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An Ehrenfeucht-Fraisse Game Approach to Collapse Results in Database Theory [article]

Nicole Schweikardt
2002 arXiv   pre-print
We present a new Ehrenfeucht-Fraisse game approach to collapse results in database theory and we show that, in principle, this approach suffices to prove every natural generic collapse result.  ...  This, as a side product, also leads to an Ehrenfeucht-Fraisse game proof of the theorem of Ginsburg and Spanier, stating that the spectra of FO(<,+)-sentences are semi-linear.  ...  I thank Thomas Schwentick for helpful advice especially in the early stages of my research and for drawing my attention to collapse considerations in database theory.  ... 
arXiv:cs/0212049v1 fatcat:slxlikn3d5cfnchbd5vbh3xogm

An Ehrenfeucht-Fraïssé game approach to collapse results in database theory

Nicole Schweikardt
2007 Information and Computation  
Pursuing an Ehrenfeucht-Fraïssé game approach to collapse results in database theory, we show that, in principle, every natural generic collapse result may be proved via a translation of winning strategies  ...  for the duplicator in an Ehrenfeucht-Fraïssé game.  ...  An Ehrenfeucht-Fraïssé Game Approach In this section we present the translation of strategies for the Ehrenfeucht-Fraïssé game as a method for proving collapse results in database theory.  ... 
doi:10.1016/j.ic.2006.10.002 fatcat:wgpo3raaa5gz5fckpd5prifxhu

Page 804 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
:03038 03B70 68P15 Lautemann, Clemens (D-MNZ-IC; Mainz) ; Schweikardt, Nicole (D-MNZ-IC; Mainz) An Ehrenfeucht-Fraissé approach to collapse results for first-order queries over embedded databases.  ...  Our proofs are by means of an explicitly constructed winning strategy for Duplicator in an Ehrenfeucht-Fraissé game, and can deal with certain infinite databases where previous, highly involved methods  ... 

An Ehrenfeucht-Fraïssé Approach to Collapse Results for First-Order Queries over Embedded Databases [chapter]

Clemens Lautemann, Nicole Schweikardt
2001 Lecture Notes in Computer Science  
Our proofs are by means of an explicitly constructed winning strategy for Duplicator in an Ehrenfeucht-Fraïssé game, and can deal with certain infinite databases where previous, highly involved methods  ...  We present a new proof technique for collapse results for first-order queries on databases which are embedded in N or R 0.  ...  Moreover, our proofs are constructive in the sense that they are obtained using an Ehrenfeucht-Fraïssé game with an explicitly constructed winning strategy for Duplicator.  ... 
doi:10.1007/3-540-44693-1_40 fatcat:3lyhni4ryvecxhijezxadam2w4

Relating Structure and Power: Extended Version [article]

Samson Abramsky, Nihil Shah
2021 arXiv   pre-print
In particular, Ehrenfeucht-Fraisse games, pebble games, and bisimulation games play a central role.  ...  Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures.  ...  for the Ehrenfeucht-Fraïssé comonad is equivalent to the Ehrenfeucht-Fraïssé game between A and B.  ... 
arXiv:2010.06496v7 fatcat:gx35xqxu2nb6dllwb52vxyf73q

Relating Structure and Power: Comonadic Semantics for Computational Resources [chapter]

Samson Abramsky, Nihil Shah
2018 Lecture Notes in Computer Science  
In particular, Ehrenfeucht-Fraïssé games, pebble games, and bisimulation games play a central role.  ...  ACM Subject Classification Theory of computation → Finite Model Theory, Theory of computation → Categorical semantics In this paper, we develop a novel approach to relating categorical semantics, which  ...  It acquires additional significance in finite model theory, where model comparison games such as Ehrenfeucht-Fraïssé games, pebble games and bisimulation games play a central role [21] .  ... 
doi:10.1007/978-3-030-00389-0_1 fatcat:kuwar27movhtroa6ztlz57vdke

Relating Structure and Power: Comonadic Semantics for Computational Resources [article]

Samson Abramsky, Nihil Shah
2018 arXiv   pre-print
In particular, Ehrenfeucht-Fraisse games, pebble games, and bisimulation games play a central role.  ...  Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures.  ...  It acquires additional significance in finite model theory, where model comparison games such as Ehrenfeucht-Fraïssé games, pebble games and bisimulation games play a central role [21] .  ... 
arXiv:1806.09031v2 fatcat:tpyt23nfijdzla52ry6yfl3usu

Expressive power of unary counters [chapter]

Michael Benedikt, H. Jerome Keisler
1997 Lecture Notes in Computer Science  
That is, being able to count elements does not allow one to count terms. This paper also continues our interest in new proof techniques in database theory.  ...  Our main result shows that the stronger operator count{t(x) : ϕ}, where t(x) is a term of sort N, cannot be expressed in L(Ct).  ...  Ehrenfeucht-Fraisse games are also exploited in [11] and [12] to get complexity bounds for languages allowing counting quantifiers of the form ∃i.  ... 
doi:10.1007/3-540-63246-8_3 fatcat:5dzka76chvhv5lcadm6rjw5gqm

Expressive power of unary counters [chapter]

Michael Benedikt, H. Jerome Keisler
1997 Lecture Notes in Computer Science  
That is, being able to count elements does not allow one to count terms. This paper also continues our interest in new proof techniques in database theory.  ...  Our main result shows that the stronger operator count{t(x) : ϕ}, where t(x) is a term of sort N, cannot be expressed in L(Ct).  ...  Ehrenfeucht-Fraisse games are also exploited in [11] and [12] to get complexity bounds for languages allowing counting quantifiers of the form ∃i.  ... 
doi:10.1007/3-540-62222-5_52 fatcat:2rxgqdq7x5d63g4ufaxdkdt44y

Page 8491 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Ehrenfeucht- Fraiss¢ approach to collapse results for first-order queries over embedded databases (455—466).  ...  Contents: Olivier Danvy, Many happy returns (1); Martin Hof- mann, From bounded arithmetic to memory management: use of type theory to capture complexity classes and space behav- iour (2-3); Dag Normann  ... 

First-order expressibility of languages with neutral letters or: The Crane Beach conjecture

David A. Mix Barrington, Neil Immerman, Clemens Lautemann, Nicole Schweikardt, Denis Thérien
2005 Journal of computer and system sciences (Print)  
The CBC is closely related to uniformity conditions in circuit complexity theory and to collapse results in database theory.  ...  A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e's from any word in A * does not change its membership or non-membership in  ...  Acknowledgements We are indebted to Thomas Schwentick for bringing the database theory connection to our attention. He also took an active part in many discussions on the subject of this paper.  ... 
doi:10.1016/j.jcss.2004.07.004 fatcat:owczidjcindrbgqgki236ckj4q

Querying Spatial Databases via Topological Invariants

Luc Segoufin, Victor Vianu
2000 Journal of computer and system sciences (Print)  
The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases.  ...  The focus is on the translation of topological queries against the spatial database into queries against the topological invariant.  ...  The main result on the Ehrenfeucht-Fraiss e game of length r (henceforth called FO r -game) is that two structures I; J are FO r -equivalent i Duplicator has a winning strategy for the FO r -game on I  ... 
doi:10.1006/jcss.2000.1712 fatcat:wykfxfsqvzcqhknban5pkqwkqm

Querying spatial databases via topological invariants

Luc Segoufin, Victor Vianu
1998 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '98  
The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases.  ...  The focus is on the translation of topological queries against the spatial database into queries against the topological invariant.  ...  The main result on the Ehrenfeucht-Fraiss e game of length r (henceforth called FO r -game) is that two structures I; J are FO r -equivalent i Duplicator has a winning strategy for the FO r -game on I  ... 
doi:10.1145/275487.275498 dblp:conf/pods/SegoufinV98 fatcat:q6sn2mhhubaolfrflw33ycq2qi

On the expressive power of the relational calculus with arithmetic constraints [chapter]

Gabriel M. Kuper
1990 Lecture Notes in Computer Science  
The diagram shown in Figure 1 summarizes our expressiveness results for databases over the reals. By o-min we mean any o-minimal signature and by sparse we mean any sparse signature.  ...  Model completeness results for expansions of the ordered eld of real numbers by restricted Pfa an functions and the exponential function. Theorem 6. Let o-min be an o-minimal signature on U.  ...  The standard technique for circumventing this problem is via Ehrenfeucht-Fraisse games (cf. 12]).  ... 
doi:10.1007/3-540-53507-1_78 fatcat:mowe4zvhgnasfh3gx7dtehpqge

Definable relations and first-order query languages over strings

Michael Benedikt, Leonid Libkin, Thomas Schwentick, Luc Segoufin
2003 Journal of the ACM  
An alternative approach to definability of strings, based on classical infinite model theory rather than finite model theory, dates back to the 1960s [20, 19] .  ...  A well-known result links definability with traditional formal language theory.  ...  Note that this result can also be shown directly by an Ehrenfeucht-Fraïssé game argument.  ... 
doi:10.1145/876638.876642 fatcat:dnyytdskv5holgdahoekdxucki
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