### Table 1-1). After RAOs have been identified, for some RAOs it is necessary to develop numerical RAGs for use in remedial design and to verify that remedial action has achieved the RAOs. The RAO framework involves the following:

"... In PAGE 11: ... The closure plan presented the corrective measures study (CMS) and defines closure requirements for TSD sites that do not have contamination but nevertheless require closure (DOE-RL 1998a). Table1 -1 lists each waste site, defines the final grade, and defines the projected contaminated volume. It is possible that remedial action may also encounter waste sites adjacent to the sites listed in the TSD ROD (e.... In PAGE 15: ...Introduction Rev. 1 RDR/RAWP for the 100-NR-1 Treatment, Storage, and Disposal Units September 2000 1-7 Table1 -1. Waste Sites Identified in the Interim Remedial Action Record of Decision for the 100-NR-1 Operable Unit and in Revision 5 of the Hanford Facility RCRA Permit.... In PAGE 43: ... Clean backfill material is obtained from clean material storage areas, approved clean rubble areas, and local borrow sites. Excavations are backfilled to agreed-upon elevations ( Table1... In PAGE 48: ... Clean backfill material will be obtained from clean material storage areas, approved clean rubble areas, and local borrow sites. The sites are backfilled to agreed-upon elevations ( Table1 -1). 3.... ..."

### Table 2: Overview of pseudo-random generator constructions.

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

1999

"... In PAGE 2: ... We formally define the notion of a success pred- icate in Section 4. If we can decide the success predicate of a ran- domized 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 Table 2 represents an arbitrary class of oracles.... In PAGE 2: ... We formally define the notion of a success pred- icate in Section 4. If we can decide the success predicate of a ran- domized 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 Table 2 represents an arbitrary class of oracles.... In PAGE 2: ... If we can decide the success predicate of a ran- domized 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 Table 2 for derandomizing the process. The symbol A in Table2 represents an arbitrary class of oracles. To illustrate the power of our generalization, we apply it to the following randomized processes from different areas of theoretical computer science.... In PAGE 5: ...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 ran- dom bits, and suppose that B can efficiently check (F; ). Then the hardness conditions on the left-hand side of Table2 provide pseudo-random generators G with complexity and seed lengths s as specified 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 first analyze the complexity of an oracle B capable of effi- ciently checking the associated success predicate and then con- struct a pseudo-random generator secure against B based on a func- tion with presumed hardness against B.... In PAGE 5: ...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 ran- dom bits, and suppose that B can efficiently check (F; ). Then the hardness conditions on the left-hand side of Table 2 provide pseudo-random generators G with complexity and seed lengths s as specified 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 first analyze the complexity of an oracle B capable of effi- ciently checking the associated success predicate and then con- struct a pseudo-random generator secure against B based on a func- tion with presumed hardness against B.... In PAGE 5: ... 5 More Applications We will now apply the general framework of Section 4 to various other 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, however, that weaker assumptions can be taken (e.... ..."

Cited by 72

### Table 2: Overview of pseudo-random generator constructions.

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 8: ...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 8: ...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: ...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, however, 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 3. Performance Expectation for Hand Designs (P+G+O: Pipelined with Grouping and Overlapping, OPT: Optimal Scheduling Design).

2001

"... In PAGE 5: ... Given the trade-off between generality and performance we have estimated the performance gap between the currently automated applications in this empirical study and what a designer could achieve exploiting the overlapping of computation in the core datapath with the communication with external memory. In Table3 we compare the performance of the generated designs against an optimal solution where the memory accesses are perfectly scheduled and are fully overlapped with the computation in a zero latency scenario. Table 3.... In PAGE 5: ...While Table3 reveals there is still a substantial performance gap between the automatically generated codes and the possibly infeasible optimal version, the effort and time investment for a hand design is still substantial, in particular for a novice programmer. While our designs take a few seconds to generate and about 30 minutes to synthesize and download onto the board, a hand design can take days if not weeks to design and verify its correctness.... ..."

Cited by 9

### Table 4. Characteristics of pseudo-random pattern generators

"... In PAGE 4: ... 5. Estimated overhead As shown in Table4 , the GLFSRs differ in hardware costs and in randomness, dependent on the selected char- acteristic polynomial which was calculated from the cho- sen ( ; m) pair and the generating polynomials. Gener- ally, it can be stated that the GLFSR implementation needs more area than LFSRs and approximately the same area as LHCAs (after optimization, i.... In PAGE 4: ...HCAs (after optimization, i.e., removing redundant XOR gates). Table4 shows that the LFSRs, i.... In PAGE 4: ... The table shows also, that choosing a suitable GLFSR leads to a much better SCC and less XOR gates than any LHCA. In Table4 , num- ber 5 is the GLFSR which fulfills the requirements of low area and good SCC in the best way. Regarding test time, GLFSRs have the advantage of higher fault coverage for the same test length.... ..."

### Table 12.1: Pseudorandom generators of flelded stream ciphers

2004

### 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 1. Performance results with and without IV-setup. \Key setup quot; generates all keys for the -AU and SU hash functions, \Universal hash quot; processes the tree, and \Finalization quot; includes the F-function and generates the pseudo-random pad.

2005

"... In PAGE 11: ...hich is often not the case (e.g. in IPsec communication). Table1 gives performance numbers both with and without explicit IV-setup. On short messages: Since the amount of key material required for Badger depends on the length of the message, optimized versions can be used in applications where the message length is upper bounded.... ..."

Cited by 2