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A finite relation algebra with undecidable network satisfaction problem

R Hirsch
1999 Logic Journal of the IGPL  
We de ne 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 ; ?  ... 
doi:10.1093/jigpal/7.4.547 fatcat:74xgfcntujgzhg76zboognfb3e

Finite Relation Algebras with Normal Representations [article]

Manuel Bodirsky
2018 arXiv   pre-print
One of the traditional applications of 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] .  ... 
arXiv:1810.13335v1 fatcat:2tbrfyvyi5e5thdxk7ylebllwq

Hardness of Network Satisfaction for Relation Algebras with Normal Representations [article]

Manuel Bodirsky, Simon Knäuer
2020 arXiv   pre-print
We study the computational complexity of the general 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] .  ... 
arXiv:1912.08482v2 fatcat:z7gpd5ppxngydfsx2ns7rwg2wi

Algebraic foundations for qualitative calculi and networks [article]

Robin Hirsch, Marcel Jackson, Tomasz Kowalski
2017 arXiv   pre-print
representable 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] .  ... 
arXiv:1606.09140v3 fatcat:nrlzcnpmzjglzlaltuqsw573ii

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  ... 

Relation algebras of intervals

Robin Hirsch
1996 Artificial Intelligence  
Given 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.  ... 
doi:10.1016/0004-3702(95)00042-9 fatcat:htei3mgnl5ef3o4dbv6ktmjsou

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
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  ...  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  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

Subject index volumes 1–200

1999 Theoretical Computer Science  
. 7 nets. 1059 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  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Belief propagation in monoidal categories

Jason Morton
2014 Electronic Proceedings in Theoretical Computer Science  
We discuss 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.  ... 
doi:10.4204/eptcs.172.18 fatcat:fa37qdcblbfwpndjwedbzziowi

The complexity of constraint satisfaction problems for small relation algebras

M. Cristani, R. Hirsch
2004 Artificial Intelligence  
We give 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  ... 
doi:10.1016/j.artint.2004.02.003 fatcat:gnwwaharynhjxhe6iwwjco2oqe

The complexity of constraint satisfaction problems for small relation algebras

M CRISTANI
2004 Artificial Intelligence  
We give 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  ... 
doi:10.1016/s0004-3702(04)00026-8 fatcat:vnhmqqyyjvh2nd4acnax2ky2ly

Periodic Constraint Satisfaction Problems: Polynomial-Time Algorithms [chapter]

Hubie Chen
2003 Lecture Notes in Computer Science  
We study 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.  ... 
doi:10.1007/978-3-540-45193-8_14 fatcat:c6usdnganbaufo4ws5qzeu4z3y

Periodic Constraint Satisfaction Problems: Tractable Subclasses

Hubie Chen
2005 Constraints  
We study 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  ... 
doi:10.1007/s10601-005-0551-z fatcat:7pe2tegcofhw7huaormzcb757e

"Most of" leads to undecidability: Failure of adding frequencies to LTL [chapter]

Bartosz Bednarczyk, Jakub Michaliszyn
2021 Lecture Notes in Computer Science  
AbstractLinear Temporal Logic (LTL) interpreted on 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 .  ... 
doi:10.1007/978-3-030-71995-1_5 fatcat:nryadz3krfa6jkjxoa7itsvf7u

Lifted Relational Algebra with Recursion and Connections to Modal Logic [article]

Eugenia Ternovska
2016 arXiv   pre-print
The essence of our proposal is to lift Codd's 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).  ... 
arXiv:1612.09251v1 fatcat:ulstwcfr35c3nlqinxykjptnii
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