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Effective guessing has unlikely consequences
[article]
2021
arXiv
pre-print
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Hence there is some z ∈ Σ c such that x, y, z = x, y , z ∈ L. Note that y, z contains w(n) symbols. Let u ∈ Σ c and v ∈ Σ w(n)−c such that y, z = u, v . ...
Further, there is then some z ∈ Σ w(n)−c such that x, y, z = x, y , z ∈ L. Now y, z contains w(n) symbols, so x ∈ L[w(n)]. ...
arXiv:2111.02138v1
fatcat:nuqs2mg5wnaqjog45sqedaftnm
Bounds on series-parallel slowdown
[article]
2009
arXiv
pre-print
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Also, if x ≤ y and x ≤ z then the conclusion x ≤ max{y, z} can instead be written as x ≤ y ⊕ z. ...
arXiv:0904.4512v1
fatcat:qnyzmdxod5ggngfrmrxb7cq2e4
Transformations of representation in constraint satisfaction
2015
Constraints
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The SAT instance {x, y, z}, D, (x, y), D 2 \ {(1, 1)} , (x, y), D 2 \ {(1, 0)} , (z), D 1 \ {(1)} is usually written as (x ∨ y ) ∧ (x ∨ y) ∧ (z ). ...
This is equivalent to the CSP instance (in the variable-value representation) {x, y, z}, D, (x, y), {(0, 0), (0, 1)} , (z), {(0)} .
Definition 4 . 4 25 (domain clause). ...
doi:10.1007/s10601-015-9224-8
fatcat:lollakqzx5h7xeajtfrmaz6u4q
Macroscopes: models for collective decision making
[article]
2012
arXiv
pre-print
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We introduce a new model of collective decision making, when a global decision needs to be made but the parties only possess partial information, and are unwilling (or unable) to first create a globalcomposite of their local views. Our macroscope model captures two key features of many real-world problems: allotment structure (how access to local information is apportioned between parties, including overlaps between the parties) and the possible presence of meta-information (what each party
arXiv:1204.3860v1
fatcat:eonfmvoc5ncltnjy5w36225aym
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... s about the allotment structure of the overall problem). Using the framework of communication complexity, we formalize the efficient solution of a macroscope. We present general results about the macroscope model, and also results that abstract the essential computational operations underpinning practical applications, including in financial markets and decentralized sensor networks. We illustrate the computational problem inherent in real-world collective decision making processes using results for specific functions, involving detecting a change in state (constant and step functions), and computing statistical properties (the mean).
Exploring Instance Generation for Automated Planning
[article]
2020
arXiv
pre-print
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Many of the core disciplines of artificial intelligence have sets of standard benchmark problems well known and widely used by the community when developing new algorithms. Constraint programming and automated planning are examples of these areas, where the behaviour of a new algorithm is measured by how it performs on these instances. Typically the efficiency of each solving method varies not only between problems, but also between instances of the same problem. Therefore, having a diverse set
arXiv:2009.10156v1
fatcat:7uvnocc5zffurczhe4mzta3pve
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... of instances is crucial to be able to effectively evaluate a new solving method. Current methods for automatic generation of instances for Constraint Programming problems start with a declarative model and search for instances with some desired attributes, such as hardness or size. We first explore the difficulties of adapting this approach to generate instances starting from problem specifications written in PDDL, the de-facto standard language of the automated planning community. We then propose a new approach where the whole planning problem description is modelled using Essence, an abstract modelling language that allows expressing high-level structures without committing to a particular low level representation in PDDL.
Towards Reformulating Essence Specifications for Robustness
[article]
2021
arXiv
pre-print
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The Essence language allows a user to specify a constraint problem at a level of abstraction above that at which constraint modelling decisions are made. Essence specifications are refined into constraint models using the Conjure automated modelling tool, which employs a suite of refinement rules. However, Essence is a rich language in which there are many equivalent ways to specify a given problem. A user may therefore omit the use of domain attributes or abstract types, resulting in fewer
arXiv:2111.00821v1
fatcat:mu3efptrozdcdaakkerxw24ua4
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... nement rules being applicable and therefore a reduced set of output models from which to select. This paper addresses the problem of recovering this information automatically to increase the robustness of the quality of the output constraint models in the face of variation in the input Essence specification. We present reformulation rules that can change the type of a decision variable or add attributes that shrink its domain. We demonstrate the efficacy of this approach in terms of the quantity and quality of models Conjure can produce from the transformed specification compared with the original.
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
2010
Artificial Intelligence
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It is known [36] that MAX-ONES is NP-hard (in fact, APX-complete) even when restricted to instances whose clauses are all of the form φ(x i , x j , x k ), where φ(x, y, z) = ¬x ∨ ¬y ∨ ¬z. ...
doi:10.1016/j.artint.2010.03.002
fatcat:emwukrqjlfdphcydgqzrdcecsq
Classification of annotation semirings over containment of conjunctive queries
2014
ACM Transactions on Database Systems
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Indeed, considers the equivalence of CQs and UCQs over integers Z. In contrast, as discussed in Sec. 3.1, Z-containment is vacuous. ...
For example, by considering the usual order ≤ on the semiring Z of integers, one can easily verify that the empty UCQ is not Z-contained in any non-empty UCQ. ...
doi:10.1145/2556524
fatcat:keokxlm5cvbxjald3etormf5jm
Automatic Discovery and Exploitation of Promising Subproblems for Tabulation
[chapter]
2018
Lecture Notes in Computer Science
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Preliminaries A constraint satisfaction problem (CSP) is defined as a set of variables X, a function that maps each variable to its domain, D : X → 2 Z where each domain is a finite set, and a set of constraints ...
doi:10.1007/978-3-319-98334-9_1
fatcat:75g7q4brcbdpng6febatib6e6u
Classification of annotation semirings over query containment
2012
Proceedings of the 31st symposium on Principles of Database Systems - PODS '12
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Superlinear Lower Bounds Based on ETH
[article]
2022
arXiv
pre-print
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Next, we apply Lemma 10 with f (n), w(n) = z(α, k) log(n), and t(n) = n. Therefore DTIWI(2 g(n)/z(α,k) , g(n)) ⊆ DTIME(2 (α k+1 )•g(n)/z(α,k) ). ...
By Theorem 12, we have that for all k ∈ N, DTIWI(n, z(α, k) log(n)) ⊆ DTIME(n α k+1 ). Let f (n) = 2 g(n)/z(α,k) if g(n) ≥ z(α, k) log(n) and f (n) = n otherwise. ...
arXiv:2008.06805v5
fatcat:nj6uovce4zetzdxoc5uhmeudhq
A Framework for Constraint Based Local Search using Essence
2018
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
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Structured Neighbourhood Search (SNS) is a framework for constraint-based local search for problems expressed in the Essence abstract constraint specification language. The local search explores a structured neighbourhood, where each state in the neighbourhood preserves a high level structural feature of the problem. SNS derives highly structured problem-specific neighbourhoods automatically and directly from the features of the Essence specification of the problem. Hence, neighbourhoods can
doi:10.24963/ijcai.2018/173
dblp:conf/ijcai/AkgunAGJMNSSW18
fatcat:5qfze7zsmjh7pkvrl5ntyk564m
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... resent important structural features of the problem, such as partitions of sets, even if that structure is obscured in the low-level input format required by a constraint solver. SNS expresses each neighbourhood as a constrained optimisation problem, which is solved with a constraint solver. We have implemented SNS, together with automatic generation of neighbourhoods for high level structures, and report high quality results for several optimisation problems.
Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints
[chapter]
2019
Lecture Notes in Computer Science
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., {x = 1, y = 0, z = 0} is usually denoted {x, ¬y, ¬z}). A satisfying assignment of a Boolean function f is an assignment that makes the function evaluate to 1. ...
- x which is an integer variable with domain {1, 2, 3}; -y which is an integer variable with domain {−2, −1, 0, 1}; and z and t that are Boolean variables. ...
doi:10.1007/978-3-030-30048-7_2
fatcat:vxndqomfzrbxxdcasnlql7eqnq
Superlinear Lower Bounds Based on ETH
2022
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Z. Salamon and M. Wehar 55:9 Proof. Let α be a rational number such that 1 < α < 2. Let z(α, k) = Σ k i=0 α i . Note that z(α, k) = α k+1 − 1 α − 1 . Suppose that DTIWI(n, log(n)) ⊆ DTIME(n α ). ...
Z. Salamon and M. Wehar 55:7 Proof. Suppose that DTIWI(t(n), w(n)) ⊆ DTIME(t ′ (n)). Let a function w ′ be given. Let L ∈ DTIWI(t(n), w(n) + w ′ (n)) be given. ...
doi:10.4230/lipics.stacs.2022.55
fatcat:mfwhafgahzh35by4qrvgvaoikm
Perfect Constraints Are Tractable
[chapter]
Lecture Notes in Computer Science
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By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the "all-different" constraint. In each of these cases we show that the associated microstructure of the problem is a perfect graph, and hence they are all part of the same larger family of tractable problems.
doi:10.1007/978-3-540-85958-1_35
fatcat:7ri5vke2gfcgvpeptnm5euku7a
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