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A finite relation algebra with undecidable network satisfaction problem

1999
*
Logic Journal of the IGPL
*

We de ne

doi:10.1093/jigpal/7.4.547
fatcat:74xgfcntujgzhg76zboognfb3e
*a*nite*relation**algebra*and show that the*network**satisfaction**problem*is*undecidable*for this*algebra*1 . ...*A**Finite**Relation**Algebra**with**Undecidable**Network**Satisfaction**Problem*If N(m; n) is an atom of*A*for all m; n 2 nodes(N) then the*network*N is called an atomic*network*. ... If 0 has k tiles then*A*( 0 ) 6*A**Finite**Relation**Algebra**with**Undecidable**Network**Satisfaction**Problem*has 2k + 28 atoms. They are: e 0 ; w 0 e i ; w i ; +1 i ; ? ...##
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Finite Relation Algebras with Normal Representations
[article]

2018
*
arXiv
*
pre-print

One of the traditional applications of

arXiv:1810.13335v1
fatcat:2tbrfyvyi5e5thdxk7ylebllwq
*relation**algebras*is to provide*a*setting for infinite-domain constraint*satisfaction**problems*. ... The present article translates the recent findings into the traditional*relation**algebra*setting, and points out*a*series of open*problems*at the interface between model theory and the theory of*relation*... There are*finite**relation**algebras**A*where this*problem*is*undecidable*[Hir99] . ...##
###
Hardness of Network Satisfaction for Relation Algebras with Normal Representations
[article]

2020
*
arXiv
*
pre-print

We study the computational complexity of the general

arXiv:1912.08482v2
fatcat:z7gpd5ppxngydfsx2ns7rwg2wi
*network**satisfaction**problem*for*a**finite**relation**algebra**A**with**a*normal representation B. ... If B contains*a*non-trivial equivalence*relation**with**a**finite*number of equivalence classes, then the*network**satisfaction**problem*for*A*is NP-hard. ...*A**finite**relation**algebra**with*an*undecidable**network**satisfaction**problem*has been found by Hirsch [Hir99] . ...##
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Algebraic foundations for qualitative calculi and networks
[article]

2017
*
arXiv
*
pre-print

representable

arXiv:1606.09140v3
fatcat:nrlzcnpmzjglzlaltuqsw573ii
*algebra*has*a**finite*qualitative representation; the representability*problem*for (the atom structures of)*finite*non-associative*algebras*is NP-complete; the*network**satisfaction**problem*... However, for*a*wide range of*relation**algebras*including the point*algebra*, the Allen Interval*Algebra*, RCC8 and many others,*a**network*is satisfiable if and only if it is qualitatively satisfiable. ... Indeed there are*finite**relation**algebras*for which the*network**satisfaction**problem*is*undecidable*[Hir99] . ...##
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Page 3871 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

Comer (1-CITA; Charleston, SC)
2000f:03195 03G15 03D35
Hirsch, Robin (4-LNDUC-C; London)

*A**finite**relation**algebra**with**undecidable**network**satisfaction**problem*. (English summary) Log. ... The*network**satisfaction**problem*(NSP) over # is For the web version of Mathematical Reviews, see http: //www.ams.org/mathscinet ...##
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Relation algebras of intervals

1996
*
Artificial Intelligence
*

Given

doi:10.1016/0004-3702(95)00042-9
fatcat:htei3mgnl5ef3o4dbv6ktmjsou
*a*representation of*a**relation**algebra*we construct*relation**algebras*of pairs and of intervals. ... The complexity of*relation**algebras*is studied and it is shown that every pair*algebra**with*infinite representations is intractable. ... Then the*network**satisfaction**problem*for*A*reduces to the*network**satisfaction**problem*for l3. Proof. ...##
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Verification of Infinite State Systems
[chapter]

2003
*
Lecture Notes in Computer Science
*

Verification

doi:10.1007/978-3-540-45220-1_7
fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m
*problems*can be reduced to checking behavioural equivalence or implementation (simulation)*relations*, or to checking the*satisfaction*of properties described in temporal logics or fixpoint ... During the two last decades, significant achievements have been obtained in the case of*finite*-state systems (systems*with**finitely*many states). ... Verification*problems*can be reduced to checking behavioural equivalence or implementation (simulation)*relations*, or to checking the*satisfaction*of properties described in temporal logics or fixpoint ...##
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Subject index volumes 1–200

1999
*
Theoretical Computer Science
*

. 7
nets. 1059

doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
*finite*syntactic monoid, 35 13 test set, 1464*finite*Thue systems, 339, 611, 1652*undecidability*questions for -, 484*with*decidable word*problem*, 697*finite*tiers, 2322 tilings ... , combination of -, 2378 unbounded fan-in, 715, 1465.2238*undecidability*of*finitely*generated stable transitive*relations*on free terms, 113 1 unbounded nondeterminism, 474,794, 1298, 1858.*undecidability*...##
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Belief propagation in monoidal categories

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We discuss

doi:10.4204/eptcs.172.18
fatcat:fa37qdcblbfwpndjwedbzziowi
*a*categorical version of the celebrated belief propagation algorithm. ... This provides*a*way to prove that some algorithms which are known or suspected to be analogous, are actually identical when formulated generically. ... The category in which numerical linear*algebra*takes place is vector spaces and linear transformations, where the vector spaces are augmented by orthonormal bases which define spiders. ...##
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The complexity of constraint satisfaction problems for small relation algebras

2004
*
Artificial Intelligence
*

We give

doi:10.1016/j.artint.2004.02.003
fatcat:gnwwaharynhjxhe6iwwjco2oqe
*a*complete classification of the complexities of the general constraint*satisfaction**problem*for small*relation**algebras*. ... We also classify the complexity of the constraint*satisfaction**problem*over fixed*finite*representations of any*relation**algebra*. ... We would also like to thank*a*lot Ivo Düntsch for having pointed us the relevant literature and Roger Maddux for his invaluable comments. The first author was ...##
###
The complexity of constraint satisfaction problems for small relation algebras

2004
*
Artificial Intelligence
*

We give

doi:10.1016/s0004-3702(04)00026-8
fatcat:vnhmqqyyjvh2nd4acnax2ky2ly
*a*complete classification of the complexities of the general constraint*satisfaction**problem*for small*relation**algebras*. ... We also classify the complexity of the constraint*satisfaction**problem*over fixed*finite*representations of any*relation**algebra*. ... We would also like to thank*a*lot Ivo Düntsch for having pointed us the relevant literature and Roger Maddux for his invaluable comments. The first author was ...##
###
Periodic Constraint Satisfaction Problems: Polynomial-Time Algorithms
[chapter]

2003
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-540-45193-8_14
fatcat:c6usdnganbaufo4ws5qzeu4z3y
*a*generalization of the constraint*satisfaction**problem*(CSP), the periodic constraint*satisfaction**problem*. ... An input instance of the periodic CSP is*a**finite*set of "generating" constraints over*a*structured variable set that implicitly specifies*a*larger, possibly infinite set of constraints; the*problem*is ... Periodic constraint*satisfaction**problems*. This paper investigates*a*strict generalization of the CSP, the periodic constraint*satisfaction**problem*. ...##
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Periodic Constraint Satisfaction Problems: Tractable Subclasses

2005
*
Constraints
*

We study

doi:10.1007/s10601-005-0551-z
fatcat:7pe2tegcofhw7huaormzcb757e
*a*generalization of the constraint*satisfaction**problem*(CSP), the periodic constraint*satisfaction**problem*. ... An input instance of the periodic CSP is*a**finite*set of "generating" constraints over*a*structured variable set that implicitly specifies*a*larger, possibly infinite set of constraints; the*problem*is ...*A*constraint*satisfaction**problem*(CSP) is*a*set C of constraints, each of which is over the same variable set V and domain language is*a**finite*set of*relations*which are all over the same set (and may ...##
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"Most of" leads to undecidability: Failure of adding frequencies to LTL
[chapter]

2021
*
Lecture Notes in Computer Science
*

AbstractLinear Temporal Logic (LTL) interpreted on

doi:10.1007/978-3-030-71995-1_5
fatcat:nryadz3krfa6jkjxoa7itsvf7u
*finite*traces is*a*robust specification framework popular in formal verification. ... Our*undecidability*proofs not only sharpen most of the*undecidability*results on logics*with*arithmetics interpreted on words known from the literature, but also are fairly simple. ...*A*Kripke structure is composed of*a**finite*set S of states,*a*set of initial states I ⊆ S,*a*total transition*relation*R ⊆ S × S, and*a**finite*labelling function : S → 2 AP . ...##
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Lifted Relational Algebra with Recursion and Connections to Modal Logic
[article]

2016
*
arXiv
*
pre-print

The essence of our proposal is to lift Codd's

arXiv:1612.09251v1
fatcat:ulstwcfr35c3nlqinxykjptnii
*relational**algebra*from operations on*relational*tables to operations on classes of structures (*with*recursion), and to add*a*direction of information propagation ... We propose*a*new formalism for specifying and reasoning about*problems*that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and ...*Satisfaction**Relation*for the Calculus of Binary*Relations*Definition 8 (*Satisfaction*, Dynamic*algebra*). ...
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