### Table 2. Complexity Classes of Resource Allocation, n = size of task set #02, m = size of operation set #0A

"... In PAGE 14: ... We define different categories of difficulties of the problem and present complexity results for them. Table2 summarizes these complexity results. To address these formalized problems, we define the notion of Dynamic Distributed Constraint Satisfaction Problem (DyDCSP) and present a generalized mapping from distributed resource allocation to DyDCSP.... ..."

### Table 1: Complexity Classes of Resource Allocation, D2 = size of task set A2, D1 = size of operation set AA. Columns represent task complexity and rows represent inter-task relationship complexity. SCF WCF OC

in Distributed Resource Allocation: Formalization, Complexity Results and Mappings to Distributed CSPs

"... In PAGE 10: ...3 Subclasses of Resource Allocation Given the above properties, we can define 9 subclasses of problems according to their task com- plexity and inter-task relationship complexity: SCF and AGD2 D2 AH-exact, SCF and AGD2CZ AH-exact, SCF and unrestricted, WCF and AGD2 D2 AH-exact, WCF and AGD2CZ AH-exact, WCF and unrestricted, OC and AGD2 D2 AH-exact, OC and AGD2CZ AH-exact, OC and unrestricted. Table1 summarizes our complexity results for the subclasses of resource allocation problems just defined. The columns of the table, from top to bottom, represent increasingly complex tasks.... In PAGE 22: ... We experiment with distributed constraint problems obtained from applying Mapping II to various target and sensor configurations. Experimenting with Mapping II is appropriate because it addresses WCF resource allocation problems, which are more complex than the SCF problems addressed by Mapping I as seen in Table1 . Note that these are not toy examples but rather real problems from hardware sensor configurations similar to that shown in Figure 4.... ..."

### Table 8. Complexity classes of all exact minimal ESOPs of 3 variables # ALLBF = 256

"... In PAGE 13: ... Evidently, in the set of such Boolean functions that require the largest number of cubes in their shortest ESOP, there is a subset of functions that belong to the set of functions with the largest number of cubes in its SNF. See for example Table8 . There are 66 functions of three variables that require three cubes in their shortest ESOP.... In PAGE 15: ... These Tables confirm that the maximal number of cubes in an exact minimal ESOP occur in most complex functions. However, Table8... ..."

### Table 1: Relative complexity for certain problems restricted to the graph classes I, UD, P, and TL.

in Improper

"... In PAGE 3: ...Table1 for a summary of what is known about these problems, comparing the restrictions to interval graphs, to unit disk graphs, to planar graphs, to disk graphs and to weighted induced subgraphs of the triangular lattice. Later, we shall be able to add two rows to this table that correspond to k-IMPROPER CHROMATIC NUMBER and MAX k-DEPENDENT SET.... ..."

### Table2. Complexity classes of automata with logarithmically space-bounded tape and empty alternation

1994

"... In PAGE 5: ... In the following, for X 2 fLOG, PDA{TIME(pol), PDA, P, PSPACEg and a function g, where we again admit the cases that g is a constant or that g is unbounded, let EA log g X denote the set of all languages recognized by logspace Turing machines augmented with storage of type X, which make g(n) 1 empty alternations. The main results of this chapter are collected in Table2 , which is the \empty quot; analogue of Table 1. 3.... ..."

Cited by 2

### Table 1: A summary of the complexity results. complexity class

in Abstract

"... In PAGE 6: ... Conclusions Motivated by a number of real-world applications that re- quire solutions that are either diverse or similar, we have pro- posed a range of similarity and diversity problems. We have presented a detailed analysis of their computational com- plexity (see Table1 ), and developed a number of algorithms and global constraints for solving them. Our experimental Table 1: A summary of the complexity results.... ..."

### Table 1: Monitoring Complexities for Property Classes of g

2001

"... In PAGE 12: ...As Table1 shows, most of the properties described in this section belong to di erent complexity classes for monitoring. Many of the properties are in fact inclusions of each other.... In PAGE 13: ... So to monitor property 3 (together with property 1) we can compose the algorithms for P6 and P7. The complexity of such an algorithm is the sum of the complexities of the two algorithms as shown in Table1 , which is essentially the complexity of the P7 part (2W B2 2B). 7 Conclusions and Related Work This paper is most closely related to work on passive test- ing [7].... ..."

Cited by 19

### Table 1: Complexity of path model checking

2005

"... In PAGE 2: ... Again, for those subcases, we should look at the existence of specialized techniques. The results that we have obtained for the model checking problems of the three real-time logics over the six classes of restricted sets of timed paths are given in Table1 . To the best of our knowledge, only the three results from the first line were known, all the other results are new.... ..."

Cited by 2

### Table 1: Monitoring Complexities for Property Classes of g

"... In PAGE 12: ...As Table1 shows, most of the properties described in this section belong to di erent complexity classes for monitoring. Many of the properties are in fact inclusions of each other.... In PAGE 13: ... So to monitor property 3 (together with property 1) we can compose the algorithms for P6 and P7. The complexity of such an algorithm is the sum of the complexities of the two algorithms as shown in Table1 , which is essentially the complexity of the P7 part (2W B2 2B). 7 Conclusions and Related Work This paper is most closely related to work on passive test- ing [7].... ..."

### Table 1 Complexity of path model checking

"... In PAGE 3: ... Again, for those subcases, we should look at the existence of specialized techniques. The results that we have obtained for the model checking problems for the four real-time logics over the six classes of restricted sets of timed paths are given in Table1 . To the best of our knowledge, only the three results from the first line were known, all the other results are new.... ..."