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Trees and Ehrenfeucht–Fraı̈ssé games

Stevo Todorčević, Jouko Väänänen
1999 Annals of Pure and Applied Logic  
Trees are natural generalizations of ordinals and this is especially apparent when one tries to ÿnd an uncountable analogue of the concept of the Scott-rank of a countable structure.  ...  For example, one of the methods is the tree-analogue of the successor operation on the ordinals.  ...  This quasi-ordering of trees arises naturally in inÿnitary model theory, especially in the investigation of Ehrenfeucht-Fra ssà e games [7] .  ... 
doi:10.1016/s0168-0072(98)00064-5 fatcat:6bva7mizgnhqnm6g5zexsh2n6a

Ehrenfeucht-Fraïssé Games [chapter]

Leonid Libkin
2004 Elements of Finite Model Theory  
SYNONYMS Ehrenfeucht games, EF-games DEFINITION The Ehrenfeucht-Fraïssé game (EF-game, for short) is played by two players, usually called the spoiler and the duplicator (in the literature, the two players  ...  MAIN TEXT EF-games are a tool for proving expressivity bounds for query languages. They were introduced by Ehrenfeucht [1] and Fraïssé [3] .  ...  SYNONYMS Ehrenfeucht games, EF-games DEFINITION The Ehrenfeucht-Fraïssé game (EF-game, for short) is played by two players, usually called the spoiler and the duplicator (in the literature, the two players  ... 
doi:10.1007/978-3-662-07003-1_3 fatcat:4hevsy5uxjbgvjoniclo557lja

A Practical Approach to Courcelle's Theorem

Joachim Kneis, Alexander Langer
2009 Electronical Notes in Theoretical Computer Science  
The proof uses a new technique based on using Hintikka game properties in dynamic programming.  ...  The standard proof of Courcelle's Theorem is to construct a finite bottom-up tree automaton that recognizes a tree decomposition of the graph.  ...  We call these Ehrenfeucht-Fraïssé-games local.  ... 
doi:10.1016/j.entcs.2009.08.028 fatcat:335kmrop5bg5lhtk4c5l3vod6e

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.  ...  Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and synchronization-tree  ...  , when instantiated to the case of Ehrenfeucht-Fraïssé games and tree-depth, is used extensively in [41] .  ... 
arXiv:2010.06496v7 fatcat:gx35xqxu2nb6dllwb52vxyf73q

Page 4719 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
The paper also extends the arguments of the main theorem to tree approximations of the Ehrenfeucht-Fraissé game of length w, and to 7 which are x*-like instead of w-like. Bienvenido F.  ...  This paper extends the results to Ehrenfeucht- Fraissé games of length w,. Here player V chooses elements from an @)-well-ordering y.  ... 

The Tenacity of Zero-One Laws

Joel H. Spencer, Katherine St. John
2000 Electronic Journal of Combinatorics  
The Ehrenfeucht-Fraisse game is a two-person game of perfect information which is connected to the Zero-One Laws of first order logic.  ...  We measure the tenaciousness of the second player ("Duplicator") in playing the Ehrenfeucht-Fraisse game, by bounding the numbers of moves Duplicator can play and win with probability $1-\epsilon$.  ...  for every k-move Ehrenfeucht-Fraisse game played on M 1 and M 2 .  ... 
doi:10.37236/1616 fatcat:ut2z3ymhsvgjvmmd5466k2w6sa

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.  ...  Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraïssé comonad, tree-width for the pebbling comonad, and synchronization-tree  ...  We shall consider three forms of model comparison game: Ehrenfeucht-Fraïssé games, pebble games and bisimulation games [21] .  ... 
doi:10.1007/978-3-030-00389-0_1 fatcat:kuwar27movhtroa6ztlz57vdke

The Freedoms of (Guarded) Bisimulation [chapter]

Erich Grädel, Martin Otto
2014 Outstanding Contributions to Logic  
Yet modal logics, transition systems and game graphs bridge the apparent gap in a natural manner and typically allow us to understand behavioural comparisons  ...  and the fact that satisfiable guarded formulae have models of bounded tree width.  ...  As the quintessential back-and-forth notion for two-player combinatorial games it may not only be regarded as a special case in the model-theoretic tradition of Ehrenfeucht-Fraïssé games but may also be  ... 
doi:10.1007/978-3-319-06025-5_1 fatcat:mi4q4wbo65fepnxvrbrafxcwxu

Graded modal logic and counting bisimulation [article]

Martin Otto
2019 arXiv   pre-print
This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation  ...  For M ↾ N ℓ (w), w is rooted tree-like: Lemma 1. 6 6 (c-graded modal Ehrenfeucht-Fraïssé theorem).  ...  Lemma 1.3 (graded modal Ehrenfeucht-Fraïssé theorem).  ... 
arXiv:1910.00039v1 fatcat:v7htrysqvbep7kx7ayxdtnytte

Page 5794 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
A third method is to study the winning strategies for an Ehrenfeucht-Fraissé-game played between the two models, and the properties of the resulting equivalence and nonequivalence trees.  ...  Our exposition combines un- countable models, Ehrenfeucht-Fraissé games and infinitary logic.  ... 

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.  ...  Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and synchronization-tree  ...  We shall consider three forms of model comparison game: Ehrenfeucht-Fraïssé games, pebble games and bisimulation games [21] .  ... 
arXiv:1806.09031v2 fatcat:tpyt23nfijdzla52ry6yfl3usu

FO Model Checking of Interval Graphs

Robert Ganian, Petr Hlineny, Daniel Kral, Jan Obdrzalek, Jarett Schwartz, Jakub Teska, Martin Grohe
2015 Logical Methods in Computer Science  
The main positive result is that FO model checking and successor-invariant FO model checking can be solved in time O(n log n) for n-vertex interval graphs with representations containing only intervals  ...  We describe possible courses of the d-round Ehrenfeucht-Fraïssé games by rooted trees.  ...  If the full d-EF-trees of R and R are EF-equivalent, then the duplicator wins the d-round Ehrenfeucht-Fraïssé game for R and R . Proof.  ... 
doi:10.2168/lmcs-11(4:11)2015 fatcat:o4p2ujoglbhf5hgaiqmesbi25y

Order-Invariant MSO is Stronger than Counting MSO in the Finite

Tobias Ganzow, Sasha Rubin, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
Courcelle showed that for restricted classes of structures both order-invariant MSO and CMSO are equally expressive, but conjectured that, in general, order-invariant MSO is stronger than CMSO.  ...  An Ehrenfeucht-Fraïssé game for CMSO The Ehrenfeucht-Fraïssé game capturing expressiveness of MSO parameterised by the quantifier-rank (cf.  ...  Definition 3 . 2 ( 32 Ehrenfeucht-Fraïssé game for CMSO). Let M ⊆ fin N + and r ∈ N.  ... 
doi:10.4230/lipics.stacs.2008.1353 dblp:conf/stacs/GanzowR08 fatcat:ga4fi4tb3vc2zhwndxsx7asjay

Adjunct Elimination Through Games in Static Ambient Logic [chapter]

Anuj Dawar, Philippa Gardner, Giorgio Ghelli
2004 Lecture Notes in Computer Science  
Games Ehrenfeucht games are played between two players Spoiler and Duplicator on a pair of structures T and U (in our case trees).  ...  Hx.A = Nx.x R A Nx.A = Hx.A ∧ ¬ c x Alternative Proof We provide an alternative proof of Lozes' result based on Ehrenfeucht-Fraïssé-style games. • Gives a more transparent proof of the result. • Provides  ... 
doi:10.1007/978-3-540-30538-5_18 fatcat:2v66wk3j6fchxnoyjeuj4fs7xq

Abelian p-groups with no invariants

Alan Mekler, Juha Oikkonen
1993 Journal of Pure and Applied Algebra  
Our result shows that there is a group which is too complicated to be characterized up to isomorphism by the Ehrenfeucht-Fraisse game approximated by a fixed ordering.  ...  This means that such a group cannot have any complete invariants which are bounded in the sense of these approximations of the Ehrenfeucht-Frai'ssC game.  ...  Acknowledgment We thank Gregory Cherlin, Paul Eklof, Lauri Hella, Taneli Huuskonen, Tapani Hyttinen and Heikki Tuuri for discussions on matters related to this paper.  ... 
doi:10.1016/0022-4049(93)90068-5 fatcat:42eblme64vdsndcdmskettw7mm
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