### Table 1: Time and Space complexity comparision of Probabilistic algorithms to generate equations.

in Towards an Efficient Algorithm to Find Annihilators by Solving a Set of Homogeneous Linear Equations

### Table 1. Time and Space complexity comparision of Probabilistic algorithms to gen- erate equations.

### Table 3: Complexity of Probabilistic Causality

"... In PAGE 20: ... We also analyze the complexity of computing the probability of a causal formula. Our complexity results are summarized in Table3 . In detail, deciding probabilistic causal irrelevance is Ca30... ..."

### Table 2: Comparison of performance on practical examples;; the probabilistic

1998

"... In PAGE 8: ... We also tried a modi ed version of the EA which rst runs APGAN and then inserts the computed topological sort into the initial population. Table2 shows the results of applying GDPPO to the schedules generated by the various heuristics on several practical SDF graphs;; the satellite re- ceiver example is taken from [16], whereas the other examples are the same as considered in [3]. The probabilistic algorithms ran once on each graph and were aborted after 3000 tness evaluations.... In PAGE 8: ... Additionally, an exhaustive searchwithamaximum run-time of 1 hour was carried out;; as it only com- pleted in two cases 3 , the search spaces of these problems seem to be rather complex. In all of the practical benchmark examples in Table2 the results achieved by the EA equal or surpass those generated by RPMC. Compared to APGAN on these practical examples, the EA is neither inferior nor superior;; it shows both better and worse performance in two cases each.... ..."

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### Table 2 Online computational complexity

"... In PAGE 6: ...performance. Table2 presents the required online op- erations as well as the computational complexity of each step. Assuming fixed dimension for the motion parameter vector, the overall complexity for each case is O(m).... ..."

### Table 1: Complexity of probabilistic reasoning under coherence.

"... In PAGE 15: ..., 1-conjunctive). Our complexity results are compactly summarized in Table1 . It turns out that deciding g-coherence, g- coherent consequence, and tight g-coherent consequence are complete for NP, co-NP, and BWC8, respectively, while computing tight intervals under g-coherent entailment is BYC8C6C8-complete.... ..."

### Table 1. Examples of the TTS-related complexity scoring for several languages (including 5 South Asian languages).

2003

"... In PAGE 7: ...optional vowel symbols and the Tibetan script with no spaces between words (these two languages have high complexity scores in Table1 ). In order to solve the problems with such scripts machine learning tech- niques both for vowel insertion and for word extrac-... ..."

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### Table 2. Comparison of performance on practical examples;; the probabilistic algo-

1998

"... In PAGE 8: ... We also tried a slightly modi ed version of the Evolutionary Algorithm which rst runs APGAN and then inserts the computed topological sort into the initial population. Table2 shows the results of applying GDPPO to the schedules generated by the various heuristics on several practical SDF graphs;; the satellite receiver ex- ample is taken from [15], whereas the other examples are the same as considered in [2]. The probabilistic algorithms ran once on each graph and were aborted after 3000 tness evaluations.... In PAGE 8: ... Additionally, an exhaustive searchwitha maxi- mum run-time of 1 hour was carried out;; as it only completed in two cases 5 , the search spaces of these problems seem to be rather complex. In all of the practical benchmark examples that makeup Table2 the results achieved by the Evolutionary Algorithm equal or surpass the ones generated byRPMC.Compared to APGAN on these practical examples, the Evolution- ary Algorithm is neither inferior nor superior;; it shows both better and worse performance in two cases each.... ..."

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### Table 1: Space Complexity

2001

"... In PAGE 4: ... This will become clear in Section 3 where algorith- mic routing is explained in detail. Table1 summarizes the space complexity analysis. Computational complexity for flat routing, which adopts the Dijkstra algorithm, is C7B4C6BFB5.... ..."

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### TABLE II SPACE COMPLEXITY

2001

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