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Pebble Games with Algebraic Rules
[chapter]

2012
*
Lecture Notes in Computer Science
*

The general framework we introduce includes as special cases the

doi:10.1007/978-3-642-31585-5_25
fatcat:jh5yppz4ergalfjidv3w6hgps4
*pebble**games*for finite-variable logics*with*and without counting. ... We define a general framework of partition*games*for formulating twoplayer*pebble**games*over finite structures. ... It turns out that the*games*for ≡ L k and ≡ C k can be formulated as partition*games*, by replacing the*algebraic**rules*of the matrix-equivalence*game**with*weaker conditions that the partitions need to ...##
###
Pebble games with algebraic rules
[article]

2012
*
arXiv
*
pre-print

The general framework we introduce includes as special cases the

arXiv:1205.0913v2
fatcat:4fv64do3vzgpzn3y2jghj73eay
*pebble**games*for finite-variable logics*with*and without counting. ... We define a general framework of partition*games*for formulating two-player*pebble**games*over finite structures. ... It turns out that the*games*for ≡ L k and ≡ C k can be formulated as partition*games*, by replacing the*algebraic**rules*of the matrix-equivalence*game**with*weaker conditions that the partitions need to ...##
###
Relation algebras with n-dimensional relational bases

2000
*
Annals of Pure and Applied Logic
*

We study relation

doi:10.1016/s0168-0072(99)00022-6
fatcat:paa6mjxotfahxjbciu3wlqoadi
*algebras**with*n-dimensional relational bases in the sense of Maddux. Fix n*with*3 ≤ n ≤ ω. ... Write B n for the class of non-associative*algebras**with*an ndimensional relational basis, and RA n for the variety generated by B n . ... The*game*EF p r (A, B) is defined as follows. (Here, we use bold font for EF. Soon we will define a similar*game*, denoted EF .) It is a*game*played by ∀, ∃,*with*r rounds and p pairs of '*pebbles*'. ...##
###
Page 9538 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

Summary: “Existential k-

*pebble**games*, k > 2, are combinato- rial*games*played between two players, called the Spoiler and the Duplicator, on two structures. ... Summary: “We define process*algebras**with*a generalised oper- ation 5° for choice. ...##
###
Page 3259 of Mathematical Reviews Vol. , Issue 81H
[page]

1981
*
Mathematical Reviews
*

Authors’ summary: “We study a one-person

*game*played by plac- ing*pebbles*, according to certain*rules*, on the vertices of a directed graph. J. E. Hopcroft, Paul and L. ... 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*? ...##
###
An Infinite Pebble Game and Applications

1997
*
Information and Computation
*

We scan this derivation in reverse order (starting

doi:10.1006/inco.1997.2640
fatcat:dp3vkv77z5hg3f56c7k2c77gay
*with*the last production), and play a*pebble**game*as follows: If at the current step the derivation applies the*rule*S ;! ... Some of the generalizations of the*game*on nite dag's are the \black-and-white*pebble**game*", the \*pebble**game**with*auxiliary pushdown stores", the \edging*game*", and the \parallel*pebble**game*" (see 13] ...##
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Page 6454 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

*with*exactly 3

*pebbles*. ... Contrary to the bounded case studied by Blum and Hewitt, the hierarchy collapses: there are families recognized

*with*0,1,2, and 3

*pebbles*, but each family recognized

*with*more than three

*pebbles*is recognized ...

##
###
Page 1194 of Mathematical Reviews Vol. , Issue 81C
[page]

1981
*
Mathematical Reviews
*

The authors consider

*games*where a set of*pebbles*is placed ona subset of nodes and the*rules*have the form “a*pebble*can be moved from occupied node x to unoccupied node z provided node y is also occupied ... As a one-player*game*, the player tries to manipulate the*pebbles*to reach a specified terminal node. ...##
###
Constraint Satisfaction, Databases, and Logic

2003
*
International Joint Conference on Artificial Intelligence
*

The existential k-

dblp:conf/ijcai/Kolaitis03
fatcat:xuthjq2v7nfn3frmml6ztmzgmy
*pebble**game*(or, in short, the -*pebble**game*) is played between two players, the Spoiler and the Duplicator, on two relational structures A and B according to the follow ing*rules*: each ... A different family of*games*, known as k-*pebble**games*, has been used to study fixed-point logics and infinitary logics*with*finitely many variables (see [KV901. ... Moreover, they reveal that all tractable cases of the form CSP(A, All) can be solved by the same polynomial-time algorithm, namely, the algorithm for determining the winner in the -*pebble**game*. ...##
###
Page 5267 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
*
Mathematical Reviews
*

Paral- lelism in the first case corresponds to multiple processors and is modeled by the parallel

*pebble**game*. ... We show the effect of parallelism on the minimum space required to*pebble*a graph in the parallel*pebble**game*and derive lower bounds on tradeoffs that must be satisfied for problems such as superconcen ...##
###
Proof Complexity Meets Algebra

2018
*
ACM Transactions on Computational Logic
*

This class is also known to coincide

doi:10.1145/3265985
fatcat:hhamzk75vfhrbj4vuf7eo5lzmm
*with*the class of languages*with*Sums-of-Squares refutations of sublinear degree, a fact for which we provide an alternative proof. ... We hence ask for the existence of a natural proof system*with*good behaviour*with*respect to reductions and simultaneously small size refutations beyond bounded width. ... Then Spoiler wins the existential l-*pebble**game*on A and B, and hence also the existential (k + 2)-*pebble**game*on A and B, since k + 2 ≥ l. ...##
###
Constraint Satisfaction, Complexity, and Logic
[chapter]

2004
*
Lecture Notes in Computer Science
*

k)-

doi:10.1007/978-3-540-24674-9_1
fatcat:g3x7qgwjpfbytja66v45us2juq
*pebble**game*. ... k)-*pebble**game*on A and B? ... Concluding Remarks Constraint Satisfaction is a meeting point of • Computational Complexity • Database Theory • Logic • Universal*Algebra*. ...##
###
First-order axiomatisations of representable relation algebras need formulas of unbounded quantifier depth
[article]

2021
*
arXiv
*
pre-print

Using a variation of the rainbow construction and various

arXiv:2008.01329v3
fatcat:xhbnj6w4ebdl7ftt2i5f7yirhm
*pebble*and colouring*games*, we prove that RRA, the class of all representable relation*algebras*, cannot be axiomatised by any first-order relation ...*algebra*theory of bounded quantifier depth. ... First a straightforward adaptation of the well known Ehrenfeucht-Fraïssé*pebble**game*to relation*algebras*, and also a new colouring*game*which we call the Seurat*game*for sets, as it is a special case ...##
###
Time and space complexity of reversible pebbling

2004
*
RAIRO - Theoretical Informatics and Applications
*

Hence, the

doi:10.1051/ita:2004008
fatcat:eu2qvmnu3nanjexgkoh6vu6ina
*rules*of the*pebble**game**with*black and white*pebbles*are following: Definition 2.11. ... The*pebble**game**with*black and white*pebbles*is a*pebbling**game*that uses two kind of*pebbles*-black and white. One move of the*game*consists of applying one of the following*rules*: 1. ... Then G can be*pebbled*by a reversible computation*with*p · S(K)*pebbles*in time at most T(K). Proof. ...##
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Time and Space Complexity of Reversible Pebbling
[chapter]

2001
*
Lecture Notes in Computer Science
*

Hence, the

doi:10.1007/3-540-45627-9_26
fatcat:dh2hfkphibhg3gtwi2m5llmfue
*rules*of the*pebble**game**with*black and white*pebbles*are following: Definition 2.11. ... The*pebble**game**with*black and white*pebbles*is a*pebbling**game*that uses two kind of*pebbles*-black and white. One move of the*game*consists of applying one of the following*rules*: 1. ... Then G can be*pebbled*by a reversible computation*with*p · S(K)*pebbles*in time at most T(K). Proof. ...
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