### Table 1: Comparison of quantum vs. classical separations for query problems. Although not indicated in Table 1, the auxiliary operations required for an exact computation in the present result are very simple (as explained in Section 3): O(n) Hadamard gates plus O(n2) classical post-processing after measuring the state. Acknowledgments R.C. gratefully acknowledges the University of California at Berkeley and the California Institute of Technology where some of the writing and revisions to this paper occurred. References [1] A. Barenco, C. H. Bennett, R. Cleve, D. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter. Elementary gates for quantum computation. Physical Review A, 52:3457{3467, 1995. [2] E. Bernstein and U. Vazirani. Quantum complexity theory. SIAM Journal on Computing, 26(5):1411{1473, 1997.

2000

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### Table 1. Quantum Mechanic and Game Theory properties

"... In PAGE 9: ... The state function in quantum mechanics does not have an equivalent in Game Theory, therefore we will use state function as an analogy with Quantum Mechanics. The comparison between Game Theory and Quantum Mechanics can be shown in an explicit wayin Table1 . Ifthedefinition of rationality in Game Theory represents an optimization process, we can... ..."

### Table 1. Theories for networks, and their complexities.

"... In PAGE 15: ...1 160.0 Table1 presents six inductive theories that cover the examples. Theory T 1 is the most general theory n3e.... In PAGE 15: ... Finally, theory T 6 concisely expresses the reachability relation using a recursive rule. Table1 also presents the code lengths of the theories, according to the theory complexity measure presented in Section 2.4.... In PAGE 15: ...Thus the prior probability on theories corresponds at least to some extent to our subjective notion of theory simplicity. Note also that the n14 relation on theory complexity connects strongly with the n13 relation on models: for the theories of Table1 wehaveLn28T 1 n29n14Ln28T 4 n29n14Ln28T 6 n29 and Qn28T 1 n29 n13 Qn28T 4 n29 n13 Qn28T 6 n29. Table 2 presents the evaluation of each theory according to the MC and PC measures.... ..."

### Table 1 Summary of complexity measures for characterising CSMs

2004

"... In PAGE 8: ....3. Complexity measures Computational complexity measures are used to analyse CSMs. We define seven com- plexity measures (summarised in Table1 ). The TIME complexity of a CSM M is the number of configurations in the computation sequence of an arbitrary instance of M, beginning with the initial configuration and ending with the first final configuration.... In PAGE 10: ... Finally, one might also consider energy a natural complexity measure. In fact, energy is a function of all of the measures in Table1 , with the exception of PHASERES. Such an interpretation is consistent with the quantum theory of light.... ..."

### Table 1 Summary of complexity measures for characterising CSMs. is addressed with the freq complexity measure in the next section.

2005

"... In PAGE 9: ...3 Complexity measures Computational complexity measures are used to analyse CSMs. We de ne seven complexity measures (summarised in Table1 ). The time complexity of a CSM M is the number of con gurations in the computation sequence of an arbitrary instance of M, beginning with the initial con guration and ending with the rst nal con guration.... In PAGE 12: ... Finally, one might also consider energy a natural complexity measure. In fact, energy is a function of all of the measures in Table1 , with the exception of phaseRes. Such an interpretation is consistent with the quantum theory of light.... ..."

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### Table 1. Theories for networks, and their complexities. i

1994

"... In PAGE 15: ...1 160.0 Table1 presents six inductive theories that cover the examples. Theory T1 is the most general theory gt;.... In PAGE 15: ... Finally, theory T6 concisely expresses the reachability relation using a recursive rule. Table1 also presents the code lengths of the theories, according to the theory complexity measure presented in Section 2.4.... In PAGE 15: ... Thus the prior probability on theories corresponds at least to some extent to our subjective notion of theory simplicity. Note also that the relation on theory complexity connects strongly with the relation on models: for the theories of Table1 we have L(T1) L(T4) L(T6) and Q(T1) Q(T4) Q(T6). Table 2 presents the evaluation of each theory according to the MC and PC measures.... ..."

Cited by 11