Abstract:
A system and method is disclosed for converting an existing circuit description from a lower level description, such as RTL, to a higher-level description, such as TLM, while raising the abstraction level. By changing the abstraction level, the conversion is not simply a code conversion from one language to another, but a process of learning the circuit using neural networks and representing the circuit using a system of equations that approximate the circuit behavior, particularly with respect to timing aspects. A higher level of abstraction eliminates much of the particular implementation details, and allows easier and faster design exploration, analysis, and test, before implementation. In one aspect, a model description of the circuit, protocol information relating to the circuit, and simulation data associated with the lower level description of the circuit are used to generate an abstract model of the circuit that approximates the circuit behavior.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a divisional of U.S. patent application Ser. No. 11/811,685, filed Jun. 11, 2007, which is a continuation of International Patent Application No. PCT/IL2006/001349, filed on Nov. 23, 2006, which claims the benefit of U.S. Provisional Patent Application No. 60/748,957, filed Dec. 8, 2005, all of which are herein incorporated by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention generally relates to simulation, and more particularly to converting a simulated circuit description to a higher level of abstraction. 
       BACKGROUND 
       [0003]    The complexity of integrated circuits (ICs) being designed nowadays is continuously increasing and has resulted in complete system-on-chip (SoC) solutions. Even more, the complexity of such integrated systems is exploding thanks to advances in process fabrication. The limiting factor is now the ability to design, manage and verify such systems rather than the ability to fabricate them. 
         [0004]    The typical design process begins with a software program that describes the behavior or functionality of a circuit. This software program is written in a hardware description language (HDL) that defines a behavior to be performed with limited implementation details. Logic synthesis tools convert the HDL program into a gate netlist description. The RTL description is used to verify functionality and ultimately generate a netlist that includes a list of components in the circuit and the interconnections between the components. This netlist is used to create the physical integrated circuit. 
         [0005]    As SoC&#39;s are becoming larger, the only way to efficiently design such dense SoC&#39;s, both from the design complexity and time-to-market aspects, is by embedding Intellectual Property (IP) cores. Standards for such cores are currently evolving. Ideally, they should be reusable, pre-characterized and pre-verified. But it often desirable to change the design to create the next generation. For example, as fabrication technology changes, it is desirable to convert or migrate the design to the new process parameters. For example, an IP core may be designed and tested for 90 nm technology, but it is desirable to convert the IP core to a new process of 60 nm technology. Or it may be desirable to update the design and incorporate changes in order to create the next generation design. 
         [0006]    In order to test and explore such changes in the design, simulation must be performed, which is very time consuming. A few seconds of real-time simulation can take weeks or even months. If the simulation results are not desirable, then the design process must start over again by changing the high-level code and re-simulating. 
         [0007]    Because of such delays in simulation, designers are beginning to move the design process to a higher level of abstraction (meaning less focus on design details). At the higher level of abstraction, design exploration can be performed to evaluate which performance and power consumption can be achieved, which parts to use, etc. The preferable higher level of abstraction is called Transaction Level Modeling (TLM), which refers to the evolving design and verification space called Electronic System Level (ESL) with methodologies that begin at a higher level of abstraction than the current mainstream Register Transfer Level (RTL). The main ESL design language SystemC, is driven from C/C++ rather than from hardware languages like Verilog and VHDL. 
         [0008]    The challenge is how to rewrite or convert existing models and code at the register transfer level to models and code at the electronic system level. There are some tools available that can make such a conversion, such as VTOC available from Tenison Corporation, but these tools do a simple code conversion without changing the level of abstraction. Thus, for example, having the same level of abstraction, including the same level of design details, means that the verification and simulation are just as slow. 
         [0009]    A simple example is if an engineer wants to use an existing circuit, but increase the memory size. There are no guarantees that making such an update will work. For example, increased memory size may drain the battery too quickly rendering the circuit unmarketable. Using current tools, the designer must either physically implement the circuit to see if it works or modify the RTL code and simulate the design. Such simulation may take weeks or even months, and if the modification does not work, the process must be started over again. 
         [0010]    Thus, it is desirable to convert an existing design from a lower level of code, such as RTL, to a higher level, such as ESL, while changing the abstraction level of the design in order to gain the benefits of having the code at the higher level. 
       SUMMARY 
       [0011]    A system and method are disclosed for converting an existing circuit description, specifically its timing characteristics, from a lower level description, such as RTL, to a higher-level description, such as TLM, while raising the abstraction level. By changing the abstraction level, the conversion is not simply a code conversion from one language to another, but a process of learning the circuit using neural networks and representing the circuit using a system of equations that approximate the circuit behavior, particularly with respect to timing aspects. A higher level of abstraction eliminates much of the particular implementation details, and allows easier and faster design exploration, analysis, and test, before implementation. 
         [0012]    In one aspect, a model description of the circuit, protocol information relating to the circuit, and simulation data associated with the lower level description of the circuit are used to generate an abstract model of the circuit that approximates the circuit timing behavior. 
         [0013]    In another aspect, such generation is accomplished using machine learning algorithms and/or a neural network. The neural network generates a system of weighted equations. Input patterns are used to calculate a difference between the actual output values (using the equations) and desired values (using simulated data) and extract a deterministic behavior. The weights of the equations can then be modified. 
         [0014]    In yet another aspect, causality analysis is used in order to synthesize the model description, protocol information and simulation data. The synthesized data may then be passed more efficiently through the neural network. 
         [0015]    In another aspect, the resulting abstract model can be simulated as-is to run pure performance analysis of a system, or can be plugged into TLM functional models and used to provide timing and functional behavior during fully functional simulation. 
         [0016]    These features and others of the described embodiments will be more readily apparent from the following detailed description, which proceeds with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  is a high-level flowchart of a method for converting a circuit description from a lower-level description into a higher-level description, while changing the level of abstraction. 
           [0018]      FIG. 2  is a flowchart of a method for converting a description of a circuit simulation into a series of transactions through message extraction. 
           [0019]      FIG. 3  is a hardware diagram of a system used to convert the description of the circuit into transactions. 
           [0020]      FIG. 4  is a detailed example showing simulated signal data of the circuit description on numerous hardware lines. 
           [0021]      FIG. 5  is a detailed example of a state machine for some of the available transactions. 
           [0022]      FIG. 6  is a detailed flowchart of a method for converting the simulated circuit description into transactions. 
           [0023]      FIG. 7  is a flowchart of a method for converting a series of transactions into a super-transaction representation. 
           [0024]      FIG. 8  shows a transaction-based view of the simulation data that may be displayed to the user. 
           [0025]      FIG. 9  is a flowchart of a method for performing model extraction of the circuit. 
           [0026]      FIG. 10  is a flowchart of a method providing further details for generating an abstract model. 
           [0027]      FIG. 11  is a hardware diagram of a system used to convert transaction data into an abstract model. 
           [0028]      FIG. 12  is an example of a fork table used in generating the abstract model. 
           [0029]      FIG. 13  is an example of a latency table used in generating the abstract model. 
           [0030]      FIG. 14  is a flowchart of a method for performing causality analysis. 
           [0031]      FIG. 15  is a flowchart of a method performed by a neural network for generating a system of equations approximating the circuit behavior. 
           [0032]      FIG. 16  shows a network that may be used to implement the invention. 
           [0033]      FIG. 17  is an exemplary flowchart of a method for implementing the invention over the network of  FIG. 16 . 
       
    
    
     DETAILED DESCRIPTION 
       [0034]      FIG. 1  shows a high-level flowchart for converting a circuit description from a low-level description (e.g., HDL, RTL) to a higher level of abstraction, such as a transaction level model (TLM). The low-level description generally includes details at the signal level, while the TLM uses high level functions and equations to calculate output transactions based on inputs and is not concerned with the device-level implementation of the circuit. ESL is an emerging electronic design methodology, which focuses on the higher abstraction level. Electronic System Level is now an established approach at most of the world&#39;s leading System-on-a-chip (SoC) design companies, and is being used increasingly in system design. From its genesis as an algorithm modeling methodology with ‘no links to implementation’, ESL is evolving into a set of complementary methodologies that enable embedded system design, verification, and debugging through to the hardware and software implementation of custom SoC, system-on-FPGA, system-on-board, and entire multi-board systems. ESL can be accomplished through the use of SystemC as an abstract modeling language. 
         [0035]    At process box  10 , simulation is performed on the low-level circuit description. At process box  12 , transactions are extracted from the simulation data. The simulation and transaction extraction process are described more fully in relation to  FIGS. 2-8 , but basically the system maps signal patterns into messages using pre-defined protocols (e.g., AMBA, PCI, etc.). Then the messages are converted to transactions. At process box  14 , model extraction is performed. The model extraction is described more fully in relation to  FIGS. 9-18 , but generally the system looks to repetitive correlation (i.e., deterministic behavior) between input sequences and output messages. Neural network functions are used to calculate the output message generation and extrapolate statistical behavior of a component. Additionally, data dependencies can be extracted. Finally, in process box  16 , the model is output at the higher level of abstraction. The model, in a sense, is like a black box where input transactions/messages are analyzed to generate output transactions/messages, without a focus on signal levels and values, but more a focus on timing and relationships between messages. The resulting abstract model can be simulated as-is to run pure performance analysis of a system, or can be plugged into TLM functional models and used to provide timing and functional behavior during fully functional simulation 
         [0036]      FIG. 2  shows a flowchart of a method for converting simulation data of a circuit description to a transaction-based description, which is at a higher layer of abstraction. In process box  20 , simulation data of a circuit description is received. The circuit description may be in HDL or any other software language and it may be compiled and simulated as part of a system design flow or it may be separately compiled and simulated. Thus, the simulation can be run in combination with the conversion process to a transaction-based description, or it can be run on a separate machine at a separate time. Any desired simulator may be used, such as ModelSim®, available from Mentor Graphics Corporation, or VCD (Value Change Dump) files generated by any other simulator. In process box  24 , the simulated circuit is converted into a series of transactions associated with a predetermined protocol. The protocol used is typically provided as input into the system by the user. In process box  26 , the simulation data is output in the foam of the transactions, which is a higher level of abstraction than the received simulated circuit design. For example,  FIG. 4  shows a simulated circuit description, which is at a signal level including a plurality of signals on various hardware lines.  FIG. 8  illustrates the converted circuit description at a transaction level. The output may be achieved by a variety of techniques, such as displayed to the user on a display (not shown), output to a file, etc. 
         [0037]      FIG. 3  shows a hardware diagram of a system  38  for converting a circuit description into a circuit description at the transaction level. A storage device  40  of any desired type has stored thereon the circuit design in HDL or any other desired language that may be used to describe circuits. A compiler  42  compiles the design and a protocol library  44 . The compiler  42  may be any desired compiler and is usually included as part of a simulator package. The protocol library  44  includes messages and transactions associated with a protocol used by the circuit. Messages include part of a transaction, such as a request and an acknowledge of the bus, whereas a transaction is a complete operation, such as any of a variety of types of Read or Write transactions or control or setup transactions. A simulation kernel  46  simulates the compiled design in a well-known manner, as already described. The simulation kernel  46  outputs the simulation data  48  in any desired format. Box  48  can also represent a pre-simulated design data (VCD format). 
         [0038]    A message recognition module  50  reads the simulation data  48  and analyzes the data to convert it to messages of the protocol stored in the protocol library  44 .  FIGS. 4-6  describe this conversion more thoroughly, but generally switching signals of the simulation are compared (during various time slices) to messages within the protocol library  44  to determine what message is being processed during a particular time slice. The messages associated with the switching signals during each time slice are then stored to convert the switching signals into messages. 
         [0039]    A transaction recognition module  52  reads the messages determined by the message recognition module  50  and converts the messages into transactions using a comparison of a series of messages to predetermined messages within the protocol library  44 . If a match is found, then the transaction recognition module stores the series of messages as a transaction. The result is that the messages are converted into a series of transactions. 
         [0040]    A transaction sequence recognition module  54  converts multiple transactions into a single super-transaction sequence. For example, several Writes can be converted into a single control operation. This conversion from multiple transactions to a super-transaction sequence is described further below in relation to  FIG. 7 . If desired, the transaction sequence recognition module  54  may be bypassed or omitted, so that the transactions are output directly. Results  56  of the conversion are output onto a storage medium or a display. 
         [0041]    In any event, the simulated circuit description is taken to a higher level of abstraction, as the simulation data is converted first to messages, then to transactions, and finally, if desired, to transaction sequences. The compiler  42 , simulator kernel  46 , and modules  50 ,  52 ,  54 , may all be run on the same computer. Alternatively, the circuit description may be compiled and simulated in a different location so that the resultant simulation data  48  is merely on a storage medium to be input into the message recognition module  50 . In such a case, as shown at  58 , it is desirable that the some of the protocol data from the protocol library  44  is incorporated into the simulation data in a pre-processing step. 
         [0042]      FIG. 4  shows a detailed example of part of the simulated signal data  48 . Various signal data  70  on hardware lines are shown including a clock line  72 , a read/write line  74 , a bus request line  76 , a ready line  78 , address lines  80 , and data lines  82 . Simulation is also carried out on many more hardware lines, which are not shown for convenience. The signals being simulated follow a predetermined protocol  84 . A protocol is a set of rules or standards designed to enable circuit elements to communicate together and exchange information with as little error as possible. The protocol  84  is made up of a plurality of transactions  85 , such as shown at  86  (i.e., transaction A) and at  88  (i.e., transaction B). A transaction is a discrete activity, such as a Read or Write operation that moves data from one place to another in the system. The transactions  86 ,  88  are in turn made up of a series of messages  90 . For example, transaction  86  is shown as including three messages,  92 ,  94 , and  96 . A message is a smaller unit of information electronically transmitted from one circuit element to another to facilitate the transaction. Example messages include “request for bus”, “acknowledge”, “ready”, etc. Those skilled in the art will readily recognize that these are only examples of transactions and messages and others may be used. Each message is associated with a time-slice  98 , such as those shown at  100 ,  102 , and  104 . Normally, the time-slices are based on the clock signal  72 . During each time-slice, the hardware lines  70  are analyzed to determine the message being sent in correspondence with the transactions of the protocol, as further described below. Transaction  88  is similar to transaction  86  and need not be further described. 
         [0043]      FIG. 5  shows an example part of a state machine  120  stored within the protocol library  44 . Different states  122  are shown as numbered circles. Messages, such as those at  90 , are shown in boxes, and cause the state machine to move from one state to another. Transactions may be defined by a path through the state machine  120  that starts at an idle state  124  (state  0 ) and that ends at the same idle state, although those skilled in the art will recognize that the state machine  120  may be constructed in a variety of different formats. For example, a read transaction  126  is made up of numbered states  0 ,  1 ,  2 ,  3 ,  4  and  5 . The read transaction  126  is completed upon return to the idle state from state  5  to state  0 , as shown by arrow  128 . A write transaction  130  is made up of numbered states  0 ,  1 ,  2 ,  6 ,  7 ,  8 ,  9 , and  10 . The write transaction  130  is completed upon return to the idle state from state  7  to state  0 , as shown by arrow  132 . 
         [0044]      FIG. 6  shows a flowchart of a method preformed by the message recognition module  50  and the transaction recognition module  52  in order to convert the simulation data into a transaction-based description. At process box  150 , the simulated input data (see box  48  in  FIG. 3 ) is received so that it may be used by the message recognition module  50 . Such simulation data is normally within a database. In process box  152 , the analysis starts by monitoring the signal data  70  on the various hardware lines upon which messages are received. Additionally, in process box  152 , the protocol library  44  is read to access a state machine, such as state machine  120 , associated with the protocol. In process box  154 , in order to analyze a transaction, an assumption is made that the transaction starts from the idle state  124 . In process box  156 , a time-slice of data is read corresponding to the clock signal on hardware line  72 . For example, in  FIG. 4 , the data may be read starting with a time-slice  100 . Thus, the switching signals on the various hardware lines are read in order to be analyzed. In process box  158 , the data read is analyzed by comparing the switching signals to known patterns of messages stored in the protocol library  44 . Returning briefly to  FIG. 5 , from the idle state  124 , a bus request message changes the state of the state machine to state  1 . A bus request message has a particular pattern of signal data on the hardware lines, which is compared to a known pattern in the protocol library  44 . Thus, once a match is found between the known pattern of messages and the message analyzed during the currently analyzed time-slice, the message has been determined and is stored in process box  160 . In process box  162 , the current state of the state machine is updated to reflect the change of state. Continuing with the example, the new state is state  1  after a bus request message is received. In decision box  164 , a determination is made whether the state machine has returned to the idle state. If yes, this indicates that a transaction is complete and the transaction is determined in process box  166  by comparing a sequence of the stored messages to a sequence of known messages in the protocol library  44 . The sequence of stored messages are those received from the start of the idle state until the state machine returned to the idle state. Once a match is found between the sequence of stored messages and those in the protocol library, the transaction associated with those messages is easily obtained from the protocol library  44 . The determined transaction is then stored as indicated in process box  166 . In decision box  168 , a check is made whether all of the input simulated signal data has been analyzed by reading whether the database including the signal data is at the end. If yes, the method ends as shown at  170 . Otherwise, the method continues at process box  156  and the next time-slice is read (e.g., time-slice  102 ). Once the method ends, the database of signal data is converted into a series of transactions associated with the protocol found in the protocol database  44 . 
         [0045]      FIG. 7  shows a method implemented by the transaction sequence recognition module  54  (see  FIG. 3 ). It may be desirable to group transactions together in order to display to a user the circuit at an even higher level of abstraction. For example, several write/read transactions can be shown as a single control transaction as opposed to individual transactions. In process box  200 , a group of transactions is selected. For example, if there are many of the same type of transactions in sequence (e.g., Reads), such a sequence may be condensed. In process box  202 , the selected group is compared to predetermined groups. In decision box  204 , a determination is made whether there is a match between the selected group and the predetermined groups. If there is a match, then in process box  206 , the sequence of transactions is stored as a single transaction in order to convert the circuit description to an even higher level of abstraction. In decision box  208 , a check is made whether all of the transactions have been read. If yes, then the method ends at  210 . If not, then a new group of transactions is chosen at  212 , and the process starts over at process box  202 . 
         [0046]      FIG. 8  shows an example of a display showing the simulation data of  FIG. 3  at a higher level of abstraction. Particularly, instead of signals, the simulation data is shown as a series of transactions. Write transactions, such as at  240 , are shown as dotted lines and read transactions, such as shown at  242 , are shown as solid lines. Throughput is shown along the Y-axis and time is indicated along the X-axis. Thicker lines generally mean there is a grouping of many transactions so close in time that at the current zoom level they cannot be distinguished. Of course, a zoom option may be used to focus on particular transactions. As can readily be seen, the view of  FIG. 8  is much easier to read than that of  FIG. 4  and allows the designer to obtain a better overall system view of the flow of data. 
         [0047]      FIG. 9  shows a flowchart of a method for implementing model extraction  14  ( FIG. 1 ). In process box  300 , input files are received related to protocol information, model description, and simulation data for the circuit. The protocol information is provided by the user and is stored in the protocol library  44 . The model description is also provided by the user and includes an interface of the circuit model describing the input/output ports and the lasting state description of the circuit model that describes the internal states elements thereof. The simulation data may be simulation data  48  (see  FIG. 3 ) or simulation data at the transaction level  56  ( FIG. 3 ). In process box  302 , using the input files, an abstract model is generated that approximates the circuit behavior. Although particular values may be associated with the approximated circuit behavior, in general the timing aspects are the focal point. For example, a particular address and read data are of less importance than when the address arrives and when the data is output. Such parameters can be added manually as they are easier to model (functionality is in many cases more simple than timing behavior). In process box  304 , the abstract behavioral model is output. 
         [0048]      FIG. 10  is a flowchart of showing further details of process box  302 . In process box  320 , a set of tables is created that is associated with the input files. As explained further below, these tables are used to combine all of the input information into a desirable format for the causality analysis and the learning phase. In process box  322 , causality analysis is performed on the tables. The causality analysis is described further in  FIG. 14 , but generally it is an analysis on the inputs in the table and the outputs in order to find a repetitive correlation there between. When there is a high degree of repetitive correlation of particular ‘events’, such events are given higher importance. On the other hand, signals that are seen only once may be disregarded in order to lessen the analysis of the learning phase. In process box  324 , learning is performed. The learning is described further in  FIG. 15 , but generally “learning” is a standard term used in the industry, especially relating to neural networks. For example, an article entitled “Conditional Distribution Learning with Neural Networks”, IEEE Signal Processing 1997, written by Tulay Hadah, Xiao Liu, and Kemal Sonmer describes some aspects of “learning” using neural networks. In process box  326  model checking is performed in order to compare the generated model to the desired results. 
         [0049]      FIG. 11  shows a part of the system for performing the model extraction. Some aspects in  FIG. 11  have been already discussed. For example, the simulation data  56  and the protocol library  44  were discussed in relation to  FIG. 3 . Although the simulation data  56  is shown at the transaction level, it may be simulation data  48 , if desired. However, simulation data at the transaction level allows much less data to be fed into the analysis, significantly speeding the process. A protocol source file  350  is passed through a compiler  352  and the result is stored in the protocol library  44 . Lasting state information source file  354  contains information regarding the inner states of the circuit being analyzed (e.g., describes registers in the circuit) and is also compiled in compiler  356  and stored in a file called Model Data  358 . An interface source file  360  contains information regarding the input and output ports of the circuit being analyzed. File  360  is passed through compiler  362  and combined with the compiled lasting state file  354  within the model data file  358 . The above-described compiled files are passed together with the simulation data  56  to a table generator  370 . The table generator uses all of the input files to generate multiple tables, including fork tables  372 , latency tables  374 , and data tables  376 . The fork table  372  includes information regarding which path was taken during simulation when a branch was encountered in the protocol.  FIG. 12  provides an example fork table and is described further below. The latency tables  374  include information regarding the delay from a change of input until the corresponding output is changed. The data tables  376  include values associated with the output. In general, data values are not needed because timing is more interesting for the overall analysis. However, some data values may be tracked depending on options set by the user. 
         [0050]    The table generator  370  outputs the resulting tables to the causality analysis engine  380  and to a neural network  302 . As described further below, the causality analysis engine performs time-based causality analysis by applying a number of algorithms to each output message to compute the most likely causality basis. The results are also statistically analyzed and reduced so that only the most pertinent information is fed to the neural network  382 . The neural network  382  generates equations that approximate the circuit behavior. Those skilled in the art will recognize that the neural network can be replaced by any other machine learning or statistical algorithm. The model checker  384  performs a check by comparing the inputs and outputs using the generated equations to the simulated data. 
         [0051]      FIG. 12  shows an example fork table  400  generated by the table generator  370 . The fork table includes multiple rows  402  representing events and multiple columns  404 , most of which represent lasting state parameters. Column  406  includes a fork field. The fork field may include numbers (not shown) indicating which direction a fork was taken in association with an event and the associated lasting state parameters. 
         [0052]      FIG. 13  shows an example of a latency table  410 . The latency table also includes rows  412  representing events. Many columns  414  represent lasting state parameters. The last three columns  416 ,  418 , and  420  represent the event name, the time, and the latency, respectively. Some simple examples showing possible values are shown. 
         [0053]    As is well known, the format and fields within a table is design specific and a wide variety of different formats and fields may be used. 
         [0054]      FIG. 14  is a flowchart of a method showing the operation of the causality engine  380 . In process box  440 , a set of causality characters is defined. Basically, when a repetitive correlation between inputs and outputs is found, a character is assigned to such a situation. For each output message in the latency table, causality characters are defined with each character represented as a pair having the form (event, time delta). Thus, the causality character describes a situation in which the specified event causes the output message after a given period of time. In process box  442 , the number of causality characters is statistically reduced. Reduction of information ultimately provided to the learning process increases the speed of the system. Elimination of some characters can be accomplished using a hypothesis algorithm that provides a probability for a character to be part of the actual causality model. Thus, characters with limited appearances are generally eliminated. In process box  444 , the causality characters are further reduced using a genetic optimization algorithm that creates a model for the least amount of causality characters possible and still allowing to choose a cause for each output message instance. In process box  446 , tables are created including will and time tables. The will table relates to something that caused an output change, such as an input in combination with a lasting state. The time table relates contains the remaining character lines (after the reductions) with the latency time value. 
         [0055]      FIG. 15  is a flowchart of a method for performing “learning”  324  ( FIG. 10 ). In process box  460 , the tables generated in process box  446  ( FIG. 14 ) are used as well as tables generated from the table generator  370  ( FIG. 11 ) in order to create a system of weighted equations that represent the behavior of the circuit. Thus, for example, the inputs and outputs are analyzed in conjunction with state information to generate the equations. Such a generation of equations is well known in the art using standard techniques of neural networks. In process box  462 , input patterns are applied to the generated system of equations to generate actual values produced by the equations. In process box  464 , an error is calculated by using a difference between the actual values (process box  462 ) to the desired values (determined during simulation). In process box  466 , based on this difference, the weightings in the system of equations are modified in order to more closely match the desired values. In decision box  468 , a check is made whether the actual values generated by the system of equations are within an acceptable limit. If so, the flowchart is exited at  470 . In not, the flow returns to process box  462  in order to re-analyze the equations. 
         [0056]      FIG. 16  shows that portions of the system may be applied to a distributed network, such as the Internet. Of course, the system also may be implemented without a network (e.g., a single computer). A server computer  480  may have an associated database  482  (internal or external to the server computer). The server computer is coupled to a network shown generally at  484 . One or more client computers, such as those shown at  488  and  490 , are coupled to the network to interface with the server computer using a network protocol. 
         [0057]      FIG. 17  shows a flow diagram using the network of  FIG. 16 . In process box  500 , the circuit description to be transformed is sent from a client computer, such as  488 , to the server computer  480 . In process box  502 , the abstract model of the circuit description is generated that approximates or imitates the circuit behavior, as previously described. In process box  504 , the generated abstract model is checked against simulation results. In process box  506 , the results are sent though the network to the client computer  488 . Finally, in process box  508 , the results are displayed to the user. It should be recognized that one or more of the process boxes may be performed on the client side rather than the server side, and vice versa. 
         [0058]    Having illustrated and described the principles of the illustrated embodiments, it will be apparent to those skilled in the art that the embodiments can be modified in arrangement and detail without departing from such principles. 
         [0059]    In view of the many possible embodiments, it will be recognized that the illustrated embodiments include only examples of the invention and should not be taken as a limitation on the scope of the invention. Rather, the invention is defined by the following claims. We therefore claim as the invention all such embodiments that come within the scope of these claims.