### Table 2: Model Synthesis Algorithm

2007

"... In PAGE 3: ... 3.2 Synthesis A detailed description of the model synthesis algorithm is given in Table2 . An example is shown in Figure 4.... In PAGE 4: ... !(v; M) = f(q; k)j(v + q; k) 2 M and q 2 [ w : : : w]3g (2) The perceptual distance d between two sets is defined as the number of model pieces that are not shared between the two sets which is: d(P; Q) = jPj jP \ Qj (3) where jPj is the cardinality of the set P. Models that more closely resemble the example model will be pro- duced more frequently, if the following modification is applied to the algorithm in Table2 at Step 4. In Step 4, one label is chosen at the vertex v.... ..."

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### Table 6: Type Synthesis Algorithm for CC!

"... In PAGE 17: ... 2 4.2 Schematic Type Synthesis An algorithm for schematic type synthesis is given by the rules of Table6 . It is a system for deriving judgements of the form ? ` M ) X; C.... In PAGE 17: ... Intuitively, X; C schematically represent the set of types for M in ?. The algorithm makes use of two auxiliary functions, CUM and *, de ned in Table6 . These functions are analogous to the functions cum and quot; of Table 4, and are characterized by the following lemmas.... In PAGE 19: ...ypej+i. Let be extended with 7! j + i. If X 6wh Typej for any j, then X 6wh Type for any , so take = . 2 The rules of Table6 make use of an informal convention whereby level variables are required to be \new quot;. This means that the level variable cho- sen at that rule occurrence is unique to that occurrence, and di erent from that associated with any occurrence of any other rule in the derivation un- der consideration.... In PAGE 20: ...whether or not there exists a schematic term X and consistent con- straint set C such that ? ` M ) X; C is derivable. Proof (Soundness) The rst property is proved by inspection of the rules of Table6 . For the second property, consider a derivation of ? ` M ) X; C.... In PAGE 20: ... More precisely, we build a derivation of ? ` M ) X by induction on the height of . The induction proceeds by case analysis of the root node of based on the rules of Table6 . The most interesting case is when the root of is an instance of rule (a-app).... In PAGE 21: ...4 applies to extend A;B to the required cum([N=x]A2;i). (Decidability) The proof is by induction on the structure of M, keeping in mind that the rules of Table6 are syntax-directed. The base cases (Prop, Typei, and variables) are all trivial: for the case of a variable x, we need... In PAGE 35: ... ` Prop ) Type ; f 0 g ( new ) a-d-type ` Typei ) Type ; f gt; i g ( new ) a-d-var x[x:A] x ` x ) CUM x(A; ;) a-d-def x[x=M:X; G] x ` x ) LV(G)(X; G) a-d-gen ` A ) X; C ` X wh 1 x 62 Dom( ) C consistent [x:A] ` B ) Y; D ` Y wh 2 ` fx:AgB ) 1 *C[D 2 a-d-abs ` A ) X; C ` X wh x 62 Dom( ) C consistent [x:A] ` M ) Y; D ` [x:A]M ) fx:AgY; C [ D a-d-app ` M ) X; C ` X wh fx : X1gX2 ` N ) Y; D ` X1 # Y (E) ` MN ) CUM ([N=x]X2; C [ D [ E) where V assigns \new quot; level variables to each of the level variables in V, * is as in Table6 , and CUM is de ned by CUM (X; C) = CUM( (X); C). Table 10: Type Synthesis Algorithm for CC! with De nitions... In PAGE 39: ... ; C ` Prop ) Prop; Type ; f 0 g ( new ) a-ad-type ; C ` Typej ) Typej; Type ; f gt; j g ( new ) a-ad-anon ; C ` Type ) Type ; Type ; f gt; 0 g ( ; new ) a-ad-var x[x:X] x; C ` x ) x; CUM(X; ;) a-ad-def x[x=X:Y; G] x; C ` x ) LV(G)nLV(C)(X; Y; G) a-ad-gen ; C ` Q ) U; X; D X wh 1 C [ D consistent [x:U]; C [ D ` R ) V; Y; E Y wh 2 x 62 Dom( ) ; C ` fx:QgR ) fx:UgV; 1 *D[E 2 a-ad-abs ; C ` Q ) U; X; D X wh C [ D consistent [x:U]; C [ D ` R ) V; Y; E x 62 Dom( ) ; C ` [x:Q]R ) [x:U]V; fx:UgY; D [ E a-ad-app ; C ` Q ) U; X; D X wh fx : X1gX2 ; C ` R ) V; Y; E X1 # Y (F) ; C ` QR ) UV; CUM([V=x]X2; D [ E [ F) where * and CUM are as de ned in Table6 , and V is as de ned in Table 10. Table 12: Algorithm for Anonymous Universes and De nitions... ..."

### Table 2: Synthesis algorithms used in experiments

1998

"... In PAGE 7: ...+1 * * * * * 1 2 3 4 5 1 2 ab cdef g ij l m no p 1 2 3 4 (b) * * 4 5 ab cdef g h ij q m no 1 2 3 4 (c) + * * * * * 1 2 3 4 5 1 1 2 a b c d ef g h ij q l m no p (a) +1 +1 M1 M2 M3 1 2 p M3 *1 3 l * M1 *2 M2 Figure 4: Phase 2 - Detailed scheduling and module assignment ing data paths with low BIST area overhead, experi- ments were conducted on the following benchmarks: 1#29 the 2nd order di#0Berential equation - DIF, 2#29 the auto regression #0Clter element-ARF, 3#29 an 8-point FIR #0Clter - FIR, and 4#29 the elliptic wave #0Clter - EWF #5B14#5D. Dif- ferent synthesis #0Dows were considered using combina- tions of twoscheduling techniques and two register as- signment techniques shown in Table2 - Flow I #28SWT- AWT#29, Flow II #28SFT-AWT#29, and Flow III #28SFT-AFT#29. Table 3 shows the characteristics of all the synthe- sized data paths.... ..."

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### Table 1. Synthesis algorithms for 3P (a) and

1999

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### Table 1: An example of the basic synthesis algorithm.

2003

"... In PAGE 3: ... The following two tables illustrate the work of the algo- rithm synthesizing the circuits for 3 17:pla. Table1 refers to the basic approach (Tofioli gates are denoted by T and Fredkin gates by F), and Table 2 illustrates the bidirectional algorithm. Each column in the tables shows the change of the output part of the truth table as the gates from the pre- vious steps are applied.... ..."

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### Table 1 - Synthesis algorithm execution times.

2001

Cited by 25

### Table 1. Summary and comparison of four synthesis algorithms.

2006

"... In PAGE 5: ... In the worst situations, this may cause the patch-based approach to to- tally break the texture elements and violate global and local regularity in synthesized textures. Unlike the patch-based approach, the regularized patch- based approach utilizes a user-specified lattice in the syn- thesis process ( Table1 ). This lattice information is used to set the patch shape/size, patch extraction and placement lo- cations.... ..."

Cited by 1

### Table 1 - Synthesis algorithm execution times.

"... In PAGE 10: ... The implementation, together with some examples (including the one used throughout this paper), is available at [11]. In Table1 we show some execution times and sizes of synthesised LTSs for the example used in this paper, a slightly bigger version of it and a version of the ATM system (see e.... ..."

### Table 2. Performances of the synthesis algorithm on an UltraSparc 5.

1999

"... In PAGE 8: ... The scheduler for the full system con- tains states from which the optional task P 3 is actually scheduled. Table2 shows the size of the scheduler and the performances of the algorithm. 4.... In PAGE 8: ... This indicates that the scheduling constraints are really tight. Table2 shows the size of the synthesized deadlock- free scheduler 2 and the performance of the synthesis algorithm. Moreover, in the computed scheduler, the optional task MP can actually be scheduled in certain states.... ..."

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### Table 2. Performances of the synthesis algorithm on an UltraSparc 5.

1999

"... In PAGE 8: ... The scheduler for the full system con- tains states from which the optional task P3 is actually scheduled. Table2 shows the size of the scheduler and the performances of the algorithm. 4.... In PAGE 8: ... This indicates that the scheduling constraints are really tight. Table2 shows the size of the synthesized deadlock- free scheduler2 and the performance of the synthesis algorithm. Moreover, in the computed scheduler, the optional task MP can actually be scheduled in certain states.... ..."

Cited by 43