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Generalized quantifiers and pebble games on finite structures

Phokion G. Kolaitis, Jouko A. Väänänen
1995 Annals of Pure and Applied Logic  
limits of generalized quantifiers in finite model theory.  ...  We show that equivalence of finite structures relative to U:,(Q) can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht-FmYssk games.  ...  expressibility in finite model theory.  ... 
doi:10.1016/0168-0072(94)00025-x fatcat:awup6imfonb4tfu3ovybcfyvhe

Definability with bounded number of bound variables

Neil Immerman, Dexter Kozen
1989 Information and Computation  
We g i v e a model-theoretic method for establishing the k-variable property, i n volving a restricted Ehrenfeucht-Fraisse game in which e a c h player has only k pebbles.  ...  We also establish new k-variable properties for various theories of bounded-degree trees, and in each case obtain tight upper and lower bounds on k.  ...  An Ehrenfeucht-Fraisse Game with Bounded Number of Pebbles Let be a theory in a rst-order language L with equality.  ... 
doi:10.1016/0890-5401(89)90055-2 fatcat:a7odctjg7ranpgirf6oinctzli

Whither Semantics? [article]

Samson Abramsky
2020 arXiv   pre-print
As an example, we discuss some recent work on encapsulating model comparison games as comonads, in the context of finite model theory.  ...  It acquires additional significance in finite model theory, where model comparison games such as Ehrenfeucht-Fraïssé (EF)-games, pebble games and bisimulation games play a central role [Lib04] .  ...  Model theory and deception In a sense, the purpose of model theory is "deception".  ... 
arXiv:2010.13328v1 fatcat:crfp4vez2vcnzoe2phm6ejur6a

Page 4049 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
The blue pebble game analyses are similar in many respects to the cases for the red pebble game.  ...  In fact, there are two versions of the game: the red pebble game, in which a limited (fixed) number of peb- bles may be placed or slid at a time, and the red and blue pebble game, which is just the same  ... 

Page 3259 of Mathematical Reviews Vol. , Issue 81H [page]

1981 Mathematical Reviews  
This model (called the pebble game) has been used to study register allocation, recursive schemata, and time-space tradeoffs.  ...  The pebbling problem is: Given a pebble game G and a specified vertex, v, in G, can v be pebbled using no more than s pebbles?  ... 

Page 5856 of Mathematical Reviews Vol. , Issue 89J [page]

1989 Mathematical Reviews  
The second class consists of dynamic problems defined as differential games, that serve as models of search in bounded regions of a plane. The theory is illustrated by a numerical example.  ...  This question expressed by means of pebble games is: Do white pebbles help? The paper gives a positive an- swer.  ... 

Page 319 of Mathematical Reviews Vol. , Issue 82a [page]

1982 Mathematical Reviews  
For algorithms in subrecursive classes, a theory similar to that developed by A. N.  ...  It is proved that the two-person acyclic pebble game problem is P-space-complete and the one-person acyclic pebble game problem is NP-complete.  ... 

Preservation theorems in finite model theory [chapter]

Eric Rosen, Scott Weinstein
1995 Lecture Notes in Computer Science  
We d e v elop various aspects of the nite model theory of L k (9) a n d L k 1! (9). We establish the optimality of normal forms for L k 1!  ...  language and let ' be a sentence of L: Mod(') = fA j A j = 'g is the L-class determined by ' and Mod f (') = fA 2 F j A j = 'g is the boolean query expressed by ': We s a y t h a t C is L-de nable, just in  ...  Introduction In this paper we i n vestigate the status of preservation theorems in nite model theory.  ... 
doi:10.1007/3-540-60178-3_99 fatcat:ta5q7jzkinc2jfcvr265blwoti

Pebbling In Watkins Snark Graph

Ms.Sreedevi S, Dr.M.S Anilkumar
2019 International Journal of Research in Advent Technology  
The pebbling theory is a study of a mathematical game that is played over a graph.  ...  In this game, a pebbling movement means removing two pebbles from a given vertex and adding one pebble to one of its neighbors and removing the other pebble from the game.  ...  The pebbling methodology of these games can be used in structural graph theory and theoretical computer science.  ... 
doi:10.32622/ijrat.72201964 fatcat:j6vjsjfy6naqxke2hepggw5bra

The pebbling comonad in Finite Model Theory

Samson Abramsky, Anuj Dawar, Pengming Wang
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Pebble games are a powerful tool in the study of finite model theory, constraint satisfaction and database theory.  ...  Winning strategies for Duplicator in the k-pebble game for structures A and B are equivalent to morphisms from A to B in the coKleisli category for this comonad.  ...  Acknowledgement: The work reported here was initiated at the programme on Logical Structures in Computation at the Simons Institute for the Theory of Computing, Berkeley.  ... 
doi:10.1109/lics.2017.8005129 dblp:conf/lics/AbramskyDW17 fatcat:mxmtmosgyvhwrbsemoqz7oqhfm

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

Samson Abramsky, Nihil Shah
2018 arXiv   pre-print
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures.  ...  In particular, Ehrenfeucht-Fraisse games, pebble games, and bisimulation games play a central role.  ...  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

Structure and Power: an emerging landscape [article]

Samson Abramsky
2022 arXiv   pre-print
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics.  ...  Another instance recovers the k-pebble game, the finite-variable fragments, the corresponding equivalences, and the combinatorial parameter of treewidth.  ...  The Ehrenfeucht-Fraïssé game ([20]) Model comparison games in general are especially important in finite model theory, where the compactness theorem is not available. The EF-game between A and B.  ... 
arXiv:2206.07393v4 fatcat:ijpzxnk7nvfovndpewwi4hg3zm

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.  ...  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] .  ... 
doi:10.1007/978-3-030-00389-0_1 fatcat:kuwar27movhtroa6ztlz57vdke

The Pebble-Relation Comonad in Finite Model Theory [article]

Yoàv Montacute, Nihil Shah
2021 arXiv   pre-print
The pebbling comonad, introduced by Abramsky, Dawar and Wang, provides a categorical interpretation for the k-pebble games from finite model theory.  ...  We further show how the coKleisli morphisms of the pebble-relation comonad provide a categorical interpretation to Duplicator's winning strategies in Dalmau's pebble-relation game.  ...  The standard Ehrenfeucht-Fraïssé game appears in many introductory texts on model theory [15] .  ... 
arXiv:2110.08196v1 fatcat:7zp5zd6ujzf6vhhz3yx6fakrne

On sufficient conditions for unsatisfiability of random formulas

Albert Atserias
2004 Journal of the ACM  
Our result is a consequence of designing a winning strategy for one of the players in the existential pebble game.  ...  The second contribution of our work is the connection between finite model theory and propositional proof complexity.  ...  The first one is in finite model theory, proper.  ... 
doi:10.1145/972639.972645 fatcat:mt4ad4lbivfijafeusxqq73tla
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