Abstract:
In a method for improving a circuit having a logically false path through static analysis of a software model, a computer receives information describing the false path, determines a true path alternate to the false path, and analyses the circuit model with respect to the true path.

Description:
This application is a continuation of application Ser. No. 08/318,002, filed Sep. 30, 1994 now abandoned, which is a continuation of application Ser. No. 07/897,789, filed Jun. 12, 1992 now abandoned. 
    
    
     REFERENCE TO APPENDIX 
     A source code listing of an embodiment of the invention is attached as Appendix A. 
     A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure as it appears in the Patent and Trademark Office file or records, but otherwise reserves all copyright rights whatsoever. 
     BACKGROUND OF THE INVENTION 
     This invention relates to static timing verification of integrated circuit designs. 
     Prototyping a VLSI (very large scale integrated circuit) design is extremely expensive: fabbing (fabricating) a pass of a prototype full-custom VLSI chip would take several months and would cost several hundred thousand dollars. If the chip design is flawed, the chip itself is almost impossible to probe to isolate the problem and determine corrections to the design. For this reason, virtually all VLSI chips are designed and thoroughly verified by software modelling before the first actual silicon is fabbed. 
     A timing verifier is one program in the suite of tools used by a VLSI designer. Timing verification is the process of analyzing the circuit model to ensure that the signals propagate through the logic quickly enough to meet the timing requirements at a specified clock frequency. (A timing verifier may also may additionally include other analysis tools, for instance for race conditions or other logic problems.) Once the circuit has been largely designed using other tools of the suite, the timing verifier is used to improve it, e.g., to eliminate bottlenecks that would force the circuit to be run at a slow clock frequency. The timing verifier takes as input a description of the circuit and its interconnections, the impedances and/or loading of the wires, specifications of the devices in the logic path, and descriptions of the clocked elements, and produces as output timing of the slowest paths, i.e., the &#34;critical paths&#34;, from which the designer can deduce the maximum clock frequency at which the circuit can be run. The designer can then redesign the critical paths to speed them up, thus speeding up the entire circuit. This process is typically iterative: the designer runs the timing verifier, and modifies his circuit design using the information generated. He repeats this process until the number of critical paths with the same timing limit is so large that reducing the time of all of them becomes impractical. 
     In a synchronous integrated circuit (IC) design, major signals are captured in latches at clock edges and are held at stable values when and while the clock is deasserted. The value of the signal at the output of a latch, a latched signal, is only allowed to change during the time the clock signal is asserted. During the time the clock is asserted, changes on the D input to the latch immediately propagate through the latch to the Q output; thus the clock assertion is said to make the latch transparent. The latched signals propagate downstream through combinatorial logic to other latches. The timing verifier reports any latches (or other clocked element) whose inputs are not stable in time to meet the requirements of the latch&#39;s clock. 
     FIG. 1 depicts a simple illustrative circuit, which will be considered under a simplified model of timing constraints and design rules. Two input signals A 100 and B 102 are latched by latches 108 and 110. Thus, signals A&#39; 112 and B&#39; 114 are stable except when the two latches 108 and 110 are transparent, which occurs when clocks Ck A  104 and Ck B  106 are asserted. Once A&#39; and B&#39; have been latched, they remain stable, and combinatorial logic CL 1  116, CL 2  120, and CL 3  122 compute signals Y 124 and Z 126. Each of CL 1 , CL 2 , and CL 3  impose a certain delay in this computation. The downstream part of the design (not shown) relies on Y 124 and Z 126 being latched by latches 132 and 134 on clocks Ck Y  128, and Ck Z  130. Thus, CL 1 , CL 2 , and CL 3  must be fast enough to meet the setup requirements of latches 132 and 134. 
     FIG. 2 presents a timing diagram for the circuit of FIG. 1. The first three lines show the clocks Ck A  104, Ck B  106, Ck Y  128, and Ck Z  130. In this example, A and B are latched on the same clock. Signals A and B must be stable far enough before the falling edge of Ck A  /Ck B  206 to accommodate a &#34;setup time&#34; 208, a characteristic of latches 108 and 110. Once latches 108 and 110 become transparent during Ck A  /Ck B  204, (assuming that the setup time and the data-to-output time of the latches are equal) signals A&#39; and B&#39; are allowed to transition until they are latched on the falling edge of Ck A  /Ck B  206. A&#39; and B&#39; drive CL 1 , CL 2 , and CL 3 , which in turn produce signals X, Y, and Z. Under the simplified timing rules, the timing constraints of the circuit are satisfied if the propagation delay 208 of latch 108 plus the propagation delays through CL 1  216 plus CL 2  220 plus the setup time 232 of latch 132 is less than the time from the fall of clock Ck A  /Ck B  to the fall of clock Ck y  228, and if the propagation delay 208 of latch 110 plus the time delay through CL 1  216 plus CL 3  222 plus the setup time 234 of latch 134 is less than the time from the fall of clock Ck A  /Ck B  to the fall of clock Ck Z  230. The paths of A&#39;-CL 2  -Y and B&#39;-CL 3  -Z must also meet the timing requirements of latches 132 and 134, but these will be trivially satisfied because they are clearly faster than paths A&#39;-CL 1  -X-CL 2  -Y and B&#39;-CL 1  -X-CL 3  -Z. When all these conditions are satisfied, the circuit is said to pass timing verification. 
     If the circuit fails timing verification, the timing verifier will report the critical paths that failed. Either the logic on the slow paths needs to be redesigned to be faster, or the clock frequency needs to be slowed down to accommodate the timing of the circuit. 
     Timing verifiers operate on one of two general paradigms: dynamic or static. 
     In dynamic timing verification, the circuit design is simulated through time. The engineer must determine model input stimuli with which to drive the circuit model, called test vectors. Applying dynamic timing verification to the sample circuit to FIG. 1, the timing verifier would successively apply twelve stimuli where either A or B or both undergo transitions: AB→AB={00→01, 00→10, 00→11, 01→00, 01→10, 01→11, 10→00, 10→01, 10→11, 11→00, 11→01, 11→10 } and run a loop to simulate time, during which model clock Ck A  /Ck B  would undergo several transitions. The circuit model would be operated through time to see at what time signals Y and Z stabilize. Dynamic timing verification is effective in that it is capable of diagnosing all timing problems, at least for the test vectors applied. But in modern circuit designs, the super-exponential combinatorics on tens of thousands of signals is fatal to the dynamic approach: there simply isn&#39;t time to test all possible combinations of inputs (most of which would never arise in actual operation), nor for a human to filter out a set of meaningful test vectors that will test all the effective paths. 
     In the second paradigm, static analysis, there is no loop simulating the passage of time. Static analysis is to dynamic analysis as theorem proving is to case analysis: instead of attempting to simulate a &#34;large enough&#34; number of specific cases, a static timing verifier &#34;reasons&#34; about the circuit model and draws inferences about whether the circuit will meet its timing constraints. This generally involves analyzing every node--i.e., every wire--in a circuit and calculating transition times based on the arrival time of inputs and the propagation delay through the structures. As the times of the transitions of the inputs to a node are analyzed, only the latest transition (in time) is saved, and the algorithm immediately stops tracing any path that is known not to be the worst case. This process, called information pruning, is required to keep the execution times reasonable. 
     One known algorithm for static timing verification is a depth-first search (DFS) of the circuit starting at each signal guaranteed on a clock edge, labelling each node with the currently best-locally-known worst-case timing information. After all nodes have been labelled, a second pass examines all timing constraints to tell the designer whether the circuit as a whole meets its timing constraints. 
     Consider the circuit of FIG. 3, in which a first stage of the circuit has two paths of different delay times, which join at a multiplexer. The output of the multiplexer fans out in a second stage of two paths of different delay times, which are joined at a second multiplexer. The DFS algorithm represents each node of a circuit by a data structure as shown in FIG. 4. The node has a name, a &#34;worst case arrival time,&#34; and a pointer to the node that drove this worst-case transition. 
     FIGS. 5a-e depict a DFS analysis of the circuit of FIG. 3: FIG. 5a shows a time-sequence of stack states, and FIGS. 5b-e show a time sequence of states of data structures. 
     In the DFS algorithm, the graph of the nodes of the circuit is walked in a depth-first order. The algorithm&#39;s walker maintains a current &#34;arrival time,&#34; and a stack of nodes. (Since this is a static analyzer, note that the &#34;arrival time&#34; does not &#34;tick&#34; off time incrementally, it moves forward and back by the discrete amounts of delay of the logic walked.) The DFS walker pushes nodes onto the stack as it traces paths downstream, and pops them as it unwinds back upstream. The walker increments its arrival time as it walks downstream through logic by the time delay of the logic, and decrements it the same amount as it unwinds back. As the algorithm pushes each node, if the walker&#39;s arrival time is later than the current &#34;worst case arrival time&#34; (or simply &#34;.time&#34;) of the node, then the node is updated with the value of the DFS arrival time, and the node&#39;s &#34;worst case predecessor&#34; (or simply &#34;.predecessor&#34;) is pointed at the predecessor node down which the DFS walk came, and the DFS continues down the successor nodes. If the DFS arrival time is equal to or earlier than the current node&#39;s worst case arrival time, the probe of this path is abandoned, and the node is popped off the stack. 
     In FIG. 5a, each column depicts a step 300 identified by number, and the value of the DFS arrival time 302 during that step. The state of the DFS stack 304 is also shown, with the top of the stack in bold. The term &#34;labelled&#34; is used to describe information permanently (though overwritably) stored in the representation of the circuit. &#34;Unvisited&#34; is used in a local sense: a node is unvisited if it as not been visited via the current path, even if it has been previously visited via a different path. 
     step 1: FIG. 5b shows the configuration of the nodes for the circuit of FIG. 3 as the algorithm visits the first node of the circuit, node A 310. All the node names have been filled in. A.predecessor and A.time have been filled in (by the process about to be described in detail). 
     step 2: Assume that A&#39;s list of successor nodes is ordered such that the algorithm visits C, then B. Thus, the algorithm walks to node C. Since the logic connecting A to C, CL 2 , consumes 11ns, the DFS algorithm carries the arrival time 12 as it arrives at C. The algorithm, finding C not already labelled, labels C.time with 12 and points C.predecessor to A. 
     step 3: The only successor of C is D, through logic consuming 1ns, so the algorithm proceeds to D and sets D.time 13 and points D.predecessor to C. Assume that D&#39;s list of successor nodes is ordered such that the algorithm visits node E, then F. 
     step 4: Node E is filled in with time 26 and predecessor D. 
     step 5: Node G is filled in with time 29 and predecessor E. The walk would continue downstream from node G. 
     The intermediate state after step 5 is shown in FIG. 5c. The &#34;worst-case arrival times&#34; 322 have been filled in with a preliminary estimate of the latest transition time. The .predecessor pointers 320 show a preliminary estimate of the critical path to G, A-C-D-E-G. After the algorithm has visited all downstream logic and popped its stack to G: 
     step 6: DFS pops its stack to back E. E has no unvisited successors. 
     step 7: DFS pops its stack back to D. D has an unvisited successor, F. 
     step 8: Node F is filled in with time 32 and predecessor D. 
     step 9: When DFS arrives at node G with arrival time 33, it finds the node already labelled, but with a time earlier than the current DFS arrival time. Thus, G is updated with time 33, and G.predecessor is updated to point to node F. Note that pointing G.predecessor from E to F &#34;prunes&#34; from the graph all analysis downstream of E that was computed between steps 5 and 6. The algorithm has proved that E cannot possibly be on the critical path to G nor any node downstream of G. Because G has been relabelled, the nodes downstream of G must be walked again to have their times updated. 
     The intermediate state after step 9 is shown in FIG. 5d. 
     step 10: DFS pops its stack back to node F. 
     step 11: DFS pops its stack back to node D. D has no unvisited successors. 
     step 12: DFS pops its stack back to node C. 
     step 13: DFS pops its stack back to node A. The next unvisited successor of A is B. 
     step 14: B is labelled with time 8 and predecessor A. 
     step 15: DFS arrives at node D with arrival time 9. The arrival time is earlier than the current time of node D; thus, the algorithm stops probing along this path: all paths downstream of node D through node B are also said to be &#34;pruned.&#34; By the same reasoning used in step 9, the algorithm has proved that the critical path to all nodes downstream of D must pass through C, not B. 
     step 16: DFS pops its stack back to node B. 
     step 17: DFS pops its stack back to node A. Node A now has no unvisited successors. 
     Finding no unvisited successors of A, the DFS algorithm is complete. The result of the algorithm is the critical path graph of FIG. 5e. For instance, the critical path to node G can be discovered by tracing the .predecessor pointers from a node; e.g., the critical path to G is seen to be A-C-D-F-G. The critical path graph will be of the form of a forest of trees, each tree rooted at one of the input nodes or interior latches. Paths B-D and E-G have been pruned; no larger path that would have used these paths will be analyzed. 
     There may be multiple critical path graphs built for a single circuit, for instance one for a rising clock edge and one for a falling edge. Each node will have at most a single out-edge pointing to the latest-transitioning driver node for the given clock edge (or to one of several equally-late transitioning). The critical path graphs superimpose without effect on each other. Without loss of generality, the disclosure will discuss single critical path graphs. 
     Once the timing verifier has identified the critical path to every node, the designer will redesign parts of the circuit to speed up the logic on the critical path, and then run the timing verifier again. If the designer successfully speeds up a structure on the critical path, subsequent runs of the timing verifier on the altered circuit will very likely produce a different critical path graph. 
     Pruning is essential to making static analysis practical. A naive DFS walk of a circuit would take time exponential in the number of edges between the nodes of the circuit. Though it is possible to construct artificial examples in which DFS algorithms, even with pruning, exhibit exponential time complexity, in practice pruning reduces the time complexity from exponential to nearly linear. With pruning, a single run of DFS and violation sorting of a full microprocessor design can take about fifteen CPU minutes. Without pruning, such analysis would be infeasible. 
     In dynamic timing verification, the designer creates test vectors that exercise active, meaningful paths of the circuit. Static timing verification, by its nature, ignores the designer&#39;s logical intent and tests all paths through the circuit. The blessing of this more complete coverage is also a curse: unused, meaningless paths that will never be exercised during actual use of the circuit are also tested. 
     Consider again the circuit of FIG. 3. All further discussion in this disclosure will assume that X and Y are mutually exclusive, rendering the path A-C-D-F-G logically impossible. This could occur for a number of reasons, including: 
     1. dependencies in the logic generating nodes X and Y, 
     2. architectural constraints affecting X and Y, 
     3. logic A, B, E, and F is shared for differing functions. 
     Proper timing verification of this circuit should discover that the worst-case timing of node G is 29ns along path A-B-D-F-G instead of 33ns along A-C-D-F-G. The path A-C-D-F-G is called a &#34;false path&#34; or &#34;logic exclusivity.&#34; However, the known DFS with standard pruning will prune node D such that only the C-D path remains (i.e., the B-D path is pruned away). Because node D does not have any path data structures pointing to node B, the true critical path A-B-D-F-G will not be generated by the tool. This can result in a number of undesired results including: 
     1. Inaccurate timing estimates for logic containing false paths. The timing verifier can generate overly-optimistic or overly-pessimistic estimates. 
     2. Pruning eliminates the edges forming the real critical path; the real critical path is left unanalyzed. 
     Existing timing verifiers handle false paths by requiring the user to manually insert timing estimates on the false path portion of the circuit, by executing multiple verification passes of the circuit or by manually annotating them and eliminating them altogether. 
     In manual insertion of timing estimates, the user specifies either absolute or relative timing estimates for nodes that are part of a false path. For instance, in the example, the user would annotate node F with time 32. The manual timing estimates method has the following charactersistics: 
     1. A manual step introduces risk that incorrect timing will be specified, 
     2. A user may not have an accurate timing estimate for the node needing the timing, 
     3. If the circuit design is modified, the manually-specified timing estimate must be manually updated. 
     4. The manually-specified timing estimate will be invalid if the cycle time is varied. 
     In another known technique, called &#34;case analysis,&#34; the user specifies the valid combinations of certain input nodes. The verifier then uses these values to perform multiple passes through the network, much in the manner of dynamic timing verification. In the example of FIG. 4, if nodes X and Y are known to be exclusive, then a case analysis approach would call for three separate passes to be performed on the circuit: one with X deasserted and Y asserted, one with X asserted and Y deasserted and finally one with both X and Y deasserted. This does indeed allow the verifier to ignore the false path from A to F. However, 2n-3n passes of analysis are required, where n is the number of false path relationships in the network. Case analysis increases exposure to exponential time complexity. The output from the multiple runs must be merged into a single result. 
     In yet another prior art technique, the circuit designer specifically annotates his circuit model with information indicating the false paths, directing the timing verifier to ignore those paths in its analysis. For instance, for the circuit of FIG. 3 (with the assumption that X and Y are mutually exclusive), the designer might add the statement 
     
         path.sub.-- logically.sub.-- impossible C,F 
    
     to his model, indicating that all paths that include both C and F are false paths. In this technique, an additional check is added as each node is pushed onto the DFS stack: the algorithm checks that the node is not the downstream node of any &#34;path --  logically --  impossible&#34; pair. If it is, and the upstream node of the pair is on the stack, then the path is abandoned. 
     Referring to FIG. 6a and applying this algorithm to the same example circuit of FIG. 3, steps 1-7 proceed exactly as in steps 1-7 of FIG. 5a-5c. In step 8, the DFS finds that the current node, F, is indeed the downstream node of an impossible path, and that the upstream node of the path, C, is on the stack. The algorithm abandons the walk and pops node F--having visited F without processing it, and without labelling nodes F and G with the edges 330 of FIGS. 5d and 5e. The visit of node G of step 9 of FIG. 5a never occurs. Steps 9-15 of the modified algorithm proceed exactly as in steps 11-17 of FIG. 5a. The result is the critical path graph of FIG. 6b. Node G has been labelled with time 27, but node F appears unvisited: no critical path to F has been calculated. Worse, the algorithm has failed to find the real critical path of the circuit, A-B-D-F-G. The too-optimistic timing estimate on node G, 27, masks the real worst-case arrival time of 29. This error may lead to catastrophic failure of the circuit. 
     SUMMARY OF THE INVENTION 
     The invention provides static timing verification of circuit structures in the presence of logically false paths. To be effective on a circuit with false paths, a timing verifier must be able to identify (possibly with user assistance) the false paths and eliminate them from consideration, limiting the analysis to the paths that in fact contribute to the circuit&#39;s function and performance. 
     In general, in one aspect, the invention provides a method for improving a circuit having logically false paths through static analysis of a software model. In the invention, a computer receives information describing the false path, determines a true path alternate to the false path, and analyzes the circuit model with respect to the true path. 
     An advantage of the method is that it provides accurate timing verification of large VLSI designs containing false paths. The method offers significant run time advantage--up to 50 times--over tools that are based on case analysis techniques. The method generates a single result; there is no requirement for merging the results of multiple analyses. The manual annotation of the model is symbolic, so that the timing verifier can automatically maintain consistency in subsequent runs. These advantages are magnified in a large design, for instance a large microprocessor, where the false paths can number in the hundreds. 
     Other advantages and features of the invention will become apparent from the following description and from the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a hypothetical circuit. 
     FIG. 2 is a timing diagram for the circuit of FIG. 1. 
     FIG. 3 is a schematic diagram of a hypothetical circuit. 
     FIG. 4 is a data structure diagram. 
     FIGS. 5a-5e illustrate a time sequence of states during timing verification. 
     FIGS. 6a-6b illustrate a time sequence of states during timing verification. 
     FIGS. 7a-7c are data structure diagrams. 
     FIGS. 8a-e illustrate a time sequence of states during timing verification. 
     FIGS. 19a-b illustrate a time sequence of states during timing verification. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A timing verifier using the invention will typically be run iteratively. A run using the simple pruning method will print the false path as the critical path of the circuit. The designer, after manual analysis, will determine that the reported critical path is really a false path, and will annotate his design to so inform the timing verifier. In subsequent runs, the timing verifier will use a selective pruning method to remove the false path from consideration, and to verify the discovered true path. 
     The output of a timing verifier using the invention is presented in the same format as the output of the prior art timing verifiers. The output will be different in that, even in the presence of user-declared false paths, the timing verifier will analyze and print all significant real paths, i.e., the masking effect will not occur. 
     The invention has been implemented as a modification to NTV, a timing verifier in internal use at Digital Equipment Corporation. NTV is written in the C language. The implementation of the invention centers in improvements to the data structures, and modifications to the DFS routines. 
     Introducing this feature into a static timing verifier requires changing a few of the foundation assumptions on which the verifier is built, and implementing code modifications throughout the verifier to account for these changed assumptions. 
     Past static timing verifiers have assumed that the time of the worst-case output from a node would depend on the time of its worst-case input. This assumption is invalidated in any verifier that addresses the false path issue; for instance, the worst-case output of node F of FIG. 3 depends on the second-worst transition time of input node D. 
     Past static timing verifiers have been constrained to model a fixed number of transitions on each node per clock cycle. Timing verifiers using the invention must track multiple transitions per node. The number of transitions of a node cannot be predicted before the analysis begins, so the data structures must allow for a varying number of transition labels per node. 
     In NTV, the &#34;worst case time&#34; and &#34;worst case predecessor&#34; are de-embedded from the node structure into a &#34;transition&#34; data structure, so that a node may be labelled by multiple transitions. Each transition data structure has an &#34;owning&#34; node (indicated by the name of the node in parentheses), and the worst-case time and predecessor for the transition. The time of each transition is expressed as a (phase boundary, offset relative to the phase boundary) ordered pair. 
     Static timing verifiers consider clocks as a distinct class of inputs from all other signals. Clocks are treated as independent variables--as the givens of the system. The times of all other signals are stated relative to the clock&#39;s phase boundaries. In NTV, the base case for the DFS&#39; recursion is a &#34;primary input node,&#34; the nodes at the &#34;left edge&#34; of a circuit. The user must specify timing information for these primary input nodes. The circuit&#39;s actual clock signals, for instance Ck A  and Ck B  of FIG. 1, are primary input nodes. The timing of the clocks is known to the designer at the clock generators, and is specified relative to the phase boundaries of a &#34;mathematically ideal&#34; clock. The timing verifier propagates the clock signals through the clock logic of the circuit, applying the appropriate delay relative to a phase boundary at each of the clock buffers. As a simplification, the invention is described in terms of a scalar time relative to a zero base. 
     The DFS walker carries a current &#34;arrival time.&#34; The arrival time is computed by adding the time delay of the logic last walked through to the time of the transition of the node in the next-to-top slot of the stack. 
     The algorithm is modified: instead of the prior art&#39;s all-or-nothing decision to trace or prune, the modified algorithm traces some paths speculatively. Some paths that the old algorithm would have chosen to abandon outright are traced using transition data structures in a stack, rather than building the transitions in permanent memory. If the algorithm determines that the speculative path is a &#34;true path&#34; parallel to a false path, it copies the transitions from the stack to permanent memeory to annotate the true path. 
     Somewhat simplified (to remove fields for other NTV features not related to the invention), the data structures of the NTV implementation of the invention are presented in the following tables. Table 1 is the &#34;transition&#34; data structure, table 2 is the &#34;node&#34; data structure, and table 3 is the data structure for the stack entries. 
     
                       TABLE 1______________________________________The transition data structure:______________________________________struct transition {struct node *node;     /* Node that the transition is */                  /* on */int          arrival.sub.-- time;                  /* the time stamp. */struct transition       *predecessor;                  /* latest-transitioning driver */struct transition       *next;     /* Next transition for &#34;node&#34; */};______________________________________ 
    
     Member &#34;.node&#34; indicates the owning &#34;struct node&#34; (see table 2). Member &#34;.arrival time&#34; labels the &#34;worst case transition time.&#34; Member &#34;.predecessor&#34; is the &#34;worst case predecessor,&#34; and points to the latest-transitioning &#34;struct transition&#34; driving &#34;node.&#34; Member &#34;.next&#34; threads the linked list of &#34;struct transitions&#34; on the node. A diagram of the transition data structure is shown in FIG. 7a. 
     
                       TABLE 2______________________________________The node data structure:______________________________________struct node {struct name *node.sub.-- name;                    /* name of the node */struct device       *Successors.sub.-- head;                    /* list of consumer dev&#39;s */struct transition       *transitions.sub.-- head;                    /* list of transitions */______________________________________ 
    
     Member &#34;.node --  name&#34; is a pointer to a string naming the node. Member &#34;.successors --  head&#34; is the head of the linked list of the devices driven by the node. The devices, in turn, will point to the nodes immediately downstream of the node. Member &#34;.transitions --  head&#34; is the head of the linked list of transitions owned by the node. A diagram of the node data structure is shown in FIG. 7b. 
     
                       TABLE 3______________________________________The DFS stack data structure______________________________________struct dfs.sub.-- stack.sub.-- item {struct node.sub.-- rec       *node;      /* data node pointer */struct device.sub.-- rec       *mos;       /* the device driving */                   /* &#34;node&#34; */int      arrival.sub.-- time;struct transition       *transition;                   /* new transition */struct transition        old.sub.-- transition;                   /* restore path when false */                   /* path */unsigned     unreal.sub.-- transition : 1;};______________________________________ 
    
     Member &#34;.node&#34; is a pointer to the node shown in the stack of FIGS. 5a, 6a, and 8a. Member &#34;.mos&#34; is the device driving &#34;.node.&#34; &#34;.arrival --  time&#34; is the value of the arrival time maintained by the algorithm. Member &#34;.transition&#34; is a pointer to a transition data structure that has been committed to permanent storage. Member &#34;.old --  transition&#34; is a transition data structure that is part of the stack, and thus in temporary storage. &#34;.old --  transition&#34; is used while the algorithm is speculatively tracing a path that would have been pruned in the prior art algorithm, but which is speculatively traced because it may turn out to be the critical path parallel to a false path. Member &#34;.unreal --  transition&#34; is a true/false flag used when the algorithm is speculatively tracing a path downstream of a node that has been determined to lie on a false path. If .unreal --  transition is true, the .transition member should be ignored in deference to the .old --  transition member. A diagram of the node stack structure is shown in FIG. 7c. 
     An overview of the process is presented below in Table 4, and the detailed pseudocode is provided in attached appendix B. 
     
                       TABLE 4______________________________________Modified DFS algorithm: an overview______________________________________IF the current node is the downstream member of a &#34;PLI&#34; pairAND the mate is on the stackTHENBEGINabandon trace.mark all interior nodes of the false path.pop back one node.ENDIF the current arrival time is the worbt case time for the nodeTHENBEGINwhether or not this node is a flase path node is irrelevant--the speculative path must be the real path.FROM current node BACK TO where speculative trace began DOpull speculative transitions out of stack into permanentmemoryEND DOcontinue tracing, noting that trace is not speculativeENDELSE /* the current arrival time is not the worst case */BEGINIF current node is marked as an interior node of a false pathTHENBEGINnote that this step of the trace is speculative.Algorithm will continue speculatively tracing until thecurrent node is NOT an interior node of a false path.ENDELSEAbandon trace -- this path can be pruned.ENDRecursive call: if trace is not abandoned, trace the downstreamsuccessor nodes______________________________________ 
    
     In line 400 of the code shown in Table 4, the algorithm tests whether the current node is the downstream member of any &#34;path --  logically --  impossible&#34; pair. If so, the algorithm walks through the stack back to the upstream member of the pair, marking the nodes between the endpoints of the false path &#34;.false --  path&#34;. Lines 409, 412, and 423 ensure that when execution reaches line 426, the arrival time is not the worst, but that the current node is on a false path. The algorithm records that the trace is speculative, and proceeds to the successor nodes. In line 414, the algorithm has found that the speculative path was a true path, and so the speculative path is copied into permanent memory. 
     Referring briefly to Appendix B, provided is a more detailed explanation of the algorithm. Of particular interest is routine &#34;its --  a --  worst --  case(). Whenever a path is pruned, either because the exisiting time of the transition is later than or equal to the DFS arrival time (in which case the path currently being traced is pruned), or because the existing time is earlier than the DFS arrival time (in which case the old path is pruned), the transition for the pruned path is copied into the stack&#39;s .old --  transition slot before being overwritten. This information is used to recover paths when the algorithm finds that a speculatively-traced path must be made permanent. 
     FIG. 8e shows the data structures that NTV will generate for the circuit of FIG. 3, with the &#34;path --  logically --  impossible C,F&#34; statement having been added to the model. 
     The data structures for nodes A, B, and C--that is, the modified node with a single transition data structure per node--are conceptually equivalent to the node data structures built in the prior art schemes. 
     Node D has two transition data structures: one pointing to node C showing the critical path and D&#39;s latest-transitioning driver node discovered by the unmodified search, and one transition pointing to node B (the latest-transitioning node not on the false path) showing the transition driving nodes D and F. These two transition data structures are on a linked list threaded off node D, indicated by the two-headed arrow 550. (The numeral in the name of the transition is for labelling purposes only. NTV does not number transitions this way.) 
     The node and transition data structures for nodes E and F are conceptually similar to the node data structures of the prior art scheme, though the connectivity is different. Note that the critical path to E is annotated by transition data structures A1-C1-D1-E1, and the critical path to node F is annotated by transition data structures A1-B1-D2-F1. 
     Node G indirectly has a false path associated with it (from node C), and thus the algorithm restricts the critical path analysis of G (and nodes downstream of G) to only the transition data structures labelling nodes D and F. The resulting critical path to node G will then be A-B-D-F-G, not A-C-D-F-G. This gives the proper timing estimate of 29ns worst-case for node G, not the 27ns or 30ns computed by the prior art timing verifiers. 
     As NTV begins execution, it reads in the external representation of the circuit model, i.e., the wire list, and constructs the node data structures. The &#34;path --  logically --  impossible&#34; directives are read and stored. The designer may want to verify only a selected region of the circuit; he specifies the input transitions for the primary input nodes to that region. The driver routine calls the modified DFS algorithm starting at each of those primary input nodes. 
     FIGS 8a-8e show the execution of the algorithm on the circuit of FIG. 3. 
     step 1: The algorithm arrives at node A. Since node A is previously unlabelled (.transitions --  head is NIL). Thus, a new &#34;transition&#34; is created, labelling node A with time 1. 
     step 2: The algorithm walks to node C. Since the logic connecting A to C, CL2, consumes 11ns, on entry to the routine, the top stack element arrives pointing to node C, with .arrival --  time 12. Finding C not already labelled, the algorithm creates a new transition and fills it in with time 12 and .predecessor to transition A1. 
     step 3: The only successor of C is D, through logic consuming 1ns, so the algorithm proceeds to D. Node D is labelled with a transition whose arrival --  time is 13 and .predecessor is transition C1. 
     step 4: Node E is labelled with a transition whose arrival --  time is 26 and .predecessor is D. 
     step 5: Node G is labelled with a transition whose arrival --  time is 27 and .predecessor is E. 
     The configuration after step 5 is shown in FIG. 8b. 
     step 6: not shown. The stack is popped back to node E. 
     step 7: not shown. The stack is popped back to node D. 
     step 8: The algorithm arrives at node F. The check finds that F is the downstream node of a false path, and the corresponding upstream node, C, is on the stack. Accordingly, all nodes on the stack between nodes C and F, i.e., node D, are marked false --  path=TRUE, as noted by the &#34;F&#34; in node D in FIG. 8c. The DFS probe is abandoned without labelling F. 
     The configuration after step 8 is shown in FIG. 10c. 
     step 9: not shown. The stack is popped back to node D. 
     step 10: not shown. The stack is popped back to node C. 
     step 11: not shown. The stack is popped back to node A. 
     step 12: Node B is labelled with a transition whose arrival --a  time is 8 and .predecessor is A1. 
     step 13: When the algorithm arrives at node D, the .arrival --  time on the stack is 9, earlier than the arrival --  time of transition D1, which is 13. But the algorithm notices that node D is labelled &#34;.false --  path.&#34; Thus, a tentative transition D2 with .arrival --  time 9 is built in the stack&#39;s &#34;.old --  transition&#34; slot, and &#34;.unreal --  transition&#34; is set, noted by the &#34;u&#34; mark 500 in the stack entries of steps 13 and 14 of FIG. 10a. Note in FIG. 10d that there is no pointer from node D to transition D2--yet. 
     step 14: The algorithm arrives at node E. Since E is not marked &#34;.false --  path&#34; and transition E1&#39;s .arrival --  time, 26, is later than the DFS .arrival --  time, 22, the DFS probe is pruned. 
     The configuration after step 14 is shown in FIG. 10d. 
     step 15: The stack is popped back to node D. The top stack frame indicates unreal --  transition D2 with .arrival --  time 9. 
     step 16: The algorithm walks to the remaining successor to D, i.e., node F, with .arrival --  time 28. F is the downstream node of a &#34;path --  logically --  impossible&#34; directive, but the corresponding node, C, is not on the stack; thus the current path is not a false path. A non-false path to a previously unlabelled node is by definition the worst case; the algorithm therefore must build a critical path to F in this step. The path through D2 is unreal; thus the algorithm copies transition D2 out of the stack frame (using routine make --  unreal --  real), links the new permanent D2 onto the linked list of transitions for D, and builds a real transition F1 for node F with time 28 and predecessor D2. 
     step 17: The algorithm arrives at node G with .arrival --  time 29 and predecessor .transition F1. The time of G&#39;s current worst case transition is G1 with .arrival --  time 27. Transition G1 is updated with .arrival --  time 29 and .predecessor transition F1. 
     The configuration after step 17 is shown in FIG. 8e. steps 18-22: not shown. 
     Nodes G, F, D, B, and A are popped off the stack and the algorithm is complete. 
     Consider an alternate scenario in which the successor lists of nodes A and D are in a different order: B will be visited before C, and E before F. The sequence of stack states is shown in FIG. 9a. The algorithm proceeds through step 18 in a manner analogous to the basic DFS scheme presented in the background, though the actions are somewhat different than presented in FIGS. 5a-5d because of the successor ordering. In step 9, the DFS .arrival --  time is 29 which is later than the time previously labelling transition G1, so G1.time is updated from time 23 to 29, and G1.predecessor from E1 to F1. In step 15, transition D1 is updated: first, D1 is copied into a the stack .old --  transition slot, then D1.time is updated from 9 to 13, and D1.predecessor from B1 to C1. In step 16, E1.time is updated from 22 to 26. In step 17, transition G1 has time 29 (from step 9) and the DFS arrival time is 27, so the path is abandoned. In step 19, the process is back to node D, ready to visit node F, and the configuration is as shown in FIG. 9b. The edge from F1 to D1 is shown dotted, because the edge is stale: transition D1 was updated in step 15, and F has not been revisted to make corresponding updates. 
     In step 20, the algorithm walks into node F and finds that the path from C is a false path. Once the false path is identified, the algorithm checks to see if there are any stale edges, by comparing the times on the transition path back from the node to the arrival times in the .old --  transitions in the stack, and if the current transition, e.g., F1, points to the previous node on the stack, e.g., node D. If the algorithm cannot prove that the edge is not stale, it makes the worst-case assumption, i.e., that the edge is stale. Had this path not been a false path, then the stale edge would have been removed when the new F1.time was written. Note from FIG. 8e that the algorithm should create a transition D2 with .time 9 and .predecessor B1; however NTV currently does not have the information available to reconstruct the A-B-D-F path. When the stale edge is found, the &#34;.impossible --  path --  messup&#34; bit in the transition data structure is set TRUE to force generation of a warning diagnostic when the transition is reported in the output. 
     Two methods have been considered for reconstructing the path A-B-D-F, but both have been rejected as expensive to implement, one in memory, the other in time. One method would be to save all of the old transitions for each node; the other method would be to make a second pass over the circuit to regenerate the lost transitions. 
     Information which may be useful in connection with the invention, including data structure information, is set forth in copending U.S. patent application No. 5,355,321, issued Oct. 11, 1994, filed on the same day as this application, titled &#34;Static Timing Verification&#34;, assigned to the same assignee as this invention, and incorporated by reference&#34;. 
     Other embodiments are within the scope of the following claims. 
     The method is readily adaptable to timing verifiers that use other basic algorithms. For instance, the depth-first search could be replaced by a a topological sort on the nodes of the circuit; the walk would be done in a natural order, queueing each node onto a ready list when all its driving nodes have been visited. In this case, the part one time propagation and part two comparison would be modified analogously. 
     The method can be used with timing verifiers that compute timing information for multiple phases and senses, and with timing verifiers that work on transistor-, gate- or functional block-level designs. 
     The method can be used in other problem domains with algorithms that trace graphs with logic exclusivity, for instance PERT charts and related scheduling problems, and traffic flow analyses. ##SPC1##