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Abstract: this paper by reducing 3k + 1 to k + 1, or k, or even a constant. We will prove this by modifying Cai's result [3] and by modifying the reduction used in [7]. Section 2 provides a brief review the notion of "first-order incremental evaluation systems ". Section 3 establishes a necessary technical lemma, which is a variant of Cai's theorem. Section 4 gives the proof of the above theorem. 2 First-Order Incremental Evaluation Systems (Update)
Context of citations to this paper: More
...their example query that proved the strict inclusion of IES(FO) k in IES(FO) k 1 had input arity 6k. Even more recently, Dong and Zhang [20] separated IES(FO) k from IES(FO) k 1 using an example query of arity 3k 1. However, it is open if there is an IES(FO) for transitive...
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0.2: Incremental Recomputation in Local Languages - Dong, Libkin, Wong (2003) (Correct)
0.2: Incremental Recomputation of Recursive Queries with Nested.. - Libkin, Wong (1997) (Correct)
0.2: Some Relationships between the FOIES and ... Arity Hierarchies - Dong, Wong (1996) (Correct)
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0.3: Some Relationships between the FOIES and Σ11 Arity.. - Dong, Wong (1996) (Correct)
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BibTeX entry: (Update)
G. Dong and L. Zhang. Separating Auxiliary Arity Hierarchy of First-Order Incremental Evaluation Using (3+1)-ary Input Relations. TR 97/13, Computer Science Dept, University of Melbourne. http://citeseer.ist.psu.edu/dong97separating.html More
@article{ dong00separating,
author = "Guozhu Dong and Louxin Zhang",
title = "Separating Auxiliary Arity Hierarchy of First-Order Incremental Evaluation Systems Using (3k+1)-ary Input Relations",
journal = "International Journal of Foundations of Computer Science",
volume = "11",
number = "4",
pages = "573-578",
year = "2000",
url = "citeseer.ist.psu.edu/dong97separating.html" }
Citations (may not include all citations):775 Foundations of Databases (context) - Abiteboul, Hull et al. - 1995
189 Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolensky - 1987
51 Lower bounds for the size of circuits of bounded depth with .. (context) - Razborov - 1987
43 Incremental and decremental evaluation of transitive closure.. (context) - Dong, Su - 1993
43 Incremental and decremental evaluation of transitive closure.. (context) - Dong, Su - 1995
30 Incremental evaluation of datalog queries (context) - Dong, Topor - 1992
27 Dyn-FO: A parallel dynamic complexity class - Patnaik, Immerman - 1994
23 Space bounded FOIES (context) - Dong, Su - 1995
15 Nonrecursive incremental evaluation of datalog queries - Dong, Su et al. - 1995
13 A note on the theorem of Razborov (context) - Barrington - 1987
12 Lower bounds for constant-depth circuits in the presence of .. (context) - Cai - 1990
6 Arity Bounds for First-Order Incremental Evaluation and Defi.. (context) - Dong, Su
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