### Table 1. Decidability of the model property for timed automata with behavioural re- strictions wrt. speci cations from di erent fragments of Duration Calculus. The frag- ments are named after the shapes of allowed atomic formulae.

"... In PAGE 9: ... To the best of our knowledge, these are the rst e ective procedures available for a dense-time Duration Calculus with metric time, the chop modality, and unrestricted negation. Table1 provides an overview over the decidability results for model-checking timed automata against various fragments of dense-time Duration Calculus. A particular implication of these ndings is that even extremely abstract real-time formalisms can be integrated into the design process of embedded controllers through key-press techniques.... ..."

### Table 2: Synchronization Instruction Overhead

"... In PAGE 4: ... 3.2 Instruction-Level Overhead Table2 quanti es the instruction-level overhead of a range of syn- chronization instructions on two widely-used modern CPU archi- tectures, the Intel Xeon and the IBM POWER4. The performance gures for each instruction are normalized to the cost of a regular instruction that hits in the top-level cache, on each architecture.... In PAGE 4: ... Measuring overheads of single instructions on modern super- scalar microprocessors requires extreme care.1 The approach used to generate the results in Table2 was to measure a long series of in- structions, but to execute them in a loop. For the rst six rows of the 1For example, sampling a high-precision time source before and after the instruc- tion will give wildly inaccurate results due to instruction reordering by the CPU, in fact, negative values may be produced by such methods.... ..."

### Table 2: Properties and Sizes of Their Automata Representations.

"... In PAGE 13: ...eloper V6.0.1. The first is the TBS system intro- duced in Section 1 and consisting of five partners and seven invocation-type activities. Table2 lists sizes of monitoring automata constructed from the TBS properties in Table 1. For example, a0 a1 in- cludes 6 events between 3 partners and is repre- sented by an automaton with 6 states and 23 transi- tions.... In PAGE 13: ... These activities are in- voked via asynchronous or synchronous message passing. Two safety properties of OSS, a0 a1a0 and a0 a39 in Table2 , correspond to A premium customer al- ways gets a discount on his/her purchase and An order cannot be billed before being marked com- plete by the customer , respectively. The liveness property of OSS, a0 a1a2 , is A completed order will be eventually billed .... ..."

### Table 2. Implementability of asynchronous automata with multiple initial states

2004

"... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). The paper is organized as follows.... ..."

### Table 2. Implementability of asynchronous automata with multiple initial states

2004

"... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). The paper is organized as follows.... ..."

### Table 2. Implementability of asynchronous automata with multiple initial states

"... In PAGE 2: ...) In [Zie89], Zielonka characterized the transition systems that can be imple- mented as an asynchronous automata modulo language equivalence. Combin- ing this result with several others from the literature, we show that the imple- mentability problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , column 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ... Combin- ing this result with several others from the literature, we show that the imple- mentability problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, column 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). Partly motivated by the complexity results, in the last part of the paper we present new prototype implementations for asynchronous automata synthesis... ..."

### Table Automata

2002

### Table 3: Procedure create-eulerian-cycle

"... In PAGE 12: ... Thus, the seen flag of a vertex v is changed to 1, and back to 0, as many times as there are cycles which pass through it. The main procedure, which governs the actions of R, is create-eulerian- cycle; see Table3 . It employs two subroutines, explore (Table 4) and retrace (Table 5).... In PAGE 14: ... 6.3 The Create-Eulerian-Cycle Procedure We shall refer to lines 3,4 and 8 of Table3 as the Scan behavior. Procedure create-eulerian-cycle uses explore and retrace to perform a deterministic version of Preparatory.... ..."

### Table 3: Procedure create-eulerian-cycle

"... In PAGE 12: ... Thus, the seen flag of a vertex v is changed to 1, and back to 0, as many times as there are cycles which pass through it. The main procedure, which governs the actions of R,iscreate-eulerian- cycle; see Table3 . It employs two subroutines, explore (Table 4) and retrace (Table 5).... In PAGE 14: ... 6.3 The Create-Eulerian-Cycle Procedure We shall refer to lines 3,4 and 8 of Table3 as the Scan behavior. Procedure create-eulerian-cycle uses explore and retrace to perform a deterministic version of Preparatory.... ..."