advanced database applications are long lived. Some last for several minutes or hours such as compiling code or printing a complete layout of a VLSI chip. When these operations are part of a transaction, ....

....Many of the ideas implemented in the mechanisms we survey in the rest of the paper have 21 actually been discussed earlier in other contexts. For instance, some of the ideas related to multilevel transactions, long transactions and cooperative transactions were discussed by Davies in 1978 [Davies 78] 6 SUPPORTING LONG TRANSACTIONS Many of the operations performed on data in advanced database applications are long lived. Some last for several minutes or hours such as compiling code or printing a complete layout of a VLSI chip. When these operations are part of a transaction, they result in ....

Davies, C. T. "Data Processing Spheres of Control." IBM System Journal 17, 2, 1978, pp. 179-198.

....in some database systems by restricting updates on view relations. Although this restriction is normally due to conceptual and implementation problems, rather than being a deliberate feature of a database system design, it may be used to some effect for this purpose. Some systems, for example IMS [82], go further than this, and the database programmer can allow or disallow insertions, deletions, or modifications of data in view relations. This allows a fine grain of control for data protection purposes. Views on persistent data may be constructed using abstract data types in Napier88. The ....

Davies CT. Data Processing Spheres of Control. IBM Systems Journal 1978; 17,2:179-198

....restaurant and hotel, it is decided to book tickets at the cinema. Obviously other forms of transaction composition are possible, e.g. t5 could execute in parallel to tc1. Much research on structuring applications out of transactions has been influenced by the ideas of spheres of control [7]. There are several ways in which some or all of the application requirements outlined above could be met. However, it is unrealistic to believe that the one size fits all paradigm will suffice, i.e. a single high level model approach to extended transactions is unlikely to be sufficient for ....

C. T. Davies, "Data processing spheres of control", IBM Systems Journal, Vol. 17, No. 2, 1978, pp. 179-198.

....issues related to coordinated execution across long computations using the notion of invariants. However they do not address the type of coordinated execution requirements discussed in this paper. They provide a high level discussion on how rollback dependency can be handled if spheres of control [8] are available in a system. Also, none of the above discuss the race conditions created due to failures along parallel threads of execution within a workflow. The need for mutual exclusion of steps from concurrent workflow processes to ensure correct interleavings has also been discussed in [1] ....

C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

....the effects of corruption from the database image, and present an algorithm which implements this model as a modification of the Dal recovery algorithm. Recovery from errors when the error is not immediately detected (for example, not detected until after the transaction commits) is discussed in [5], but the deletetransaction model algorithm presented in this paper is the first concrete proposal we are aware of for defining and implementing corruption recovery in a transaction processing system. To ascertain the performance of our algorithms for detecting and recovering from physical ....

....corruption can be very difficult, with problems ranging from accurate tracing of corruption over much longer times to dealing with external actions associated with transactions. We are nevertheless convinced that 1) automatic tools can be a significant aid in this process, following the outline of [5], and 2) as with the implementation of read logging for the delete transaction model, such tools can benefit significantly from support within the DBMS. Acknowledgments We would like to thank Dennis Leinbaugh for insightful discussions on codeword maintenance. ....

C. Davies, Jr. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

....lines whose goal is to preserve serializability are [17] 26] 32] Most proposals, however, do not preserve serializability. A number of such proposals are described in [11] see also [4] An early paper that introduced issues related to decomposition using the spheres of control model is [9]. A major issue that arises in systems that permit non serializable schedules is that a transaction, T , might externalize intermediate results prior to committing. Such results might affect concurrent transactions and cannot simply be rolled back if T aborts. Instead, compensation is used. ....

C. Davies. Data processing spheres of control. IBM Systems Journal, 17(2), 1978.

....released upon termination means that the transactions must be terminating and may not exchange results with other transactions. Spheres of control release their results early, but may undo and redo the consuming computations if the results prove to be invalid thus, the consumers have no autonomy [2]. Extended transactions release results liberally, but restrict the autonomy of their components by requiring compensating subtransactions to undo the effects of data that are invalidated [3] Workflows ignore the integrity aspects, but capture the data flow required by specific applications [4] ....

Davies Jr., C.T. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179-198, 1978.

....and has authority over some information resources, on the basis of which it can enter into commitments about those resources. 3.1 Spheres of Control To best appreciate our approach, it is instructive to see how spheres of control (SoCs) work. SoCs, which were proposed about two decades ago [ Davies, 1978 ] capture some of the same intuitions as the extended transaction models. The database community is seeing a resurgence of interest in SoCs as the limitations of traditional transactions are being realized [ Gray Reuter, 1993, pp. 174 180 ] Intuitively, SoCs attempt to contain the effects ....

Davies, Charles T. Jr.; 1978. Data processing spheres of control. IBM Systems Journal 17(2):179--198.

....are no further rules defining do insert the pure evaluation terminates at this point. It is time to change the current state. The evaluation engine creates a new subtransaction by sending a request to the scheduler. This subtransaction will serve as a rollback sphere (cf. spheres of control [Dav78] which is used to enable local rollback without aborting the whole transaction (see also [GR93] for this use of the nested transaction concept) As we have three alternative update branches (see Figure 8) backtracking may be necessary, and corresponding provisions are made by starting the new ....

C. T. Davies. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

....but have to do with flow control. The ConTract model, first proposed in [Reut89] tries to provide the formal basis for defining and controlling long lived, complex computations, just like transactions control short computations. It was inspired by the concept of spheres of control [Davi78] and by the mechanisms for managing flow that are provided by some TP monitors, like queues, context databases, etc. GrRe91] Since ConTracts introduce a unit of work and control that consists of the whole application instead of individual database state transitions, they define a control ....

....programming languages do not know about the semantics of aborts. How to manage transactions with dependencies efficiently and correctly is beyond the scope of this paper, since this is still an open question of current research. First steps to the required concepts and techniques can be found in [Davi78, ChRa91, Klein91, HGK91] 7.3.4 User Interface for Controlling Large Distributed Applications Since ConTracts maintain the structure of an activity, they consequently need a means for administering the flow of control. The following paragraphs exemplify three important mechanisms for controlling ....

[Article contains additional citation context not shown here]

Davies, C.T. Data Processing Spheres of Control. IBM Systems Journal, Vol. 17(2), pp. 179-198, 1978.

....made more precise in the following sections. 4 Nested Transaction Concepts Before we can describe our approach to realize cooperation and recovery, we have to introduce some basic concepts of nested transactions. The nested transaction paradigm has its roots with the spheres of control of Davies [Dav78] and became well known by Moss approach [Mos85] The main idea is to give transactions a tree like structure by allowing them to start child transactions. To the outside, a nested transaction looks like a conventional flat transaction, but its inner structure offers some advantages. First, ....

C.T. Davies, Jr. Data processing spheres of control. IBM Systems Journal, pages 179--199, 1978.

....entails that outputs be released only when a transaction completes. Thus, the producer of data is restricted, but the consumer has full autonomy, unless it also is a transaction. Spheres of control (SoCs) release results early, but may undo and redo the consumers thus, consumers have no autonomy [8]. Extended transactions release results liberally, but restrict the autonomy of their components by requiring compensating subtransactions to undo the effects of data that are invalidated [8] Workflows ignore the integrity aspects, but capture the data flow required by specific applications [10] ....

.... (SoCs) release results early, but may undo and redo the consumers thus, consumers have no autonomy [8] Extended transactions release results liberally, but restrict the autonomy of their components by requiring compensating subtransactions to undo the effects of data that are invalidated [8]. Workflows ignore the integrity aspects, but capture the data flow required by specific applications [10] They allow autonomy, but are not flexible. Spheres of commitments are discussed below. Support Provided (columns) Integrity Autonomy Organizational 1 Ericsson New Concepts Group, Research ....

Charles T. Davies, Jr., "Data Processing Spheres of Control", IBM Systems Journal, 17(2):179-198, 1978.

....of type T5) will first examine the status of an order and will read the quantity of the order only if the status is paid or shipped paid . 3 Principles of Open Nested Transactions In this section, we review the main principles of open nested transactions [BSW88, MRKN92, RGN90, WS92] cf. also [Da78, Gr81]) on which our approach to OODBS concurrency control is based. An open nested transaction is essentially a tree of operation invocations, usually referred to as actions . The edges in the tree represent the callercallee relationship between actions; that is, the children of a node in the ....

Davies, C.T., Data Processing Spheres of Control, IBM Systems Journal Vol.17 No.2, 1978

....transactions for advanced database system applications can be found in [MP90] and [MRKN91] 13.2 The Multilevel Transaction Model 13.2. 1 Concepts of Multilevel Transactions The idea of open nested transactions [Gr81, Tr83] grew out of the seminal work on spheres of control by Bjork and Davies [Bj73, Da73, Da78]. 4 Chapter 13. Multilevel Transactions and Open Nested Transactions The special case of multilevel transactions (also known as layered transactions ) is a variant of nested transactions where the nodes in a transaction tree correspond to executions of operations at particular levels of ....

Davies, C.T. Data Processing Spheres of Control. IBM Systems Journal Vol.17 No.2, 1978.

.... takes place at different levels and schedulers can be connected in arbitrary ways correctness of the whole system has to be provided [1] Secondly, we decouple transactional properties in order to assign execution guarantees more flexibly to (sub)processes by exploiting the notion of spheres [5]. ....

C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

....from transactions (including ETMs) to generaly workflows to create transactional workflows [41] whose steps primarily correspond to database transactions. Similarly the workflow community has borrowed ideas from ETMs, e:g: spheres of joint compensation [30] motivated by spheres of control [8] and Sagas [14] in an effort to improve the correctness properties offered by WFMSs. It has also been demonstrated that the semantics of some of the ETMs can be implemented using y In this paper, general workflows are those that integrate independently developed applications. Most commercial ....

C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

....car, or the speed of the car. Normaly one is not interested in all state variables, but only in the subset of state variables that is significant for the given purpose. A significant state variable is called a real time (RT) entity. Every RT entity is in the sphere of control (SOC) of a subsystem [Davies 1978], i.e. it belongs to a subsystem that has the authority to change the value of this RT entity. Outside its sphere of control, the value of an RT entity can be observed, but cannot be modified. The observation of RT entities in the controlled object is stored as a real time image in the computer ....

Davies, C. (1978). Data Processing Spheres of Control. IBM Systems Journal. Vol. 17. pp. 179-198.

....paging of the original implementation of Flask. Thus within Flask either mechanism may be chosen to suit the characteristics of a particular application. 2 The Flask Architecture Flask is a layered architecture which has the flexibility to support different models of concurrency, such as atomic [4, 5, 7] and nested transactions [13] over the same data. Flask also permits the use of different recovery mechanisms such as shadow paging and logging over the same data. The architecture does not have a built in notion of concurrency control. Instead Flask provides a framework in which concurrency ....

Davies, C.T. "Data Processing Spheres of Control". IBM Systems Journal, 17, 2 (1978) pp 179-198.

....Objects start transaction commit transaction Figure 1 Coordinated error recovery performed by a CA action. 1.3 Related work The traditional domain for transaction processing is database systems [Gray 1978] C.T. Davies pioneered the development of the atomic transaction concept [Davies 1973][Davies 1978]. He addressed many concepts concerned with concurrent systems, recovery and integrity within an overall scheme that he called data processing spheres of control. However, subsequent early work on transactions, though influenced by Davies, was much less ambitious in its goals. Basic transaction ....

C.T. Davies, "Data Processing Spheres of Control," IBM System Journal, vol.17, no.2, pp.179-198, 1978.

....cooperation. We are primarily concerned with concurrency control and do not explicitly address failure recovery, although recovery of some sort is usually required. Most of the papers mentioned are relatively recent, but note that many of their ideas were foreshadowed in the 1970 s [Davies 73, Davies 78] The reader is assumed to be familiar with the conventional atomic transaction model [Bernstein et al. 87] and its main implementation mechanisms, such as two phase locking [Eswaran et al. 76] multi version timestamp ordering [Reed 78] optimistic validation [Kung and Robinson 81] ....

C.T. Davies, Jr. Data processing spheres of control. IBM Systems Journal 17(2):179-198, 1978.

....being done) something that cannot be readily achieved by the use of conventional transaction based systems. 1.4 Related work The traditional domain for transaction processing is database systems [Gray 1978] C.T. Davies pioneered the development of the atomic transaction concept [Davies 1973][Davies 1978]. He addressed many concepts concerned with concurrent systems, recovery and integrity within an overall scheme that he called data processing spheres of control. Spheres of control are intended to deal with various problems including coordinating multiple processes within recovery regions, ....

C.T. Davies, "Data Processing Spheres of Control," IBM System Journal, vol.17, no.2, pp.179-198, 1978.

....as needed [ Elmagarmid, 1992 ] Both of the above leave it to the application to handle errors or discrepancies that arise after a given transaction has completed. By contrast, Spheres of Control publish their results early, but require control over the activities consuming the results [ Davies, 1978 ] Toward an ontology of commitments. We believe social commitment is the key abstraction for supporting coherent interactions, while preserving autonomy. The DB approaches deal with passive objects, and view commitments as depending solely on the computation that commits, not on the ....

Davies, Charles T. Jr.; 1978. Data processing spheres of control. IBM Systems Journal 17(2):179--198.

....requirements by supporting different protocols within the DT hierarchy. Thus we get a configurable hierarchy which guarantees different levels of consistency and recovery support. 3 Nested Transaction Concepts The nested transaction paradigm has its roots with the spheres of control of Davies [Dav78] and became well known by Moss approach [Mos85] The main idea is to give transactions a tree like structure by allowing them to start child transactions. To the outside, a nested transaction looks like a conventional flat transaction, but its inner structure offers some advantages. First, ....

C.T. Davies,Jr. Data processing spheres of control. IBM Systems Journal, pages 179--199, 1978.

.... [SS84, We89, LMWF93] Allowing such semantically rich operations to invoke further operations on the same or other objects leads to the model of open nested transactions [Gr81, GR93, BSW88,BBG89,Wei91, WS92] which can be traced back to the seminal work on spheres of control by Bjork and Davies [Da78]. Typically, the conflict definition reflects the general (i.e. state independent) commutativity of operations and considers only the name and the input parameters of the operations [Ko83, SS84] In addition, state dependent commutativity may be exploited, for example, by considering also the ....

Davies, C.T., Data Processing Spheres of Control, IBM Systems Journal Vol.17 No.2, 1978

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Charles T. Davies Jr. Data processing spheres of control. IBM Systems Journal, 17(2):179--198, 1978.

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C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

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Davies, Charles T. Jr.; 1978. Data processing spheres of control. IBM Systems Journal 17(2):179--198.

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C.T. Davies, "Data processing spheres of control," IBM Systems Journal, vol. 17, no. 2, pp.179198, 1978.

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Davies, C.T. [1978], "Data processing spheres of control", IBM Sys. J. 17:2, pp. 179-198.

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C. T. Davies, "Data processing spheres of control", IBM Systems Journal, Vol. 17, No. 2, 1978, pp. 179-198.

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Davies, C.T. "Data Processing Spheres of Control", IBM Systems Journal 17,2 (1978) pp 179-198.

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Davies, C.T. "Data Processing Spheres of Control". IBM Systems Journal, 17, 2 (1978) pp 179-198.

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Davies, C.T. "Data Processing Spheres of Control". IBM Systems Journal 17,2 (1978) pp 179-198.

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C. T. Davies. Data Processing Spheres of Control. IBM Systems Journal, 17(2):179--198, 1978.

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