### Table 2: Overview of pseudo-random generator constructions. To illustrate the power of our generalization, we apply our technique to the following fundamental constructions from di erent areas of theoretical computer science. 2

in Graph Nonisomorphism Has Subexponential Size Proofs Unless The Polynomial-Time Hierarchy Collapses

"... In PAGE 3: ... We formally de ne the notion of a success predicate in Section 4. If we can decide the success predicate of a randomized process with polynomial size B-oracle circuits, then the hardness assumption on the left-hand side of Table2 provides a pseudo-random generator G with the characteristics on the right-hand side of Table 2 for derandomizing the process. The symbol A... In PAGE 3: ... We formally de ne the notion of a success predicate in Section 4. If we can decide the success predicate of a randomized process with polynomial size B-oracle circuits, then the hardness assumption on the left-hand side of Table 2 provides a pseudo-random generator G with the characteristics on the right-hand side of Table2 for derandomizing the process. The symbol A... In PAGE 3: ...Table2... In PAGE 9: ...heorem 4.2 Let A be a class of oracles and B an oracle. Let (F; ) be a randomized process using a polynomial number of random bits, and suppose that B can e ciently check (F; ). Then the hardness conditions of the left-hand side of Table2 provide a pseudo-random generator G with complexity and seed length s as speci ed on the right-hand side of the table such that for some constant d gt; 0 and any input x of length n j Pr [ (x; ) = 1] ? Pr [ (x; Gnd( )) = 1]j 2 o(1): The parameter s in Table 2 can be any space constructible function. In order to reduce the randomness of a randomized process, we will rst analyze the complexity of an oracle B capable of e ciently checking the associated success predicate and then construct a pseudo-random generator secure against B based on a function with presumed hardness against B.... In PAGE 9: ...heorem 4.2 Let A be a class of oracles and B an oracle. Let (F; ) be a randomized process using a polynomial number of random bits, and suppose that B can e ciently check (F; ). Then the hardness conditions of the left-hand side of Table 2 provide a pseudo-random generator G with complexity and seed length s as speci ed on the right-hand side of the table such that for some constant d gt; 0 and any input x of length n j Pr [ (x; ) = 1] ? Pr [ (x; Gnd( )) = 1]j 2 o(1): The parameter s in Table2 can be any space constructible function. In order to reduce the randomness of a randomized process, we will rst analyze the complexity of an oracle B capable of e ciently checking the associated success predicate and then construct a pseudo-random generator secure against B based on a function with presumed hardness against B.... In PAGE 9: ... 5 More Applications and New Derandomizations We will now apply the general framework of Section 4 to various fundamental constructions in computational complexity. As customary, we only state our results in terms of the strongest of the assumptions in Table2 , yielding polynomial time deterministic simulations. It should be noted, how- ever, that weaker assumptions can be taken (the weakest being that the polynomial-time hierarchy does not collapse) in order to achieve weaker, but still subexponential, deterministic simulations.... ..."

### Table 5: Author-Persona-Topic distributions for Daphne Koller, sorted by the number of papers per persona. Koller annotates papers on her publications web page with topical labels. These include \Bayesian Networks, quot; \Computational Game Theory, quot;\Computational Biology, quot;\Learning Graphical Models, quot;\Natural Language, quot; \Text and Web quot; and \Theoretical Computer Science quot;

"... In PAGE 6: ... The personas discovered by the APT model are also co- herent and interpretable. Examples of personas for two Computer Science researchers are shown in Table 4 (David Karger) and Table5 (Daphne Koller). We also list in the captions of those tables subject terms that the researchers themselves chose for their own papers, as listed on their web pages.... ..."

### Table 5: Author-Persona-Topic distributions for Daphne Koller, sorted by the number of papers per persona. Koller annotates papers on her publications web page with topical labels. These include \Bayesian Networks, quot; \Computational Game Theory, quot;\Computational Biology, quot;\Learning Graphical Models, quot;\Natural Language, quot; \Text and Web quot; and \Theoretical Computer Science quot;

"... In PAGE 6: ... The personas discovered by the APT model are also co- herent and interpretable. Examples of personas for two Computer Science researchers are shown in Table 4 (David Karger) and Table5 (Daphne Koller). We also list in the captions of those tables subject terms that the researchers themselves chose for their own papers, as listed on their web pages.... ..."

### Table 1: A Conventional View of Computational Sciences development potentially share nothing except the instrument of computing. And Computa- tional Science does not pursue a systematic understanding of computing as a phenomenon free of context, but as a tool that relates to scienti c reasoning and discovery. Our conclusion is that computational science, viewed as a disparate collection of instances (computational biology, physics, geology, etc.), is not a fruitful scienti c notion. It is a valuable description of challenging intellectual activity, but is likely to lead to systematic understanding only in the individual parent science through its role as another theoretical tool. We will argue in what follows for an alternative view of computational science that does lead to theoretical understanding of computation in science.

"... In PAGE 5: ... Rather than slicing up the computa- tional sciences horizontally into computational volcanology, physics, etc. as in Table1 , we propose many vertical slices as in Table 2. The next few sections will develop our meaning by examining in some detail various generic tasks from science.... In PAGE 12: ... New View of Computational Science The previous sections have explicated the concept of generic tasks in considerable detail. The view advanced here, which is intended to found a computational science on a scienti c basis, contrasts with the orthodox view of the computational sciences depicted previously in Table1 . Table 4 exempli es the new view, which is an elaborated (and transposed) version of Table 2.... ..."

### Table 2: Summary of results on query languages

1994

"... In PAGE 40: ...29 The safety of Boolean combinations of conjunctive queries in RC(S), RC(Sleft); RC(Slen), RC(Sreg) and RC(Sreg;left) is decidable. Table2 summarizes the results of the section. 5 Conclusion There has been significant interest in theoretical computer science in understanding the structure of the regular lan- guages, and in identifying subclasses of the regular languages that have special properties [67, 65].... ..."

Cited by 9

### Table 6: Sample clique for the bibliographic dataset

"... In PAGE 26: ... However, those clusters that were detected provided insightful summaries on groups of authors that were active at certain conferences at a certain time. Table6 shows an excerpt from one of the eight clusters that were detected using fi = 65 and minsup = 0:005 when performing full-dimensional clustering. This particular cluster captured a total of 260 publications in theoretical Computer Science by authors that co-published or appeared at the same time at the same conferences.... ..."

### Table 5 Perceptions of Computer Science

"... In PAGE 14: ....1.3 Content statements For this part of the questionnaire, students were asked to indicate whether they agreed, disagreed or were neutral with respect to a list of statements. The results are shown in Table5 . The first three columns of figures indicate... In PAGE 15: ...025 (Sheskin, 2000). As can be seen from Table5 , significant differences were only found for two statements. For both statements, a significant portion of students moved to- wards agreeing with the statements, one which stated that working with com- puters is boring, and one which stated that Computer Science is not interesting because it is about machines rather than people.... In PAGE 19: ... (1998) and Herbert (2000) where respondents appeared to have little understanding of the nature of Computer Science or the types of careers that are available. Questions relating to the availability of good jobs which appear in Table 2 and Table5 show that students are positive about their prospects even if they do not know what they are. This agrees with the results of Herbert (2000).... In PAGE 21: ...athematics. This requires further research. 5.3 Working with computers In Table5 , the only two statements with significant differences in changed proportions deal with working with computers, and whether Computer Sci- ence is interesting. In both cases, around 20% of the sample became more in agreement that working with computers is boring or not interesting.... ..."