Abstract:
A method and system are provided. The method includes separating a predicate that specifies a set of events into a temporal part and a non-temporal part. The method further includes comparing the temporal part of the predicate against a predicate of a known window type. The method also includes determining whether the temporal part of the predicate matches the predicate of the known window type. The method additionally includes replacing (i) the non-temporal part of the predicate by a filter, and (ii) the temporal part of the predicate by an instance of the known window type, responsive to the temporal part of the temporal predicate matching the predicate of the known window type. The instance is parameterized with substitutions used to match the temporal part of the predicate to the predicate of the known window type.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a Continuation application of co-pending U.S. patent application Ser. No. 14/584,255, filed Dec. 29, 2014, which is incorporated herein by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    Technical Field 
         [0003]    The present invention relates generally to information processing and, in particular, to discovering windows in temporal predicates. 
         [0004]    Description of the Related Art 
         [0005]    For event processing, it is often useful to specify a collection of events using a temporal predicate. A temporal predicate is a Boolean formula that refers to time (i.e., a Boolean formula with a variable “now”). Given the current time and a set of events that have already occurred, the problem is to compute the set of events that satisfy the temporal predicate. Using a temporal predicate is both powerful (since predicates can be expressive) and intuitive (since Boolean formulas are easy to comprehend). As time progresses, the truth value of the predicate for each individual event may change. The challenge is to efficiently maintain the collection of events that satisfy the predicate. 
         [0006]    One prior art approach to event processing involves tracking the truth of predicates for each event separately. However, this approach suffers from drawbacks. For example, whenever time progresses, the system must discover all stored historical events whose truth values have changed. This discovery operation is expensive in terms of, e.g., computational resources. 
         [0007]    Another prior art approach to event processing involves an explicitly-specified window. However, this approach also suffers from drawbacks. For example, the use of an explicitly-specified window restricts expressiveness and can make the program less intuitive. 
       SUMMARY 
       [0008]    According to an aspect of the present principles, a method is provided. The method includes separating a predicate that specifies a set of events into a temporal part and a non-temporal part. The method further includes comparing the temporal part of the predicate against a predicate of a known window type. The method also includes determining whether the temporal part of the predicate matches the predicate of the known window type. The method additionally includes replacing (i) the non-temporal part of the predicate by a filter, and (ii) the temporal part of the predicate by an instance of the known window type, responsive to the temporal part of the temporal predicate matching the predicate of the known window type. The instance is parameterized with substitutions used to match the temporal part of the predicate to the predicate of the known window type. 
         [0009]    According to another aspect of the present principles, a system is provided. The system includes a temporal predicate separator for separating a predicate that specifies a set of events into a temporal part and a non-temporal part. The system further includes a predicate-to-window matcher for comparing the temporal part of the predicate against a predicate of a known window type and determining whether the temporal part of the predicate matches the predicate of the known window type. The system also includes a temporal predicate replacer for replacing (i) the non-temporal part of the predicate by a filter, and (ii) the temporal part of the predicate by an instance of the known window type, responsive to the temporal part of the temporal predicate matching the predicate of the known window type. The instance is parameterized with substitutions used to match the temporal part of the predicate to the predicate of the known window type. 
         [0010]    According to yet another aspect of the present principles, a computer program product is provided for discovering windows in temporal predicates. The computer program product includes a computer readable storage medium having program instructions embodied therewith. The program instructions are executable by a computer to cause the computer to separate a predicate that specifies a set of events into a temporal part and a non-temporal part. Further, the program instructions are executable by a computer to cause the computer to compare the temporal part of the predicate against a predicate of a known window type. Also, the program instructions are executable by a computer to cause the computer to determine whether the temporal part of the predicate matches the predicate of the known window type. Additionally, the program instructions are executable by a computer to cause the computer to replace (i) the non-temporal part of the predicate by a filter, and (ii) the temporal part of the predicate by an instance of the known window type, responsive to the temporal part of the temporal predicate matching the predicate of the known window type. The instance is parameterized with substitutions used to match the temporal part of the predicate to the predicate of the known window type. 
         [0011]    These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0012]    The disclosure will provide details in the following description of preferred embodiments with reference to the following figures wherein: 
           [0013]      FIG. 1  shows an exemplary processing system  100  to which the present principles may be applied, in accordance with an embodiment of the present principles; 
           [0014]      FIG. 2  shows an exemplary system  200  for discovering windows in temporal predicates, in accordance with an embodiment of the present principles; and 
           [0015]      FIG. 3  shows an exemplary method  300  for discovering windows in temporal predicates, in accordance with an embodiment of the present principles. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0016]    The present principles are directed to discovering windows in temporal predicates. 
         [0017]    In an embodiment, we describe each known window type w by a temporal predicate p. Given a temporal predicate p that specifies a collection of events, compare the temporal predicate p against each known window type w to determine if a match exists there between. If the temporal predicate p and a known window type w match, we use the known window type w to implement the temporal predicate p. 
         [0018]    Some of the many attendant advantages of the present principles include, but are not limited to, the following. For several types of windows, there are techniques for tracking window contents efficiently. Once a replacement window has been found for a predicate, these techniques become directly applicable. Since the replacement was discovered automatically, the user was still able to use a temporal predicate to specify the collection, retaining expressiveness and ease-of-use. 
         [0019]      FIG. 1  shows an exemplary processing system  100  to which the present principles may be applied, in accordance with an embodiment of the present principles. The processing system  100  includes at least one processor (CPU)  104  operatively coupled to other components via a system bus  102 . A cache  106 , a Read Only Memory (ROM)  108 , a Random Access Memory (RAM)  110 , an input/output (I/O) adapter  120 , a sound adapter  130 , a network adapter  140 , a user interface adapter  150 , and a display adapter  160 , are operatively coupled to the system bus  102 . 
         [0020]    A first storage device  122  and a second storage device  124  are operatively coupled to system bus  102  by the I/O adapter  120 . The storage devices  122  and  124  can be any of a disk storage device (e.g., a magnetic or optical disk storage device), a solid state magnetic device, and so forth. The storage devices  122  and  124  can be the same type of storage device or different types of storage devices. 
         [0021]    A speaker  132  is operatively coupled to system bus  102  by the sound adapter  130 . A transceiver  142  is operatively coupled to system bus  102  by network adapter  140 . A display device  162  is operatively coupled to system bus  102  by display adapter  160 . 
         [0022]    A first user input device  152 , a second user input device  154 , and a third user input device  156  are operatively coupled to system bus  102  by user interface adapter  150 . The user input devices  152 ,  154 , and  156  can be any of a keyboard, a mouse, a keypad, an image capture device, a motion sensing device, a microphone, a device incorporating the functionality of at least two of the preceding devices, and so forth. Of course, other types of input devices can also be used, while maintaining the spirit of the present principles. The user input devices  152 ,  154 , and  156  can be the same type of user input device or different types of user input devices. The user input devices  152 ,  154 , and  156  are used to input and output information to and from system  100 . 
         [0023]    Of course, the processing system  100  may also include other elements (not shown), as readily contemplated by one of skill in the art, as well as omit certain elements. For example, various other input devices and/or output devices can be included in processing system  100 , depending upon the particular implementation of the same, as readily understood by one of ordinary skill in the art. For example, various types of wireless and/or wired input and/or output devices can be used. Moreover, additional processors, controllers, memories, and so forth, in various configurations can also be utilized as readily appreciated by one of ordinary skill in the art. Further, while described as a processing system, system  100  can be an event processing system or part of an event processing system. These and other variations of the processing system  100  are readily contemplated by one of ordinary skill in the art given the teachings of the present principles provided herein. 
         [0024]    Moreover, it is to be appreciated that system  200  described below with respect to  FIG. 2  is a system for implementing respective embodiments of the present principles. Part or all of processing system  100  may be implemented in one or more of the elements of system  200 . 
         [0025]    Further, it is to be appreciated that processing system  100  may perform at least part of the method described herein including, for example, at least part of method  300  of  FIG. 3 . Similarly, part or all of system  200  may be used to perform at least part of method  300  of  FIG. 3 . 
         [0026]      FIG. 2  shows an exemplary system  200  for discovering windows in temporal predicates, in accordance with an embodiment of the present principles. The system  200  can be a stand-alone system or part of an event processing system. 
         [0027]    The system  200  includes a temporal predicate determiner  210 , a temporal predicate separator  220 , a predicate-to-window matcher  230 , and a temporal predicate replacer  240 . 
         [0028]    The temporal predicate determiner  210  determines temporal predicates that specify respective sets of events. The temporal predicate determiner  210  can determine the temporal predicates on its own, or receive already determined temporal predicates. For example, in an embodiment, the temporal predicate determiner  210  includes a user input device  211  (e.g., a mouse, a keyboard, a microphone, etc.) for receiving temporal predicates specified by a user of system  200 . In an embodiment, the temporal predicate determiner  210  includes a communication interface  212  (e.g., a network interface card, a transceiver, and so forth) for receiving temporal predicates from a remote source. These and other variations of temporal predicate determiner  210  are readily determined by one of ordinary skill in the art, while maintaining the spirit of the present principles. 
         [0029]    The temporal predicate separator  220  separates a temporal predicate p into a temporal part tp and a non-temporal part ntp. 
         [0030]    The predicate-to-window matcher  230  compares the non-temporal part ntp of a temporal predicate p to a predicate of a known window type w to determine if a match exists there between. In an embodiment, the predicate-to-window matcher  230  can include a syntactic match identifier  231  and/or a satisfiability solver(s)  232  and/or a window discovery language augmenter  233 . The syntactic match identifier  231  identifies syntactic matches between the temporal part tp of the temporal predicate p and the known window type w. The satisfiability solver(s)  232  identifies matches between the temporal part tp of the temporal predicate p and the known window type w, and can use satisfiability-modulo-theories techniques. Of course, other types of satisfiability solvers can also be used in accordance with the teachings of the present principles, while maintaining the spirit of the present principles. The window discovery language augmenter  233  augments the language used to describe temporal predicates with features that facilitate window discovery. For example, such features can include, but are not limited to, language phrases directly characterizing window size or bucket size. These and other variations of predicate-to-window matcher  230  are readily determined by one of ordinary skill in the art, while maintaining the spirit of the present principles. 
         [0031]    The temporal predicate replacer  240  replaces the non-temporal part ntp of the temporal predicate p by a filter f and replaces the temporal part tp of the temporal predicate p by an instantiation of the known window type w. In an embodiment, the temporal predicate replacer includes a substitution parameterizer  241  for parameterizing the known window type w by any substitutions needed to match the known window type w to the temporal part tp of the temporal predicate p. For example, these substitutions can include, but are not limited to, window size or bucket size. 
         [0032]    In the embodiment shown in  FIG. 2 , the elements thereof are interconnected by a bus  201 . However, in other embodiments, other types of connections can also be used. Moreover, in an embodiment, at least one of the elements of system  200  is processor-based. Further, while certain elements of system  200  are shown as part of other elements, in other embodiments one or more of the certain elements can be implemented as standalone elements. These and other variations of the elements of system  200  are readily determined by one of ordinary skill in the art, given the teachings of the present principles provided herein, while maintaining the spirit of the present principles. 
         [0033]      FIG. 3  shows an exemplary method  300  for discovering windows in temporal predicates, in accordance with an embodiment of the present principles. 
         [0034]    At step  310 , receive or determine a temporal predicate p that specifies a set of events e. 
         [0035]    At step  320 , separate the temporal predicate p into a temporal part tp and a non-temporal part ntp. In an embodiment, step  320  can be performed using a conjunctive normal form. 
         [0036]    At step  330 , compare the temporal part tp of the temporal predicate p against a predicate of a known window type. 
         [0037]    At step  340 , determine if a match exists between the temporal part tp of the temporal predicate p and the predicate of the known window type. If so, then the method proceeds to step  350 . Otherwise, the method proceeds to step  360 . In an embodiment, step  340  can be performed by finding a syntactic match. However, for more general cases, satisfiability solvers can be used. Such satisfiability solvers include, but are not limited to, satisfiability modulo theories. 
         [0038]    At step  350 , replace (i) the non-temporal part of the predicate by a filter, and (ii) the temporal part of the predicate by an instantiation of the known window type, responsive to the temporal part of the temporal predicate matching the predicate of the known window type. In an embodiment, step  350  can include parameterizing the known window type w by any substitutions needed to match the predicate of the known window type w to the non-temporal part ntp of the temporal predicate p. 
         [0039]    At step  360 , determine if there are any more known window types. If so, the method proceeds to step  370 . Otherwise, the method is terminated. 
         [0040]    At step  370 , retrieve the next known window type, and return to step  330  (so as to repeat steps  330  through  350  for the next known window type). 
         [0041]    We now describe an example for the sake of illustration, in accordance with an embodiment of the present principles. 
         [0042]    In the example, we define “TotalWeight” as the total weight of the luggage of all flight events during the last period of 1 hour, where the flight number of each flight event starts with “AF”. 
         [0043]    Hence, in the example “TotalWeight” functions as a rule. The rule performs an aggregation (“Total”, i.e., sum) over a collection of events e specified using the following temporal predicate p: 
         [0044]    (p1) e is a flight event 
         [0045]    (p2) AND e falls into the last period of 1 hour 
         [0046]    (p3) AND the flight number of e starts with “AF” 
         [0000]    The preceding temporal predicate p specifying the collection of events e corresponds to step  310  of method  300 . 
         [0047]    Note that temporal predicate p includes parts p1, p2, and p3. Also note that only part p2 is time-dependent, whereas parts p1 and p3 are time-independent. Hence, in this example, part p2 can be considered to be the temporal part tp of the temporal predicate p, and parts p1 and p3 can be considered to be the non-temporal part ntp of the temporal predicate p. The separation of the temporal predicate p into non-temporal parts p1 and p3 and temporal part p2 corresponds to step  320  of method  300 . We assume that once received, events are immutable, so parts p1 and p3 remain constant. We can make the predicate p more precise as follows: 
         [0000]      ( p )  e.t &gt;=now−“1 hour” AND  p 1( e ) AND  p 3( e )
 
         [0048]    where “e.t” denotes the time of event e, and “now” denotes the current time. 
         [0049]    In the example, the first known window type w for which a match is attempted in step  340  of method  300  is a sliding window of size T. The events in such a sliding window can be characterized by the following temporal predicate: 
         [0000]      ( w )  e.t &gt;=now− T  
 
         [0000]    Step  340  determines that a match exists by substituting “1 hour” for “T”. 
         [0050]    The temporal predicate p describes a simple sliding window, and the temporal part tp of p matches the window size T of the known window type w when we replace the window size T (of the known window type) by “1 hour” (from the temporal part tp of the temporal predicate p). In particular, we replace (i) the non-temporal part ntp of the temporal predicate p by a filter, and (ii) the temporal part tp of the temporal predicate p by the window size T of the known window type w, responsive to the temporal part tp of the temporal predicate p matching the known window type w (per step  350  of method  300 ). The preceding means that for this example, an efficient implementation would first filter arriving events e by p1(e) and p3(e), while all remaining events would be tracked in a sliding 1-hour window. Also, the summation can be maintained efficiently by addition and subtraction as each event enters and leaves the window. 
         [0051]    More generally, there are several other possible known window types, including but not limited to, tumbling windows, unbounded windows, coarse-grained sliding windows (a.k.a., sliding bucketed windows), and so forth. Furthermore, besides measuring time using physical units such as seconds, minutes, or hours as in the example above, windows can also measure time using logical units such as the number of events or the delta between attributes of earlier versus later events. 
         [0052]    Also, there are several other possible aggregations, including but not limited to count, average, minimum, maximum, standard deviation, argument of the minimum (arg-min), argument of the maximum (arg-max), collect, and so forth. 
         [0053]    If the collection of events is used in an aggregation, rather than materializing the collection, we instead just maintain that aggregation incrementally as events enter and leave the collection. For invertible aggregations, this involves simple addition and subtraction. For example, an incremental computation for the average aggregation works by incrementally maintaining a sum and a count. Each event that enters the collection adds its value to the sum and one to the count. Each event that leaves the collection subtracts its value from the sum and one from the count. The current value of the average is simply the sum divided by the count. 
         [0054]    Non-invertible aggregations can be handled efficiently with balanced trees as long as the aggregations are associative. For example, an incremental computation for the minimum aggregation works by keeping the values of all events in the leaves of a tree, and keeping, in each non-leaf node, the minimum of its children. When a new event enters the collection, its value is added as a leaf, and, when an event leaves the collection, the corresponding leaf is removed. In both cases, the tree is rebalanced, and all affected leaf-to-root paths are updated. Thus, the root of the tree always maintains the minimum value of all leaves. 
         [0055]    Furthermore, if the window involves buckets (also known as panes), the implementation can pre-aggregate per bucket, thus saving memory, before applying one of the other algorithms at the level of entire buckets, thus saving time. 
         [0056]    In a variation of the present principles, the language for temporal predicates is augmented with features that facilitate window discovery. In other words, the window discovery is not fully automatic, but partially automatic. For example, the discovery algorithm might automatically discover the window type and size, but the language might explicitly specify the buckets. 
         [0057]    The present invention may be a system, a method, and/or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. 
         [0058]    The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
         [0059]    Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. 
         [0060]    Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention. 
         [0061]    Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
         [0062]    These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
         [0063]    The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
         [0064]    The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
         [0065]    Reference in the specification to “one embodiment” or “an embodiment” of the present principles, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment of the present principles. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment”, as well any other variations, appearing in various places throughout the specification are not necessarily all referring to the same embodiment. 
         [0066]    It is to be appreciated that the use of any of the following “/”, “and/or”, and “at least one of”, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as readily apparent by one of ordinary skill in this and related arts, for as many items listed. 
         [0067]    Having described preferred embodiments of a system and method (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in the particular embodiments disclosed which are within the scope of the invention as outlined by the appended claims. Having thus described aspects of the invention, with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.