### TABLE 2. Equations of the autonomous calculus

### TABLE 4. Semantics of the autonomous calculus

### Table 2. Proof verification

2003

"... In PAGE 5: ... Table 2. Proof verification Table2 gives data about proof verification. The Verification time column shows the time taken by Proof_verification2.... In PAGE 6: ... (For the rest of the conflict clauses we computed the number of resolutions exactly. So we believe the lower bounds shown in Table2 are close to the real sizes.) The Confl.... In PAGE 6: ... It is not hard to see that with the exception of a few instances conflict clause proofs are smaller than resolution graph ones. (In Table2 we estimate only the initial size of a resolution graph. That is we do not take into account that, as it was mentioned in Section 5, the size of the resolution proof grows during proof verification.... In PAGE 6: ...onfl. cl. proof size (in thou- sands of literals) Ra- tio % bounded model checking, SAT-2002 [18] fifo8_200 379,992 71,971 18 fifo8_300 987,840 118,132 11 fifo8_400 4,581,450 335,752 7 Table 3. Growth of resolution proof size The size of the largest proof of Table2 (formula 7pipe) was 257 Mbyte and so we were able to verify the proof on the computer with 640 Mbytes of memory. On the other hand, the corresponding resolution graph proof contained 435 million nodes and so the resolution graph would take more than 2 Gbytes of memory (assuming that on average one needs 5 digits to label a node of the resolution graph).... ..."

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### Table 2. Proof verification

"... In PAGE 5: ...44 103,556 41.5 Table2 gives data about proof verification. The Verification time column shows the time taken by Proof_verification2.... In PAGE 5: ... (For the rest of the conflict clauses we computed the number of resolutions exactly. So we believe the lower bounds shown in Table2 are close to the real sizes.) The Confl.... In PAGE 5: ...It is not hard to see that with the exception of a few instances conflict clause proofs are smaller than resolution graph ones. (In Table2... In PAGE 6: ... cl. proof size (in thou- sands of literals) Ra- tio % bounded model checking, SAT-2002 [18] fifo8_200 379,992 71,971 18 fifo8_300 987,840 118,132 11 fifo8_400 4,581,450 335,752 7 The size of the largest proof of Table2 (formula 7pipe) was 257 Mbyte and so we were able to verify the proof on the computer with 640 Mbytes of memory. On the other hand, the corresponding resolution graph proof contained 435 million nodes and so the resolution graph would take more than 2 Gbytes of memory (assuming that on average one needs 5 digits to label a node of the resolution graph).... ..."

### Table 1: Summary of reviewed research in software architectures for autonomic computing.

"... In PAGE 4: ... How- ever, the two approaches have common con- cepts it is sometimes difficult to place a re- search project in one particular category. Table1 shows a summary of the research re- viewed in this section. 4.... ..."

### Table 1. Results from formal verification of safety with the necessary invariant constraints.

"... In PAGE 8: ... Safety was checked with the commutative correctness diagram used in [20][93][94][98]. Table1 shows the results from formal verification with the necessary invariant constraints. The old translation to CNF is without preserving the ITE-tree structure of equation arguments when eliminating equations, but using a disjunction of conjunctions.... ..."

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### Table 1. Verification statistics for the flushing approach, the commitment approach using the Good MA invariant, and the commitment approach using the Greatest Fixpoint invariant for various pipelined machines.

"... In PAGE 3: ... We implemented ALU instructions, register-register and register-immediate addressing modes, loads, stores, and branch instructions. We assign names to the pipelined machine models that are consistent with the names in the Processor column of Table1 . The model names start with a number indicating the number of stages followed optionally by the letters I , D , W , B and N indicating the presence of an instruction cache, data cache, write buffer, branch prediction abstraction scheme 1, and branch prediction abstraction scheme 2, respectively.... In PAGE 4: ... All states that are within n steps from a committed state clearly satisfy the invariant, so our proof obligation reduces to showing that the successor of any state that is n steps away from a committed state sat- isfies the invariant. As shown in Table1 , it turns out that the invariant proof is computationally expensive, account- ing for more than 98% of the verification time required by the commitment approach. 5.... In PAGE 7: ... While we tried to use idle machines, the running times we obtained could have been slightly influenced by other jobs running on the machines. Table1 shows the verification times and related statis- tics for the various pipelined machine models. The names in the Processor column start with a number indicating the number of stages followed optionally by the letters I , D , W , B , and N indicating the presence of an instruction cache, data cache, write buffer, branch prediction abstrac- tion scheme 1, and branch prediction abstraction scheme 2, respectively.... ..."

### Table 2. Systems supporting development of autonomic applications and systems

2005

"... In PAGE 11: ..., into systems, and (2) systems that investigate models, programming paradigms and de- velopment environments to support the development of autonomic systems and applica- tions. A sampling of systems belonging to these categories are summarized in Tables 1 and Table2 respectively. 6 Summary and Conclusion In this paper, we introduced the autonomic computing paradigm, which is inspired by biological systems such as the autonomic human nervous system, and enables the development of self-managing computing systems and applications.... ..."

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