A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM TODS, 20(1):3--41, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....an object oriented active database system. The concept of Triggering Graph was introduced in [BAR93] to detect the termination of a database rule set. The work was further extended in [BAR94] to support both termination and confluence by limiting the rule set to Condition Action rules. Aiken et al. [AIK95] tried to determine the termination and confluence of a database production rule set statically for both CA and ECA rules. Baralis et al. [BAR95] proposed a technique to deploy the complementary information provided by Triggering Graphs and Activation Graphs to analyze the termination of ECA rule ....

Aiken, A., Hellerstein, J., and Widom, J., "Static Analysis Techniques for Predicting the Behavior of Database Production Rules," in ACM Transactions on Database Systems, Vol. 20, No. 1, March 1995, pp. 3-41.

....system. The concept of Triggering Graph is introduced in by Baralis et al. BAR93] to detect the termination of a database rule set. The work is extended in Baralis and Widom [BAR94] to support both termination and confluence by limiting the rule set to Condition Action (CA) rules. Aiken et al. [AIK95] try to determine the termination and confluence of a database production rule set statically for both CA and Event ConditionAction (ECA) rules. Baralis et al. BAR95] propose a technique to deploy the complementary information provided by Triggering Graphs and Activation Graphs to analyze the ....

Aiken, A., Hellerstein, J., and Widom, J., "A Static Analysis Techniques for Predicting the Behavior of Database Production Rules," in ACM TODS, March 1995, pp. 3-41.

....became a popular means of IC (see Section 2.6) but they are not limited to IC. So called business rules are derived from the application domain but are supplementary to the semantics of the conceptual database schema. To efficiently maintain a large number of these rules is a well known problem [25, 37, 27, 6, 3]. Debugging and visualization of these rules is not a problem of concern in this work but is an active research field in the context of active databases and workflow modeling. The maintenance of integrity with procedural triggers is, on the other hand, very central since it allows the ....

A. Aiken et al. Static analysis techniques for predicting the behavior of active database rules. ACM Transactions on Database Systems, 20(1), March 1995.

....indicating that event E 1 occurs. The shaded circle is the place corresponding to the composite event (E 1 ; E 2 ) An auxiliary place is labeled AUX. Event detection in our environment can apply any of the above techniques, and, we will not discuss event detection in this thesis. Starburst [AHW95] rules consider the net effect of transitions of insertion, deletion, and update on the database. Rule processing is invoked at the end of each transaction, or at a point explicitly specified within a transaction. A transition may cause multiple rules to be considered for triggering. A rule is ....

....to fire rule r or not. The rule manager fires the rule r if event(r) has not occurred in the latest monitoring time interval. 4.5 Consistency Property of Rules Rules in active databases have a number of properties: termination, confluence, observable determinism, and consistency. Aiken discusses [AHW95] the first three rule properties. We discuss rule consistency property as follows. Since the action triggered by an event may perform some tasks or may reject a request for a certain task, it is possible that a set of rules contains conflicting execution specification. For example, a rule may ....

Aiken, A., Hellerstein, J.M., and Widom, J., "Static Analysis Techniques for Predicting the Behavior of Active Database Rules", ACM Transactions on Database Systems, Vol. 20, No. 1, March 1995.

....is highly desirable or even critical in systems, such as financial management systems, where the termination state must be guaranteed, unambiguous, and reproducible. Aiken et al. address termination and confluence in active databases by introducing static methods for analyzing rule programs [1,2]. Their algorithm proceeds by building a rule trigger graph from the input program. The graph is then 15 analyzed for cycles and commutative rules, pairs of rules that can execute in any order without influencing the trigger graph. The analysis either concludes that a program terminates and is ....

....heuristics, including exploiting rule parameters and moving constraints as close to event evaluation as possible. Paton further explains how these heuristics allow multiple rules to be optimized using multiple query optimizers. His methods exploit the static methods for rule analysis presented in [1] to determine when it is possible to eliminate duplicate work. Further optimization of multiple rules presented in the AI literature is often avoided [41] This is largely due to the operational semantics of most active database languages. However, in [70] Obemeyer suggests a method for trigger ....

A. Aiken, J. Hellerstein, and J. Widom, "Static analysis techniques for predicting the behavior of active database rules," ACM Transactions on Database Systems, vol. 20, no. 1, March, pp. 3-41, 1995.

....of rule execution is a possibility and thus rule analysis techniques are important for developing sets of wellbehaved rules. 3 Analysing ECA Rule Behaviour Analysis of ECA rules in active databases is a well studied topic and a number of analysis techniques have been proposed, e.g. [4, 5, 6, 8, 9, 10, 11, 16], mostly in the context of relational databases. Analysis is important, since within a set of ECA rules, unpredictable and unstructured behaviour may occur. Rules may mutually trigger one another, leading to unexpected (and possibly infinite) sequences of rule executions. Two important analysis ....

....databases. Analysis is important, since within a set of ECA rules, unpredictable and unstructured behaviour may occur. Rules may mutually trigger one another, leading to unexpected (and possibly infinite) sequences of rule executions. Two important analysis techniques are to derive triggering [4] and activation [10] relationships between pairs of rules. This information can then be used to analyse properties such as termination or confluence of a set of ECA rules, or reachability of individual rules. The triggering and activation relationships between pairs of rules are defined as ....

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A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM TODS, 20(1):3--41, 1995. 15

....if the last state is (d, i.e. the last state has no active rules. A rule execution sequence is valid if it represents a correct execution sequence: only active rules are executed, and pairs of adjacent states properly represent the effect of executing the corresponding rule; for details see [AHW95]. Definition 5: Arulesetisconfluent if, for every initial rule execution state S (produced by an initial database state followed by a set of user modifications) every valid and complete rule execution sequence beginning with S has the same final state. Definition 6: 1.LetR:CA. the function num ....

Aiken, A., Widom, J., Hellerstein, J.M., "Static Analysis Techniques for Predicting the Behavior of Database Production Rules". ACM Transactions on Database Systems, Vol. 20, nr. 1, pp. 3-41, 1995.

....specified in an adaptation model. In our study of the behavior of such a system we concentrate on the issues of termination and confluence, which are important to detect potential problems in an adaptive hypermedia application. We draw parallels with static rule analysis in active database systems [1,2]. By using common properties of AHS we are able to obtain more precise (less conservative) results for AHS than for active databases in general, especially for the problem of termination. KEYWORDS: adaptive hypermedia, user modeling, adaptation rules, termination, confluence, active databases ....

....reference model for adaptive hypermedia applications. In the next section we define the rule language associated with AHAM and explain how the rule execution works in AHAM. We then analyze termination and confluence of the AE and we draw parallels with rule execution in active database systems [1,2]. AHAM, A DEXTER BASED REFERENCE MODEL In hypermedia applications the emphasis is always on the information nodes and on the link structure connecting these nodes. The Dexter model [8,9] captures this in what it calls the Storage Layer. It represents a domain model (DM) i.e. the author s view ....

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Aiken, A., Widom, J., Hellerstein, J.M. Static Analysis Techniques for Predicting the Behavior of Database Production Rules. ACM Transactions on Database Systems, Vol. 20, nr. 1, pp. 3-41, 1995.

....on how one important property of active database systems, namely, termination of active database rules, can be formally verified using symbolic model checking. Detecting termination of active database rules is, in general, an undecidable problem. However, researchers have proposed conditions [2, 12, 13] which are sufficient to ensure termination. Thus, a given problem can be analyzed to check whether it satisfies these conditions; if it does then the rule sets are guaranteed to terminate, otherwise they may or may not. One such condition is the acyclicity of the triggering graph [2] Absence of ....

....[2, 12, 13] which are sufficient to ensure termination. Thus, a given problem can be analyzed to check whether it satisfies these conditions; if it does then the rule sets are guaranteed to terminate, otherwise they may or may not. One such condition is the acyclicity of the triggering graph [2]. Absence of cycles in a triggering graph indicates that the rules will eventually terminate. Cycles in the triggering graph indicate potential for non termination. In other words, if a cycle exists in the triggering graph, further analysis must be done before one can give a more definite answer ....

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A. Aiken, J. M. Hellerstein, and J. Widom. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. ACM Transactions on Database Systems, 20(1):3--41, March 1995.

....part, the action is executed once for each possible instantiation of delta on each document this is instance level triggering. 3 Analysing ECA Rule Behaviour Analysis of ECA rules in active databases is a well studied topic, with a number of approaches appearing in the literature e.g. [5, 6, 8, 10, 11, 12, 13, 14, 19], mostly in the context of relational databases. A key analysis question is that of termination of the rule execution, and a set of ECA rules is said to be terminating if for any initial event and any initial database state, the rule execution terminates. Triggering and activation relations ....

....initial database state, the rule execution terminates. Triggering and activation relations between rules have been used to determine whether a set of ECA rules is terminating: A rule r i may trigger a rule r j if the action of r i may generate an event which triggers r j . The triggering graph [5, 6] represents each rule as a vertex, and there is a directed arc from a vertex r i to a vertex r j if r i may trigger r j . Acyclicity of the triggering graph implies definite termination of rule execution. An activation graph [13] also represents rules as vertices. In this case an arc between two ....

A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM TODS, 20(1):3--41, 1995.

....of Rule Properties Although there is a great variety of execution models for active rules, certain fundamental properties like termination and complexity come up repeatedly and have been studied in the context of the respective execution models: Termination, Confluence, and Determinism. AWH95] develop static analysis techniques for active rules which guarantee termination, confluence, and observable determinism (i.e. whether each program produces a unique stream of observable actions) under the Starburst execution model. Rule analysis is based on a triggering graph which contains an ....

....programmer, but is considered as an internal representation which is used by the execution model, and thus is on a lower level than the EECA rules. Production Rule Semantics. Many approaches to active rules are based on a forward chaining execution model in the style of production rules, e.g. AWH95] PV95] and [Zan93,LHL95] above. 4 This is particularly true also for the PARK semantics of active rules [GMS92] which can be conceived as an inflationary fixpoint semantics extended by a mechanism to handle update literals L and GammaL, denoting insertion and deletion of L, respectively. ....

A. Aiken, J. Widom, and J. M. Hellerstein. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. ACM Transactions on Database Systems (TODS), 20(1):3--41, March 1995.

....triggering, consideration and execution. Properties of XML Active Rules. We show several examples of rules and discuss the execution of a set of rules, possibly cascading or in con ict, analysing their behavior with respect to the properties of termination, con uence, and observable determinism [3, 4, 5, 6, 20, 25]. These properties are de ned regardless of the notion of edit script, but the edit script considered by a given rule engine and in a given rule execution is one of the many equivalent edit scripts that can be produced by an XML di algorithm, which operates with a given optimization strategy for ....

A. Aiken, J. Widom and J. M. Hellerstein. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. In ACM Transactions on Database Systems, 20(1):3-41, March 1995.

....execute as A slightly shorter version appears in Proc. Intl. Workshop Logic in Databases (LID) San Miniato, Pisa, Italy, 1996, LNCS, Springer 2 The unstructured, unpredictable, and often nondeterministic behavior of rule processing can become a nightmare for the database rule programmer [AWH95] See also [Wid94, WC96, PCFW95, DHW95, FT96] closed) nested transactions whereas previous rule based approaches were limited to flat transactions. A Statelog procedure consists of a set of ECA style Datalog rules each of which defines either ffl a non state changing query, ie a (potentially ....

....specified in our logical framework. Moreover, properties like termination or expressive power can be investigated, as in [LHL95] independent of a given implementation. This complements work on termination and confluence of active rules which focuses more on specific systems like e.g. AWH92, AWH95, BCP95, KU96] In this paper, we have presented Statelog, based on a concept which integrates transactionoriented programming of complex (trans)actions with logical foundations of deductive rules in a seamless way. This framework is an extension of flat Statelog [LL94, LHL95] and uses ....

A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. TODS, 20(1):3--41, 1995.

....priorities between di erent goals. For example, in the robot re ghter example 1.3, negation as failure is used to give the goal of saving humans a higher priority than the goal of saving artifacts. Explicit priorities between rules is often used in production systems and active database systems [2, 16, 11] to in uence the way rules are executed. In such systems, whenever di erent rules can be triggered in a state, the rules which have higher priority are triggered rst. Clearly, the notion of priority that 4 negation as failure induces, is di erent from the one used in classical production and ....

A. Aiken, J.M. Hellerstein, and J. Widom. Static analysis techniques for predicting the behavior of active database rules. ACM Transactions on Database Systems, 20(1):3-41, 1995.

....is the possibility that the rules may trigger each other indefinitely. The research community has addressed this problem by focusing principally on static analysis of rule sets. The aim here has been to develop methods which can predict whether a set of rules is always guaranteed to terminate [1, 7, 4]. Since the problem is undecidable even for simple rule languages [3] these methods cannot achieve full precision. Also, given the lack of any consensus on what constitutes a typical terminating or non terminating rule set, it is not easy to compare various methods with one another. These ....

....[T,U,U,T] U,T,a 4 , T,U,a 2 ] Remark. If rule r 1 had been statement level, then execution would have halted at step 3 and definite termination from the initial state concluded. 6 Related Work Most previous work on termination analysis for active rules has dealt with static analysis. In [1], triggering graphs were first presented and later refined in in [11] and [13] where techniques for removing paths are shown. Generalisations using a method called rule reduction are described in [7] If one were to extend this method to allow incorporation of knowledge about constraints known to ....

A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM TODS, 20(1):3--41, 1995.

....of rule firings allowed e.g. in Oracle 8 this is 64. If this limit is reached, the actions of all the rules are rolled back. This has the drawback that rule execution sequences that would eventually terminate may exceed this predefined limit and be halted prematurely. Previous research, e.g. [2, 6], has predominantly dealt with developing simple sufficient conditions for ensuring rule termination, and can be overly conservative. Abstract interpretation [1] has proven a useful tool in program analysis and has been applied in functional programming languages to problems such as strictness ....

.... defining prefix, we can now unfold the applications of schedRule and reduce the functions ecq, action and : prefix = if empty ( ins(R0 ) R2 [ R3 1 R4 ) db) then if empty ( ins(R 0 ) R 3 1 R 4 ) R 5 ) db) then [ else [3] else if empty ( ins(R 0 ) R 3 1 R 4 ) R 5 ) db) then [2] else [2,3] The above transformations bring together all of the event condition query evaluations that will result from the execution of a given rule. We can now apply standard optimisation techniques to each resulting equation of execNonEmpty. Firstly, common sub queries can be abstracted out ....

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A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM Transactions on Database Systems, 20(1):3--41, 1995.

....of the cycle, in a manner similar to the optimization of invariant code motion out of loops commonly carried out in compilers [1] 6 Related Work There is a signi cant body of literature on termination analysis for active database rules. Among the earliest of these is the work of Aiken et al. [2], who Draft February 15, 2000 13 proposed using triggering graphs to reason about termination; this approach has subsequently been re ned and improved by various authors [4, 5, 7, 18, 22, 23] The general idea here is to use acyclicity of the triggering graph to infer termination; the relative ....

A. Aiken, J. M. Hellerstein, and J. Widom, \Static Analysis Techniques for Predicting the Behavior of Active Database Rules", ACM Transactions on Database Systems, vol. 20 no. 1, pp. 63-84, March 1995.

.... active rules provide a powerful mechanism for the management of several important database activities (e.g. constraint maintenance and view materialization [6, 7] and for this reason, they are now largely used in modern database applications and have been extensively studied in the last years [2, 4, 5, 9, 12, 14, 21, 22, 23]. However, in the various approaches, active rule execution is generally specified only by informal, natural language descriptions. It follows that very often, when the number of rules increases, active rule processing becomes quickly complex and unpredictable, even for relatively small rule sets ....

....22 7 Analysis of active rule processing On the basis of the results on transaction equivalence, we derive in this section a number of results about important properties of active databases. 7. 1 Confluence Confluence is a strong property and some applications may actually need a weaker notion [2]. We then propose two notions of confluence. The former is weaker than the latter since refers to a specific transaction. However, this notion can be nicely characterized and turns out to be of practical importance. Definition 7.1 (Weak confluence) An active program P is confluent with respect to ....

A. Aiken, J. M. Hellerstein, and J. Widom. Static analysis techniques for predicting the behavior of active database rules. In ACM Transaction on Database Systems, 20(1):3--41, March 1995.

....Other papers have proposed static rule analysis techniques for predicting the behaviour of rules in order to determine if a rule set satisfies the termination and or the confluence properties. These techniques analyse rules independantly from the triggering transactions. The method presented in [AHW95] is developped in the context of the Starburst system [WC96] which only considers foreach statement rules and executes them with a delayed rule processing granularity and an iterative behaviour. In [vdVS93] the analysis of rule behaviour is performed in the context of active object oriented ....

A. Aiken, J. M. Hellerstein, and J. Widom. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. ACM-TODS Transactions on Database Systems, pages 3--41, March 1995.

....THEN specify parent object type. An important problem in defining rules is the effect of interrelated rules. In order to deal with this problem, it is necessary to systematically analyse rule behaviour. The following three properties of sets of rules are generally considered important (see e.g. [AHW95]) 1. Termination: will rule processing terminate under any condition 2. Confluence: does the execution order of rules make a difference for the final result In the context of active databases the final result is required to be a unique database state, whereas in the context of schema ....

A. Aiken, J.M. Hellerstein, and J. Widom. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. ACM Transactions on Database Systems, 20(1):3--41, March 1995.

....due to the unstructured and unpredictable nature of rule processing. During rule processing, rules can trigger and untrigger each other, and the intermediate and final states of the database can depend upon which rules are triggered and executed in which order. It has been observed in the past [Aiken et al. 1995; Karadimce and Urban 1994; van der Voort and Siebes 1993] that two important and desirable properties of active rule behavior are termination and confluence. A rule set is guaranteed to terminate if, for any database state and initial modification, rule processing cannot continue forever (i.e. ....

....(i.e. rules cannot activate each other indefinitely) A rule set is confluent if, for any database state and initial modification, the final database state after rule processing is independent of the order in which activated rules are executed. Previous work on active rule analysis, e.g. [Aiken et al. 1995; Karadimce and Urban 1994; van der Voort and Siebes 1993; Weik and Heuer 1995] has developed compile time techniques that allow a rule programmer to predict in advance aspects of rule behavior such as termination and confluence. These techniques are used to statically analyze a set of rules ....

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Aiken, A., Hellerstein, J., and Widom, J. 1995. Static analysis techniques for predicting the behavior of active database rules. ACM Transactions on Database Systems 20, 1 (March), 3--41.

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A. Aiken, J. Widom, and J. M. Hellerstein. Static analysis techniques for predicting the behavior of active database rules. ACM TODS, 20(1):3--41, 1995.

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A. Aiken, J. M. Hellerstein, and J. Widom. Static analysis techniques for predicting the behavior of active database rules. ACM Trans. Database Syst., 20(1), 1995.

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Aiken, A., Hellerstein, J., Widom, J.: Static analysis techniques for predicting behavior of active database rules. ACM Transactions on Database systems 20 (1995) 3--41

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A. Aiken, J. M. Hellerstein, and J. Widom. Static analysis techniques for predicting the behavior of active database rules. In ACM Transaction on Database Systems, 20(1):3 March 1995.

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