### Table 3: The Structural Rules of Symbolic Semantics

1998

"... In PAGE 9: ... For the sake of simplicity, we will use P to range over closures as well. The structural rules of the symbolic semantics are reported in Table3 . The transition P ?! P 0 describes the evolution to P 0 of the process P .... ..."

Cited by 189

### Table 8. Denotational event structure semantics; op is the semantic counterpart of op

2001

"... In PAGE 31: ... For sequential composition, finally, the proof is straightforward. The denotational event structure semantics of Lang(Evt) is given in Table8 . It should be noted that the disjointness requirements in the denotational constructions for choice and sequen- tial composition are guaranteed to be satisfied due to the well-formedness of annotated terms.... ..."

Cited by 15

### Table 8: Denotational event structure semantics; op is the semantic counterpart of op

### Table 1. Inductive rules for EMPA interleaving semantics

1995

"... In PAGE 11: ... As a consequence, only if we know all the potential moves of the subterms of a given term, we can correctly determine its transitions and their rates. The first relation, denoted with ???! , is the least subset of G Act G satisfying the inference rule reported in the upper part of Table1 . The side condition associated with the inference rule enforces the race policy by selecting among the potentialmoves of a term those having the highest priority level, and then merges together all the potential moves in which actions with the same type and priority as well as the same target term occur.... In PAGE 13: ...3. The second relation, denoted with ` , is defined by structural induction as the least subset of G Mufin(Act G) satisfying the axiom and the inference rules reported in the lower part of Table1 . This relation computes the multiset of all the potential moves of each term, regardless of action priorities.... In PAGE 15: ...e. if we apply exactly the rules reported in Table1 ), then we obtain the LTS reported in Figure 2(c). Notice that the correct rate of both the transition from E2 to E3 and the transition from E2 to E4 is =2 instead of , because in E2 only a timed action with rate occurs hence the exit rate of E2 is .... In PAGE 15: ... Remark 3.10 In the rest of the paper, functions appearing in Table1 will be sometimes abused. However, the way in which they will be used will result clear from the context.... In PAGE 35: ... We thus define the relation ???! as the least subset of Mufin(V) Act Mufin(V) generated by the inference rule reported in the upper part of Table 4, which in turn is based on the relation ` defined as the least subset of Mufin(V) Mufin(Act Mufin(V)) generated by the axioms and the inference rules reported in the lower part of Table 4. These rules are strictly related to the rules reported in Table1 for the operational interleaving semantics of EMPA terms. There are four major differences: Intheoperationalnet semantics functionRaceis unnecessarysincetheracepolicyis inherent in the net firing rule.... In PAGE 37: ...Table1 , then we would get instead the two transitions dec(E) a;~ ???! fj 0k;id; idk; lt;b; ~ gt;:0jg dec(E) b;~ ???! fj lt;a; ~ gt;:0k;id; idk;0jg which are not consistent with the fact that the two subterms of E are independent of each other and, more important, are wrong because they are both enabled at marking dec(E) but the firing of one of them prevents the other one from being executed. Example 6.... ..."

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### Table 2: Indexing structure for semantic relationships and examples.

in Mpeg99/m4754

"... In PAGE 10: ...ections 4.3.1 and 4.3.2. Table 1 and Table2 summarize the indexing structures for the... In PAGE 12: ... We divide the semantic relationships into lexical and predicative relationships. Table2 summarizes the semantic relationships including examples. The lexical semantic relationships correspond to the semantic relationships among nouns used in WordNet [13].... ..."

### Table 2: Indexing structure for semantic relationships and examples.

"... In PAGE 6: ...ections 3.1.1 and 0. Table 1 and Table2 summarize the indexing structures for the relationships including examples. 3.... In PAGE 7: ... We divide the semantic relationships into lexical and predicative relationships. Table2 summarizes the semantic relationships including examples. Note that since semantic relationships are based on understanding of the content, we can make the same classification for relationships obtained from visual content as for relationships obtained from audio content.... ..."

### Table 1. Structured operational semantics of PA.

"... In PAGE 3: ... Trailing 0s are usually omitted. The standard (interleaving) semantics of PA is presented in Table1 where G denotes... ..."

### Table 2. The Structural Rules for Operational Semantics

1993

"... In PAGE 6: ... Relation denotes a form of overlapping of the space, as one of the locations of the former set is part (or has evolved to a location) of the latter. The rules for the operational semantics are listed in Table2 . The rule for prefixing states that an action a, executable at time n, is completed at time k = n+f(a); the number k denotes the time which passed for all the sequential subsystems of E.... In PAGE 8: ...Behavioural Semantics s s s s s a a a b b ? ? E s s s s s a a a b b ? ? c c F Figure 1. Two performance equivalent event structures Proposition 3 Let s1 ha;ni?! ?! s2 be derivable with the rules in Table2 . If s 2 s2f!g, then s is of the form n ) E, where E is sequential.... ..."

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### Table 2. The Structural Rules for the Operational Semantics.

"... In PAGE 7: ... Clock Distribution Equations. The transition relation is given through a set of inference rules, listed in Table2 , defined in a structural inductive manner (apart from the rule for recursion). It is worthwhile observing that these rules are parametric w.... In PAGE 8: ... This new formulation is given because it will be helpful i) in order to prove that performance bisimulation is a congruence for all the operators of the language; ii) in the definition of the axiomatization of the semantic congruences we are going to investi- gate, and also iii) in comparing these performance-based semantics with other non interleaving ones. The rules of Table2 define essentially a tyft system [14] for which strong bisimulation equiva- lence (hence, in this case, also performance equivalence) is a congruence. The relevant exceptions are rules Act and Rec, which do not fit in the format because they do not only exploit the top level operator name.... In PAGE 8: ... Rules Act and Rec are replaced by the axiom and inference rules reported in Table 3, which presents an additional rule for the clock prefixing operator. The whole set of operational rules includes also rules Alt01, Alt02, Par0 1 and Par0 2 which are as their corresponding rules in Table2 where the transition relation ?! is substituted for ?!. UBLCS-95-1... In PAGE 10: ...Behavioural Semantics This observation should definitely clarify that the operational semantics on extended states, defined by ?!, is exactly the same we have proposed for states in Table2 , as all the states in the same congruence class have the same semantics. Now, a result by [14] ensures that strong bisimulation is a congruence on the set of extended states.... In PAGE 10: ... Now, a result by [14] ensures that strong bisimulation is a congruence on the set of extended states. In order to prove that this is a congruence also on the subalgebra of states, it is enough to observe that there is no transition from a state to an extended state in the transition system defined by the rules in Table2 , i.... ..."

### Table 2. The Structural Rules for the Operational Semantics.

1997

"... In PAGE 6: ...3 The set of labels for the transition system is = Act N+. The transition relation is given through a set of inference rules, listed in Table2 , defined in a structural inductive manner.... In PAGE 7: ... This new formulation is given because it will be helpful i) in order to prove that performance bisimulation is a congruence for all the operators of the language; ii) in the definition of the axiomatization of the semantic congruences we are going to investigate, and also iii) in comparing these performance-based semantics with other non interleaving ones. The rules of Table2 define essentially an infinitary (i.e.... In PAGE 7: ... Rules Act and Rec are replaced by the axiom and inference rules reported in Table 3, which presents an additional rule for the clock prefixing operator. The whole set of operational rules includes also rules Alt0 1, Alt02, Par0 1 and Par0 2 which are as their corresponding rules in Table2 where the transition relation ?! is substituted for ?!. Act0 a:E lt;a;f(a) gt; ?! f(a) ) E Rec0 E[rec x: E=x] lt;a;n gt;?! t rec x: E lt;a;n gt;?! t Clock t lt;a;k gt; ?! t0 n ) t lt;a;n+k gt; ?! n ) t0 Table 3.... In PAGE 8: ...roposition 4.2 Let t1, t2 be extended states. Then, t1 lt;a;k gt; ?! t2 if and only if t1 lt;a;k gt; ?! t2. This observation should definitely clarify that the operational semantics on extended states, defined by ?!, is exactly the same we have proposed for states in Table2 , as all the states in the same congruence class have the same semantics. Now, a result by [15] ensures that strong bisimulation is a congruence on the set of extended states.... In PAGE 8: ... Now, a result by [15] ensures that strong bisimulation is a congruence on the set of extended states. In order to prove that this is a congruence also on the subalgebra of states, it is enough to observe that there is no transition from a state to an extended state in the transition system defined by the rules in Table2 , i.e.... ..."

Cited by 9