### Table 2: Network algebra axioms for relations with angelic/demonic operators; =y denotes various angelic-demonic versions for sequential/feedback operators; from each pair (A3,A3o), (A7,A7o) and (F5,F5o) one axiom is chosen in each particular case.

"... In PAGE 7: ...Table2 . Finally, using the block extension of the de nitions ( ) above we get meaning to the general block rami cation and identi cation constants, i.... In PAGE 7: ... Theorem 3.1 The axioms without feedback in Table2 and using A3o/A7 version for the A3/A7 axioms give a correct and complete axiomatisation for relations with parallel and forward demonic sequential composition and I; X; ?; ^; gt;; _ constants. (No feedback is used here.... In PAGE 7: ... The nor- mal form representation of such an f is not unique due to two reasons: (i) certain permutations may be done in an identi cation (_ni 1 ) or rami cation (^1 mi) point and (ii) more that one path may connect an input-output pair. The proof that two nor- mal form expressions that represent the same relation are equivalent in the speci ed axiomatic subsystem of Table2 is the same as in the angelic case. III.... In PAGE 7: ... It is obvious that the parallel composite of two normal forms is a normal form, too. Hence we still have to show that the forward demonic sequential composite of two normal forms may be reduced to a normal form and, moreover, to show that this reduction may be done inside the axiomatic system presented in Table2 . We apply the same technique as in [CaS91, Ste94].... In PAGE 10: ...Table2 with the A3o/A7/F5o version for the A3/A7/F5 axioms give a correct and complete axiomatisation for relations with forward demonic operators. Proof: The proof is based on the similar result in the acyclic case (Theorem 3.... In PAGE 10: ...ne may consider the backward demonic case, as well, i.e. the case given by the dual condition (b) a maximal o-disconnected outgoing path from an input vertex s destroys the creation of other outgoing paths from s. Using duality, it follows that one can axiomatize the backward demonic calculus of relations by the axioms in Table2 in which the A3/A7o/F5o version for the A3/A7/F5 axioms is used. Finally, one may consider the two{way demonic case in which both conditions (a) and (b) are required.... In PAGE 10: ...nd (b) are required. The main result of this section is the following theorem. Theorem 5.1 An axiomatisation for relations with two{way demonic operators is given by the axioms in Table2 , where the A3o/A7o/F5o version for the A3/A7/F5 axioms is used. Proof: The proof of the fact that a two-way demonic sequential composite f fbd g of two normal forms may be reduced to a normal form using properties IP0, IP1(a)0, IP1(b)0, IP2{IP4 is now a bit more complicate.... ..."

### Table 3: Efiect of limiting non-determinacy

"... In PAGE 13: ...Table 3: Efiect of limiting non-determinacy Lines M1-M2 of Table3 show the performance of FLIPPER with modes and with M set to 100 and 500. Even M = 500 gives a dramatic improvement in run-time, supporting the conjecture.... ..."

### Table 8 Protocol theory complexity overview Bounded # Roles Unbounded # Roles

1982

"... In PAGE 35: ...3. Protocol complexity matrix Table8 shows a summary of the complexity results for the main theorems pre- sented in this paper. The two main columns consider the case of whether the number of roles is bounded or unbounded.... In PAGE 36: ... Because the number is fixed, the nonces can be assumed to have been produced during initialization, and not within the roles themselves. The two rows of Table8 consider whether the term size k is fixed in all instances of the problem, or whether the term size is allowed to vary as a parameter of the problem. For each entry of the matrix in Table 8, we show the complexity result for that case, using P to indicate the problem is in polynomial time, NPC forNP-complete, DEXPC forDEXP-complete, and Undec .... In PAGE 36: ... The two rows of Table 8 consider whether the term size k is fixed in all instances of the problem, or whether the term size is allowed to vary as a parameter of the problem. For each entry of the matrix in Table8 , we show the complexity result for that case, using P to indicate the problem is in polynomial time, NPC forNP-complete, DEXPC forDEXP-complete, and Undec . for Undecidable.... In PAGE 36: ... Table 9 is a more detailed summary of the complexity results, where we show more detail about the results for the upper and lower bounds. The columns are the same as in Table8 , but now the two main rows consider whether the intruder is allowed to generate fresh values or not. These rows are further subdivided into the cases where the roles can perform disequality tests which would allow them to determine whether two fresh values are different from each other.... In PAGE 36: ... If disequality is not allowed, then this test is not performed. Table 9 shows the complexity results for these cases, using the same notation as for Table8 . The numeric references indicate the propositions about specific lower or upper bounds which we discuss in the following sections.... ..."

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### Table 6: Additional axioms for the -angelic choice (a 2 A [ f g) the auxiliar operator

"... In PAGE 6: ... Because of its behaviour with respect to the silent action, this new operator is called -angelic choice. The -angelic choice is denoted by the operator 2 in order to keep Hoare apos;s notation (see [BHR84, Hoa85]), and its de nition is given in Table6 . In order to give a nite axiomatization,... In PAGE 6: ... Now, x2y considers two cases: the rst one observes the initial actions of x and decides what will be executed (x y); the second one do the same but observing y (y x). Adding the set of equations in Table6 to BPA quot;, BPA quot;, BPA quot; and BPAF quot; the equational speci cations BPA quot; + 2, BPA quot; + 2, BPA quot; + 2 and BPAF quot; + 2 are respectively obtained. Let B2 = fBPA quot; + 2; BPA quot; + 2; BPA quot; + 2; BPAF quot; + 2g.... In PAGE 7: ... In order to do that term rewriting techniques are used. So, consider axioms A3 to A9 in Table 1 and all axioms in Table6 with the left-to-right orientation as rewrite rules, i.e.... ..."

### Table 3: E#0Bect of limiting non-determinacy

"... In PAGE 13: ...Table 3: E#0Bect of limiting non-determinacy Lines M1-M2 of Table3 show the performance of FLIPPER with modes and with M set to 100 and 500. Even M = 500 gives a dramatic improvement in run-time, supporting the conjecture.... ..."

### Table 2: Comparison of success rates for 48 complexed und 48 unbound protein structures.

2006

"... In PAGE 10: ... Pocket prediction results were divided into different cate- gories for quality assessment: Correct predictions were termed quot;TOP1-hits quot; whereas quot;TOP3-hits quot; are predictions where the respective ligand is found within the three larg- est predicted pockets. Success rates of pocket predictions are summarized in Table2 . Prediction results are given for the proposed methods and their performance on the data- set of 48 bound/unbound structures indicating TOP1- and TOP3-hits.... ..."

### Table 5 Unbound Examples.

"... In PAGE 13: ... This gave us a possibility to compare our results with the real-life solution. Table5 lists the names of the docked proteins as well as their crystal resolution. The examples were chosen as large proteins (see Table 6), that have been crystallized both in complex and as separate molecules (unbound proteins).... ..."

### Table 2: Comparison of simulation costs using demon and

1995

"... In PAGE 7: ... Weusedt tests to determine whether or not the means of various costs associated with eachsimulation were lower in the rule condition as com- pared to the demon condition. The results are presented belowin Table2 . Note that the number of pathologies predicted (PP) by the demon is almost twice... ..."

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