Method for circuit verification and multi-level circuit optimization based on structural implications
TECHNICAL FIELD OF THE INVENTION 
     This invention relates in general to the field of computer aided design (CAD) as used with very large scale integrated circuits (VLSI). More specifically, the present invention relates to a method for circuit verification and multi-level circuit optimization based on structural implications. Furthermore, the present invention relates to a method for verifying that first and second circuits are equivalent based on implication analysis. The invention also relates to a method for multi-level circuit optimization by circuit transformations based on structural implication analysis. 
     BACKGROUND OF THE INVENTION 
     In recent years, the size and complexity of integrated circuits have increased dramatically. As a result, the computer industry has increasingly moved towards automated design of integrated circuits. In fact, many different systems are currently used to aid an engineer in designing and synthesizing integrated circuits. The circuits designed by these automated systems may not be fully optimized and in fact may produce erroneous circuits. Therefore, the computer generated circuits may require further refining to verify and optimize the design. Circuit verification and circuit optimization require complicated and time consuming analysis. Tools are currently available to aid a circuit designer in verifying and optimizing an integrated circuit. 
     Heretofore known systems and methods for circuit verification typically use a functional approach. A functional approach uses the functionality of an integrated circuit to either verify or reduce the size and complexity of the circuit. A disadvantage of a functional approach is that it may not be generally applicable to different classes of practical circuits. Hence, a functional approach to circuit verification and optimization may not provide a general framework for an efficient solution. An alternative heretofore known method and system may use a structural approach to verify and optimize an integrated circuit. These structural methods may require less memory than the functional approach. However, these structural methods consume large amounts of processing time. 
     Various techniques for two-level optimization are well established in the art. However, multi-level circuit optimization is not as well delineated. Even with much recent progress, the size and complexity of today&#39;s integrated circuits leave multi-level logic optimization a major challenge in the field of computer aided circuit design. Presently, the most general synthesis techniques for combinational circuits are based on manipulation of boolean functions. Such boolean techniques may be the only techniques which may enable a designer to exploit the full range of possible transformations in a combinational network. These boolean techniques may be able to handle existing circuits of realistic size. However, they may not provide an efficient solution for the ever increasing size of integrated circuits. Structural methods are also currently available for circuit optimization. These techniques suffer from the limitation that they do not provide a general framework that allows a designer to perform all possible transformations in a circuit. 
     Accordingly, a need has arisen for a fast and efficient method for circuit verification and optimization. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, a method for circuit verification and circuit optimization which substantially eliminates or reduces disadvantages and problems associated with prior methods is provided. In one embodiment, the method comprises verifying first and second logic circuits for functional equivalence. The method begins by coupling the inputs of first and second circuits. Each node of the first and the second circuits are reset to a first pre-determined state. A pre-determined signal value is assigned to a node of the first circuit, such that the corresponding assignment creates an unjustified signal at the node. Signal value assignments for each of the other nodes in the first and second circuits are determined such that these signal value assignments result in conditions which are consistent with the original predetermined signal value. A signal value for a node of the second circuit corresponding to the predetermined signal value of the node of the first circuit is extracted. The extracted information of the internal signal relationships between the two circuits is stored in the internal memory. The steps of assigning, determining, extracting and storing for different nodes of the first and the second circuit are repeated until the logic of the two circuits are verified for equivalency based on a set of pre-stored signal relationships in the internal memory. 
     A technical advantage of the present invention inheres in the fact that it minimizes the amount of memory used in verifying or optimizing an integrated circuit. The method is based on structural techniques. Therefore, the method need only store the structural description of the circuits in the memory. Hence the memory used in implementing the method is linearly related to the size of the circuits to be analyzed. 
     Another technical advantage of the present invention inheres in the fact that the method allows relatively fast verification and optimization of integrated circuits as compared with heretofore known methods. The method uses prestored indirect implications. These indirect implications are evaluated based on a fast procedure called recursive learning. 
     Another technical advantage of the present invention inheres in the fact that it is applicable to a wide variety of practical circuits. The method uses a generalized framework based on structural techniques which considers many different transformations for circuit optimization. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete understanding of the method of the present invention may be acquired by referring to the detailed description and claims when considered in conjunction with the accompanying drawings, wherein: 
     FIG. 1 is a block diagram of a system implementing a method for verifying logic between two circuits according to the teachings of the present invention; 
     FIG. 2 is a flow chart illustrating a method of logic verification according to the teachings of the present invention; and 
     FIGS. 3a, 3b and 3c illustrate optimization of a circuit using indirect implications. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     CIRCUIT VERIFICATION 
     FIG. 1 is a block diagram of a system indicated generally at 8 implementing a method for verifying logic between first circuit 10 and second circuit 12 according to the teachings of the present invention. System 8 uses indirect implications to verify that first circuit 10 is equivalent to second circuit 12. For example, system 8 may determine whether the logic of first circuit 10 is equivalent to the logic of the second circuit 12. Each of first and second circuits 10 and 12 may comprise multi-gate logic circuits. Each of circuits 10 and 12 therefore may have a plurality of functional nodes. Due to the nature of the method of the present invention, the nodes of circuits 10 and 12 are not shown. However, the teachings of the present invention are not limited to verifying only logic circuits. An implication is a procedure whereby a signal value at a node may be derived from signal values at other nodes in the same circuit. An implication which may be derived by evaluating a truth table based on known input or output values is called a direct implication. An indirect implication is an implication which cannot be found by evaluating the truth table of logic primitives and propagating their effect in an event driven fashion. In system 8, indirect implications are used to identify nodes in the first and second circuits 10 and 12 which are functionally equivalent. Thereby, system 8 verifies the equivalence of the first and second circuits 10 and 12. 
     The input line 14 is coupled to input line 16 of the first circuit 10 and input line 18 of second circuit 12. Input lines 14, 16, and 18 may each comprise a bus having more than one bit. An output line 20 of the first circuit 10 is coupled with output line 22 of the second circuit 12 with an exclusive OR gate 24 to produce a system output 26. 
     In operation, the equivalence of the first circuit 10 and second circuit 12 is determined by the output 26 of system 8. The method implemented by system 8 is illustrated in FIG. 2. In principle, the first and the second circuits 10 and 12 are not equivalent if an input at input lines 14 may be assigned to system 8 such that the output 26 is equal to a high logic value represented by a &#34;1&#34;. Otherwise, the first and the second circuits 10 and 12 are equivalent. 
     FIG. 2 is a flow chart illustrating a method of logic verification that may be used by system 8 of FIG. 1 according to the teachings of the present invention. The method begins at block 40. At block 42, various parameters are established. For example, the maximum number of recursions implemented by the method may be established. At block 44, a description of the first circuit 10 and the second circuit 12 is read into an internal memory of a computer. The first circuit 10 and the second circuit 12 are coupled as shown and described with respect to FIG. 1. At block 46, all nodes of the first and the second circuits 10 and 12 are reset to a predetermined state. 
     At block 48, a predetermined signal value is assigned to a node of the first circuit 10, such that the corresponding assignment creates an unjustified signal at that node. An unjustified signal is one where there is a possibility of a signal inconsistency at the gate associated with the signal. The predetermined signal value may be set equal to a low logic value, 0, for an AND or a NOR gate. Alternatively, the predetermined signal value may be set to a high logic value, 1, for an OR or a NAND gate. For each node after the said assignment, all the indirect implications are found using an efficient technique called recursive learning. For example, the software program attached to the specification may be used to implement the recursive learning function to derive the indirect implication. 
     In block 50, signal value assignments for other nodes in the first and the second circuits 10 and 12 are determined such that the signal value assignments for each of the nodes result in conditions which are consistent with the predetermined signal value of the node established at block 48. In block 52, a signal value for a node of the second circuit 12 corresponding to the predetermined signal value of a node of the first circuit 10 is extracted. The extracted information of the internal signal relationships between the first circuit 10 and the second circuit 12 is stored in the internal memory of the computer. In block 56, if all the nodes have not been evaluated, the steps of blocks 48, 50, 52, 54 are repeated. If the preprocessing for all the nodes are completed, the method goes to block 58. Here, a test generator is invoked to justify the assignment of logic value one to the output 26 of system 8. A test generation is a method which determines input signal values which can detect faults in the circuit. This test generator is based on recursive learning. 
     In block 60, if the operations in block 58 do not lead to a decisive result, the method goes to block 62. Here, a decision is made whether to continue or to abort based on the user defined recursion level. If the method is aborted, it ends in block 64. If the method is not aborted, it returns to block 48. 
     In block 60, if the operations in block 58 lead to a decisive result, the result is analyzed in block 66. If the assigned output value 26 of the system 8 is justifiable, the circuits are proved not to be equivalent at block 68. Otherwise, the circuits are proved to be equivalent at block 70. 
     CIRCUIT OPTIMIZATION 
     Multi-level logic optimization plays an important role in the process of automatically designing highly integrated circuits. The goal of multi-level optimization is to transform an arbitrary combinational circuit, A into a functionally equivalent circuit, B where circuit B is cheaper than circuit A according to some cost function. This Cost function typically takes into account area, speed, power consumption and testability as the main objectives of the optimization procedures. In one embodiment, the method of the present invention focuses on optimizing the area of the given circuit. 
     The method of the present invention involves iteratively performing the following two steps in a logic circuit: 
     1) Make the logic network prime and irredundant. 
     2) If further area reduction is needed then choose a different network configuration by applying one of the four transformations described below. 
     A digital circuit is prime and irredundant if and only if all single stuck-at faults in the circuit are testable. A stuck-at fault is a fault model which models the fault as a signal connected to a logic zero or a logic one. If for some input combination to the circuit the difference between the fault-free and faulty circuit can be detected at the primary outputs of the circuit then the fault is testable. Various techniques are known in the art for making the logic network prime and irredundant. 
     In step 2, recursive learning is used to extract indirect implications in a given circuit. Based on indirect implications, one of the transformations listed below derived from Shannon&#39;s Formula is used to transform the circuit. These transformations are shown by way of example and not by way of limitation. Other transformations may be used without departing from the spirit and scope of the method of the present invention. 
     As used below, y, y1, y&#39;, y0, and f represent logic functions. The logic function y1 is equal to the function y under the condition f=1. The logic function y0 is equal to the function y under the condition f=0. After the transformation is applied to the function y it is renamed y&#39; which is functionally equivalent to y. The transformations are:* 
     
         Transformation 1 : y&#39;=y.sub.1 +ƒ                  1) 
    
     Transformation 1 is valid if and only if the implication y=0 ƒ=1 is true. 
     
         Transformation 2 : y&#39;=y.sub.0 +ƒ                  2) 
    
     Transformation 2 is valid if and only if the implication y=0 ƒ=0 is true 
     
         Transformation 3 : y&#39;=ƒy.sub.1                    3) 
    
     Transformation 3 is valid if and only if the implication y=1 ƒ=1 is true. 
     
         Transformation 4 : y&#39;=ƒy.sub.0                    4) 
    
     Transformation 4 is valid if and only if the implication y=1 ƒ=0 is true. 
     FIGS. 3a, 3b and 3c illustrate an example using the transformations described above to optimize a circuit. Recursive learning is used on circuit 72 of FIG. 3a to derive the indirect implication; y=0 implies f=0. For example, the software program attached to the specification may be used to implement the recursive learning function to derive this indirect implication. Based on this indirect implication, transformation 2 is selected. After the application of this transformation, the circuit which realizes function y0 is shown as circuit 74 in FIG. 3b. This y0 is obtained by replacing f in circuit 72 with a boolean zero. The transformed circuit, y&#39;=y 0  +ƒ, is shown as circuit 76 in FIG. 3c. The final circuit 76 is an optimized version of the original circuit 72 with respect to the number of gates used to realize the same logic function. 
     Although the present invention has been described in detail, it should be understood that various changes, substitutions and alternations can be made hereto without departing from the spirit and scope of the invention as defined by the appended claims. For example, other transformations may be used in the optimization method of the present invention. Furthermore, the circuit verification and optimization methods of the present invention are not limited for use with digital systems. The teachings are equally applicable to analog systems. ##SPC1##