### Table 7. Parallelism and optimal theoretical performance

"... In PAGE 19: ... Such measurements are only approximate, and only a small amount of information is available in this regard at present. Some information about theoretical support for parallelism may be found in Table7 in the 2 2000 clock cycles was arbitrarily chosen as a cutoff point.... In PAGE 20: ... This measure also depends on a no- tion of critical path. The conclusions of [21] are summa- rized in Table7 in the Appendix. 2.... In PAGE 32: ...efined (e.g., in Ref. [11] or [21]). Table7 provides two estimates for the number of cycles in a critical path for a 128 bit encryption. The first estimate, Crit1, is from [21]; the second estimate, Crit2, is from [11].... ..."

### Table 7. Parallelism and optimal theoretical performance

"... In PAGE 10: ... Such measurements are only approximate, and only a small amount of information is available in this regard at present. Some information about theoretical support for parallelism may be found in Table7 in the 2 2000 clock cycles was arbitrarily chosen as a cutoff point.... In PAGE 11: ... This measure also depends on a no- tion of critical path. The conclusions of [21] are summa- rized in Table7 in the Appendix. 2.... In PAGE 23: ...efined (e.g., in Ref. [11] or [21]). Table7 provides two estimates for the number of cycles in a critical path for a 128 bit encryption. The first estimate, Crit1, is from [21]; the second estimate, Crit2, is from [11].... ..."

### Table 1: Inductive rules for EMPA integrated interleaving semantics

1998

"... In PAGE 8: ..., and i(M) to denote the multiset obtained by projecting the tuples in multiset M on their i-th component. Thus, e.g., ( 1(PM2))( lt;a; gt;) in the fth part of Table1 denotes the multiplicity of tuples of PM2 whose rst component is lt;a; gt;.... In PAGE 9: ... 3(c) is exactly the result of the application to E of the rules in Table 1 equipped with the auxiliary functions mentioned above. The formal de nition of the integrated interleaving semantics for EMPA is based on the transition relation ???!, which is the least subset of G Act G satisfying the inference rule in the rst part of Table1 . This rule selects the potential moves that have the highest priority level (or are passive), and then merges together those having the same action type, the same priority level and the same derivative term.... In PAGE 9: ... The rst operation is carried out through functions Select : Mu n(PMove) ?! Mu n(PMove) and PL : Act ?! APLev, which are de ned in the third part of Table 1. The second operation is carried out through function Melt : Mu n(PMove) ?! P n(PMove) and partial function Min : (ARate ARate) ?! o ARate, which are de ned in the fourth part of Table1 . We recall that function Melt, whose introduction is motivated by the drawback cited in the example above, avoids burdening transitions with auxiliary labels as well as keeping track of the fact that some transitions may have multiplicity greater than one.... In PAGE 11: ...in the second part of Table1 according to the intuitive meaning of operators explained in Sect.... In PAGE 11: ... The normalization operates in such a way that applying Min to the rates of the synchronizations involving the active action gives as a result the rate of the active action itself, and that each synchronization is assigned the same execution probability. This normalization is carried out through partial function Norm : (AType ARate ARate Mu n(PMove) Mu n(PMove)) ?!o ARate and function Split : (ARate R I ]0;1]) ?! ARate, which are de ned in the fth part of Table1 . Note that Norm(a; ~ 1; ~ 2; PM 1; PM 2) is de ned if and only if min(~ ; ~ ) = , which is the condition on action rates we have required in Sect.... In PAGE 27: ... To solve the problem, we follow the proposal of [BBK96] by introducing a priority operator \ ( ) quot;: priority levels are taken to be potential, and they become e ective only within the scope of the priority operator. We thus consider the language L generated by the following syntax E ::= 0 j lt;a; ~ gt;:E j E=L j E[ apos;] j (E) j E + E j E kS E j A whose semantic rules are those in Table1 except that the rule in the rst part is replaced by ( lt;a; ~ gt;; E0) 2 Melt(PM (E)) E a;~ ???! E0 and the following rule for the priority operator is introduced in the second part... In PAGE 33: ...ollowing the guideline of Sect. 3.2, we de ne the transition relation ???! as the least subset of Mu n(V) ActMufin(V) Mu n(V) generated by the inference rule reported in the rst part of Table 2, which in turn is based on the multiset PM (Q) 2 Mu n(ActMufin(V) Mu n(V)) of potential moves of Q 2 Mu n(V) de ned by structural induction in the second part of Table 2. These rules are strictly related to those in Table1 for the integrated interleaving semantics of EMPA terms. The major di erences are listed below and are clari ed by the corresponding upcoming examples: 1.... In PAGE 34: ...6 Consider term E lt;a; ~ gt;:0k; lt;b; ~ gt;:0 whose decomposition is given bydec(E) = fj lt;a; ~ gt;:0 k; id; id k; lt;b; ~ gt;:0jg By applying the rules in Table 2, we get the two independent transitions fj lt;a; ~ gt;:0 k; id jg norm( lt;a;~ gt;; lt;a;~ gt;:0k; id;1) ????????????????????! fj 0k; id jg fj id k; lt;b; ~ gt;:0 jg norm( lt;b;~ gt;;id k; lt;b;~ gt;:0;1) ????????????????????! fj id k; 0 jg as expected. If we replaced the three rules for the parallel composition operator with a single rule similar to that in Table1 , then we would get instead the two alternative transitions dec(E) norm( lt;a;~ gt;; lt;a;~ gt;:0k; id;1) ????????????????????! fj 0k; id; id k; lt;b; ~ gt;:0jg dec(E) norm( lt;b;~ gt;;id k; lt;b;~ gt;:0;1) ????????????????????! fj lt;a; ~ gt;:0k; id; id k; 0 jg which are not consistent with the fact that the two subterms of E are independent, thereby resulting in a violation of the concurrency principle (see Sect. 7:4).... In PAGE 49: ... The tool driver, which is written in C [KR88] and uses Lex [Les75] and YACC [Joh75], includes routines for parsing EMPA speci cations and performing lexical, syntactic, and static semantic (closure, guardedness, niteness) checks on the speci cations. The integrated kernel, which is implemented in C, currently contains only the routines to generate the integrated interleaving semantic model of EMPA speci cations according to the rules of Table1 : this kernel will be extended by implementing a EMB checking algorithm. The functional kernel, which is written in C, is based on a version of CWB-NC [CS96] that was retargeted for EMPA using PAC-NC [CMS95].... ..."

Cited by 25

### Table 3: Robust parsing using the simple grammar from Table 1. (a) State sets generated from parsing the ungrammatical string a circle touches above a square. Dummy states (those with empty LHS) represent partial parses. States representing \maximal quot; partial parses are marked with MAX. Predictions that don apos;t lead to completions have been omitted to save space. (b) Trace of wildcard state completions resulting in a list of complete partial parses for this input.

"... In PAGE 30: ... After nishing the processing of the jth state set, the chart will contain states j : k ! X: indicating that nonterminal X generates the substring xk:::j?1. Table3 (a) illustrates the robust parsing process using the example grammar from Table 1 (p. 5).... In PAGE 32: ... The Viterbi-parse procedure when applied to a wildcard state will recover the most likely such split. Table3 (b) shows a trace of wildcard state completions used in enumerating the partial parses for the example given earlier. The total number of complete partial parses can be exponential in the length of the input.... In PAGE 32: ... Therefore, during completion, we can mark all states that contributed to a larger constituent, and later identify the unmarked states as the ones corresponding to maximal parses. (The chart in Table3 (a) has all maximal states labeled with MAX.) When completing wildcard states we simply skip all completions due to non-maximal states.... ..."

### TABLE II THE RULE USED FOR CHART PARSING

### Table 4: Garbage collection in chart parsing.

### Table 1 Syntax of BACI

2006

"... In PAGE 18: ...18 Clearly, for an arbitrary pre-process generated using the syntax of Table1 , it is easy to check if it is well formed according to the typing rules of Tables 8 and 9. In other words, there is no problem in writing a type checking algorithm for our calculus.... ..."

### Table 3: Types Syntax

2000

"... In PAGE 8: ... It is not di cult to see that v is decidable (it has nite domain). Klaim types are de ned by the abstract syntax in Table3 ; there ranges over type variables and denotes the recursive operator. Hereafter, the following notational con- vention will be used: \7! quot; binds stronger than \ quot;, that binds stronger than \, quot;.... In PAGE 9: ... Recursive types are used for typing migrating recursive processes. A type generated from the grammar in Table3 is such that any recursive type : 0 occurring in does not contain on the left of 7!. This is a simpli cation of the notion of positive type of [5].... In PAGE 9: ... In the following, we will only consider types that satisfy the condition above; they will be called legal types. Note that the syntax in Table3 is less restrictive; it also permits types such as : . The following notion will be useful in later proofs.... ..."

Cited by 47

### Table 1: Syntax of Basic LOTOS

"... In PAGE 5: ...Table 2: Standard interleaving semantics of Basic LOTOS Basic LOTOS expressions, L be the universe of observable actions, a be an action from L[f i g, A L be a set of actions, f be a function from L to L [ f i g, and x be a process identi er. Then the syntax of Basic LOTOS is recursively given by Table1 . P j[?]j Q is abbreviated as P jjj Q.... ..."

### Table 2: Type Syntax

"... In PAGE 8: ...nU g [ fnU0 g = fnU[U0g. We use , ranged over by , to denote the set of all polarities. We will write n in place of nU whenever U can be safely ignored. Klaim types are de ned by the abstract syntax in Table2 ; there ranges over type variables and denotes the recursive operator. Hereafter, the following notational con- vention will be used: \7! quot; binds stronger than \ quot;, that binds stronger than \, quot;.... In PAGE 8: ... Recursive types are used for typing migrating recursive processes. A type generated from the grammar in Table2 is such that any recursive type : 0... In PAGE 9: ... In the following, we will only consider types that satisfy the condition above and are such that in types of the form ` 7! 7! if e 62 then = ?; they will be called legal types. Note that the syntax in Table2 is less restrictive; it also permits types of the form : . The following notion will be useful in later proofs.... In PAGE 10: ... Types of nodes have the same syntax as types of processes. However, strictly speaking, the formers cannot be generated by the grammar given in Table2 , since we required ` to stand for localities and locality variables. For types of nodes, we let ` range over sites.... ..."