### Table 6. Matching possibilities.

"... In PAGE 10: ... This process is called matching. There are several methods by which matching can occur, summarized in Table6 . In one method, the role that needs to initiate the next role, and understands its specifics, can send requests to other agents that it knows about.... ..."

### Table 1. Complexity of Equational Matching Problems Theory Decision Counting Theory Decision Counting

"... In PAGE 18: ... Using the theory of #P-completeness, we identi ed the complexity of #E-Matching problems for several equational theories E. Table1 summarizes our ndings and compares the complexity of counting problems in equational matching with the complexity of the corresponding decision problems. Although in most cases the NP-completeness of the decision problem is accompanied by the #P-completeness of the associated counting problem, it should be emphasized that in general there is no relation between the complexities of these two problems.... ..."

### Table 2. Match on action.

"... In PAGE 4: ... In Table 1 we automatically understand shot 2 as the cause of what we heard in shot 1. In Table2 , called match on action, we interpret shot 1 as the beginning of the action, and shot 2 as the end, and we interpolate our- selves the middle part. Table 1.... In PAGE 4: ... In Table 1, the subject and verb is furnished by the first shot, and the object and infini- tive by the second shot. Similarly, in Table2 , the first shot expresses the subject and the auxiliary, the second one the infinitive and the adverb. Why not use these established patterns when we de- sign transitions from one screen image to another? Suppose that we have MIMIC diagram with many sensors and actuators.... ..."

### Table 12: Matching Rules

2000

"... In PAGE 26: ... Rule (3) says that a process can perform an in action by synchronizing with a process which represents a matching tuple et. Matching (de ned in Table12 ) takes as arguments the two candidate tuples, the site where the operation is executed, the type of the contin- uation (that is statically derived and retrieved from the symbol table when it is needed) and the type interpretation function of the net. The result of this synchronization is that tuple et is consumed, i.... In PAGE 27: ...Table 12: Matching Rules Finally, rule (6) deals with process invocation while rule (7) is the standard rule that relates operational semantics and structural congruence. The pattern{matching predicate used in Table 11 is de ned in Table12 , and relies on the auxiliary predicate s that we introduce below. De nition 5.... ..."

Cited by 47

### Table 3. Syntactic matching

1996

"... In PAGE 28: ...Table 3. Syntactic matching In this section we show how bisimilarity of term graphs can be tested in an equational manner using the proof system of Table3 (`syntactic matching apos;). Instead of the congruence rule of Equational Logic (see Table 2) we use (as in some algorithms for syntactic uni cation of rst-order terms [Klo92]) its reverse, the term decomposition rule.... In PAGE 29: ... Remark 3.39 Evidently, the property of bisimilarity for nite graphs is decidable, since the deductive closure T 0 of T with respect to the proof system of Table3 (see previous example) is nite for nite T ; or, since there are only nitely many relations on a pair of nite graphs. 4.... ..."

Cited by 54

### Table 2: Matching Pairs

"... In PAGE 9: ... The matched pairs for the sea gull (Fig. 1) images are given in the rst two columns of Table2 . Two matched... In PAGE 10: ... 3 are shown in Fig. 5, namely the pairs 23-12 and 31-20 from the rst column of Table2 . (NB: Using the sub-image numbering scheme of Fig.... In PAGE 10: ... Likewise, if J is I rotated 180o, then x0 =(x + 2) mod 4 and y0 = (y + 2) mod 4.) It can be seen that the matches in the rst two columns of Table2 are correct . Using eigenvectors and weight vectors, we can match sub-images even under rotation.... In PAGE 10: ...omparison involving four values. This is a signi cant speedup. Once a few sub-images are matched (and perhaps only a single match), one can determine the transformation that puts the two images in alignment. As noted above the matching pairs for the sea gull image with 90 and 180 degrees rotation are given in the rst two columns of Table2 . The third column lists the matching pairs found in an image having symmetric regions (see Fig.... In PAGE 11: ...Table 2: Matching Pairs Sub-image 02 in the original represented as sub-image 31 after a 90o rotation Sub-image 02 in the original Thus matches between pairs such as (20-13) and (01-21) represent cases for which di erent sub-images of the original are similar ignoring rotation. By setting the error threshold, , to a less restrictive value, 0:01, one sees in the fourth column of Table2 that there are four such false matches for the original image given in Fig.... In PAGE 11: ...olumn of Table 2 that there are four such false matches for the original image given in Fig. 6. Fig. 7 illustrates the rotated counterpart of a portion of the lower left quadrant of the original image. From Table2 , it apos;s clear that once we know the matching sub-image Jj-Ii, we can determine the transformation that puts the two images into pixel-by-pixel correspondence. Therefore, to determine the transformation register the images, we need only to compare two four-component vectors until at most m pairs are found where each image is partitioned into m sub-images.... In PAGE 11: ... 10. The hypertangent is a better visualization of the distance between sub-images but the quot; of Table2 is de ned directly over the Mahalanobis distance. The x-axis is an ordinal, not cardinal, sequence.... In PAGE 12: ...erfect match. One can also see that these matches occur in the same relative position as those in Fig. 8. However, due to the symmetry in the original image, there are near matches with other sub-images. These near matches are the four trailing entries of the fourth column of Table2 - the column for which the error threshold is set to the larger value. 4.... In PAGE 14: ...08784 Figure 11: In presence of Gaussian noise of the Eq. 10 is lt; 10?2, when we change the error requirements ( quot; 10?4) we reduce the number of mistaken matches to a better result as it is shown in the thrid column of Table2 . The Overall estimated time for Eq.... ..."

### Table 12: Matching Rules

"... In PAGE 27: ...Table 12: Matching Rules Rule (3) says that a process can perform an in action by synchronizing with a process which represents a matching tuple et. Matching (de ned in Table12 ) takes as arguments the two candidate tuples, the site where the operation is executed, the type of the contin- uation (that is statically derived and retrieved from the symbol table when it is needed) and the type interpretation function of the net. The result of this synchronization is that tuple et is consumed, i.... In PAGE 27: ... Finally, rule (6) deals with process invocation while rule (7) is the standard rule that relates operational semantics and structural congruence. The pattern{matching predicate used in Table 11 is de ned in Table12 , and relies on the auxiliary predicate s that we introduce below.... ..."

### Table 12 Matching rules

"... In PAGE 25: ... Rule (3) says that a process can perform an in action by synchronizing with a process which represents a matching tuple et. Matching (de ned in Table12 ) takes as arguments the two candidate tuples, the site where the operation is executed, the type of the continuation (that is statically derived and retrieved from the symbol table when it is needed) and the type interpretation function of the net. The result of this synchronization is that tuple et is consumed, i.... In PAGE 26: ...eduction. This modi cation is necessary to allow operations at s0. Finally, rule (6) deals with process invocation while rule (7) is the standard rule that relates operational semantics and structural congruence. The pattern matching predicate used in Table 11 is de ned in Table12 , and relies on the auxiliary predicate s that we introduce below. De nition 5.... ..."

### Table 3. Syntactic matching

"... In PAGE 26: ...Table 3. Syntactic matching In this section we show how bisimilarity of term graphs can be tested in an equational manner using the proof system of Table3 (`syntactic matching apos;). Instead of the congruence rule of Equational Logic (see Table 2) we use (as in some algorithms for syntactic uni cation of rst-order terms [Klo92]) its reverse, the term decomposition rule.... In PAGE 27: ... Remark 3.39 Evidently, the property of bisimilarity for nite graphs is decidable, since the deductive closure T 0 of T with respect to the proof system of Table3 (see previous example) is nite for nite T ; or, since there are only nitely many relations on a pair of nite graphs. 4.... ..."