"... In PAGE 5: ... CM about the inclusivity grammar Each of the non-terminal symbols in the grammar (concepts in Figure 6) can be determined in terms of terminal symbols that encompass its dimension, or can be further elaborated, by the use of recursive non- terminal symbols. An example is provided in Table1 , in which the non-terminal Definition is detailed. ... ..."

"... In PAGE 32: ...p sat? a0 a ` a0 p sat? a (Skip?) skip sat? (Assignment?) X := e sat? [e=X] (Sequential?) p1 sat? a1 p2 sat? a2 p1; p2 sat? a1[a2= ] (Precondition?) p sat? a b!p sat? a _ :b (Choice?) gc1 sat? a1 gc2 sat? a2 gc1 [] gc2 sat? a1 ^ a2 (Alternative?) gc sat? a if gc sat? a (Repetitive?) gc sat? a0 X 2= loc(a0) G(gc) ^ a ` a0[a= ] G(gc) ^ a ^ e = X ` a0[e lt; X= ] :G(gc) ^ a ` a ` e 0 do gc od sat? a Table1 0: Inference system for total correctness (termination) of the nonde- terministic choice language... In PAGE 33: ...assertions is the same as in table 3 CF[[X := e]] 4 = [X7!E[[e]]] [ fhF; Fig CF[[skip]] 4 = 1State [ fhF; Fig CF[[p1; p2]] 4 = CF[[p2]] CF[[p1]] CF[[if gc ]] 4 = CF[[gc]] [ (State fFg) (B[[:G(gc)]]) CF[[do gc od]] 4 = `fp ( f) (f CF[[gc]] (B[[G(gc)]]) [ (B[[:G(gc)]]) [ fhF; Fig) with respect to the standard set-theoretic order on relations CF[[b!p]] 4 = CF[[p]] (B[[b]]) [ fhF; Fig CF[[gc1 [] gc2]] 4 = CF[[gc1]] [ CF[[gc2]] [[a ` a0]] 4 = (8 ) A[[a]] A[[a0]] [[p satF a]] 4 = (8 ) CF[[p]]R(A[[a]] ) Table1 1: Semantics of the nondeterministic choice language|total correct- ness for lack of failures... In PAGE 34: ...p satF a0 a ` a0 p satF a (SkipF ) skip satF (AssignmentF ) X := e satF [e=X] (SequentialF ) p1 satF a1 p2 satF a2 p1; p2 satF a1[a2= ] (PreconditionF) p satF a b!p satF a _ :b (ChoiceF ) gc1 satF a1 gc2 satF a2 gc1 [] gc2 satF a1 ^ a2 (AlternativeF ) gc satF a a ` G(gc) if gc satF a (RepetitiveF ) gc satF a0 G(gc) ^ a ` a0[a= ] :G(gc) ^ a ` do gc od satF a Table1 2: Inference system for total correctness (lack of failures) of the nondeterministic choice language... ..."

"... In PAGE 6: ... 4 Analysis of Agent Definitions We have analyzed the definitions in terms of the properties defined in the last section. Table1 summarize the relations between the agent definitions and... ..."

"... In PAGE 4: ... Finally, our experimental validation of the models not only adjusts the routing e#0Eciency factor to better #0Ct the experi- mental values but, more importantly, applies the via impact models of Chong and Chen to the actual number of termi- nal vias instead of the estimated number. In Table1 , the number of terminal vias predicted by the Chong and Chen layer assignment models is compared to the actual number for the original experiment #28no virtual vias#29. Both Chong and Chen predict that the design will be routable in two layers, while it is barely routable in four #28!#29 The di#0Berence between the #28otherwise similar#29 layer assignment models of Chong and Chen is that Chong includes the terminal vias on the layer the wire is connected to #28although they do not really add to the blockage#29 whereas Chen only counts vias that go through the layer.... In PAGE 5: ...1 Routing Efficiency Routing Efficiency is Constant? If the routing e#0Eciency and signal net fraction are constant over all layers, then the utilization factor should monoton- ically increase with the layer number. Indeed, in our ex- periments where the wire pitches are the same on all four layers, the number of terminal vias is always larger on lower layers #28see Table1 #29. The via impact thus decreases with the layer number and applying Equation 2 results in an in- creasing utilization factor.... ..."