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Trees and Ehrenfeucht–Fraı̈ssé games
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]
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
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]
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
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]
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]
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]
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]
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
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
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]
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
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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