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Abstract: . For any k 3, we prove the following results on theories in the k-variable fragment L k of first-order logic: (1) The so-called L k -invariant is not recursively invertible. (2) There is no recursive bound on the size of the minimal model of a complete L k -theory in terms of its k-size, that is, the number of its L k -types. (3) Assume that NP 6` P=poly. Then there is no P-computatble canonization function for L k -equivalence. Our results answer questions of Dawar [3, 4] and Dawar,... (Update)
Context of citations to this paper: More
...imply the existence of a logic for ptime on arbitrary structures. What is missing is the ability to efficiently invert k invariants [Gro97] the analog of Theorem 2.2. Of course, the language just described for topological ptime is quite artificial, but serves the purpose of...
...his aforementioned result for L 2 along these lines. Unfortunately, for k 3 the mapping I k is not even recursively invertible [8]. But Dawar et al. 4] had already observed that it is not possible, but also not necessary, to invert I k in time polynomial in the size of...
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Large Finite Structures with Few L k -Types - Grohe (1997) (Correct)
Finite Variable Logics In Descriptive Complexity Theory - Grohe (1998) (Correct)
Finite Models And Finitely Many Variables - Dawar (1999) (Correct)
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BibTeX entry: (Update)
M. Grohe. Large finite structures with few L k -types. In Proceedings of the 12th IEEE Symposium on Logic in Computer Science, pages 216--227, 1997. http://citeseer.ist.psu.edu/article/grohe97large.html More
@inproceedings{ grohe97large,
author = "Martin Grohe",
title = "Large Finite Structures with Few L k -Types",
booktitle = "Logic in Computer Science",
pages = "216-227",
year = "1997",
url = "citeseer.ist.psu.edu/article/grohe97large.html" }
Citations (may not include all citations):114 Generic computation and its complexity (context) - Abiteboul, Vianu - 1991
85 Upper and lower bounds for first-order expressibility (context) - Immerman - 1982
85 Turing machines that take advice (context) - Karp, Lipton - 1982
81 Mathematical Logic (context) - Ebbinghaus, Flum et al. - 1994
78 On Moschovakis closure ordinals (context) - Barwise - 1977
57 Infinitary logic and inductive definability over finite stru.. - Dawar, Lindell et al. - 1995
37 Feasible Computation through Model Theory - Dawar - 1993
29 Deux ou trois choses que je sais de Ln (context) - Poizat - 1982
18 The expressive power of fixed-point logic with counting (context) - Otto - 1996
17 Fixed-point logics on planar graphs - Grohe - 1997
16 volume 9 of Lecture Notes in Logic (context) - Otto, Logics - 1997
11 Large finite structures with few L k -types - Grohe - 1997
9 Ptime canonization for two variables with counting - Otto - 1995
7 Types and indiscernibles in finite models (context) - Dawar
5 Enumerable sets are diophantic (context) - Matijasevic - 1970
4 Habilitationsschrift at the Albert-LudwigsUniversit at Freib.. (context) - Grohe, of - 1997
1 To appear in Computer Science Logic (context) - Grohe, -equivalence - 1997
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://sun2.mathematik.uni-freiburg.de/home/grohe/pub.html): More
On Fixed-Point Logic With Counting - Flum, Grohe (1998) (Correct)
Equivalence in Finite-Variable Logics Is Complete for Polynomial.. - Grohe (1996) (Correct)
Fixed-Point Logics on Planar Graphs - Grohe (1998) (Correct)
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