Complexity Of Infinite Domain Constraint Satisfaction

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Complexity Of Infinite Domain Constraint Satisfaction

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Author : Manuel Bodirsky
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10

Complexity Of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with Mathematics categories.

Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

On Infinite Domain Csps Parameterized By Solution Cost

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Author : George Osipov
language : en
Publisher: Linköping University Electronic Press
Release Date : 2024-04-24

On Infinite Domain Csps Parameterized By Solution Cost written by George Osipov and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with categories.

In this thesis we study the computational complexity of MinCSP - an optimization version of the Constraint Satisfaction Problem (CSP). The input to a MinCSP is a set of variables and constraints applied to these variables, and the goal is to assign values (from a fixed domain) to the variables while minimizing the solution cost, i.e. the number of unsatisfied constraints. We are specifically interested in MinCSP with infinite domains of values. Infinite-domain MinCSPs model fundamental optimization problems in computer science and are of particular relevance to artificial intelligence, especially temporal and spatial reasoning. The usual way to study computational complexity of CSPs is to restrict the types of constraints that can be used in the inputs, and either construct fast algorithms or prove lower bounds on the complexity of the resulting problems. The vast majority of interesting MinCSPs are NP-hard, so standard complexity-theoretic assumptions imply that we cannot find exact solutions to all inputs of these problems in polynomial time with respect to the input size. Hence, we need to relax at least one of the three requirements above, opting for either approximate solutions, solving some inputs, or using super-polynomial time. Parameterized algorithms exploits the latter two relaxations by identifying some common structure of the interesting inputs described by some parameter, and then allowing super-polynomial running times with respect to that parameter. Such algorithms are feasible for inputs of any size whenever the parameter value is small. For MinCSP, a natural parameter is optimal solution cost. We also study parameterized approximation algorithms, where the requirement for exact solutions is also relaxed. We present complete complexity classifications for several important classes of infinite-domain constraints. These are simple temporal constraints and interval constraints, which have notable applications in temporal reasoning in AI, linear equations over finite and infinite fields as well as some commutative rings (e.g., the rationals and the integers), which are of fundamental theoretical importance, and equality constraints, which are closely related to connectivity problems in undirected graphs and form the basis of studying first-order definable constraints over infinite domains. In all cases, we prove results as follows: we fix a (possibly infinite) set of allowed constraint types C, and for every finite subset of C, determine whether MinCSP(), i.e., MinCSP restricted to the constraint types in , is fixed-parameter tractable, i.e. solvable in f(k) · poly(n) time, where k is the parameter, n is the input size, and f is any function that depends solely on k. To rule out such algorithms, we prove lower bounds under standard assumptions of parameterized complexity. In all cases except simple temporal constraints, we also provide complete classifications for fixed-parameter time constant-factor approximation.

Complexity Classifications Of Boolean Constraint Satisfaction Problems

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Author : Nadia Creignou
language : en
Publisher: SIAM
Release Date : 2001-01-01

Complexity Classifications Of Boolean Constraint Satisfaction Problems written by Nadia Creignou and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.

Many fundamental combinatorial problems, arising in such diverse fields as artificial intelligence, logic, graph theory, and linear algebra, can be formulated as Boolean constraint satisfaction problems (CSP). This book is devoted to the study of the complexity of such problems. The authors' goal is to develop a framework for classifying the complexity of Boolean CSP in a uniform way. In doing so, they bring out common themes underlying many concepts and results in both algorithms and complexity theory. The results and techniques presented here show that Boolean CSP provide an excellent framework for discovering and formally validating "global" inferences about the nature of computation.

Complexity Of Constraints

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Author : Nadia Creignou
language : en
Publisher: Springer
Release Date : 2008-12-23

Complexity Of Constraints written by Nadia Creignou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-23 with Computers categories.

Nowadays constraint satisfaction problems (CSPs) are ubiquitous in many different areas of computer science, from artificial intelligence and database systems to circuit design, network optimization, and theory of programming languages. Consequently, it is important to analyze and pinpoint the computational complexity of certain algorithmic tasks related to constraint satisfaction. The complexity-theoretic results of these tasks may have a direct impact on, for instance, the design and processing of database query languages, or strategies in data-mining, or the design and implementation of planners. This state-of-the-art survey contains the papers that were invited by the organizers after conclusion of an International Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl Castle, Germany, in October 2006. A number of speakers were solicited to write surveys presenting the state of the art in their area of expertise. These contributions were peer-reviewed by experts in the field and revised before they were collated to the 9 papers of this volume. In addition, the volume contains a reprint of a survey by Kolaitis and Vardi on the logical approach to constraint satisfaction that first appeared in 'Finite Model Theory and its Applications', published by Springer in 2007.

Principles And Practice Of Constraint Programing Cp 2013

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Author : Christian Schulte
language : en
Publisher: Springer
Release Date : 2013-09-07

Principles And Practice Of Constraint Programing Cp 2013 written by Christian Schulte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-07 with Mathematics categories.

This book constitutes the refereed conference proceedings of the 18th International Conference on Principles and Practice of Constraint Programming (CP 2013), held in Uppsala, Sweden, in September 2013. The 61 revised papers presented together with 3 invited talks were carefully selected from 138 submissions. The scope of the conference is on all aspects of computing with constraints, including: theory, algorithms, environments, languages, models and systems, applications such as decision making, resource allocation, and agreement technologies.

Automated Reasoning

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Author : Didier Galmiche
language : en
Publisher: Springer
Release Date : 2018-07-06

Automated Reasoning written by Didier Galmiche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.

This book constitutes the refereed proceedings of the 9th International Joint Conference on Automated Reasoning, IJCAR 2018, held in Oxford, United Kingdom, in July 2018, as part of the Federated Logic Conference, FLoC 2018. In 2018, IJCAR unites CADE, TABLEAUX, and FroCoS, the International Symposium on Frontiers of Combining Systems, and, for the fourth time, is part of the Federated Logic Conference. The 38 revised full research papers and 8 system descriptions presented together with two invited talks were carefully reviewed and selected from 108 submissions. The papers focus on topics such as logics, deductive systems, proof-search methods, theorem proving, model checking, verification, formal methods, and program analysis.

Principles And Practice Of Constraint Programming

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Author : Gilles Pesant
language : en
Publisher: Springer
Release Date : 2015-08-12

Principles And Practice Of Constraint Programming written by Gilles Pesant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-12 with Mathematics categories.

This book constitutes the refereed conference proceedings of the 21st International Conference on Principles and Practice of Constraint Programming, CP 2015, held in Cork, Ireland, in August/September 2015. This edition of the conference was part of George Boole 200, a celebration of the life and work of George Boole who was born in 1815 and worked at the University College of Cork. It was also co-located with the 31st International Conference on Logic Programming (ICLP 2015). The 48 revised papers presented together with 3 invited talks and 16 abstract papers were carefully selected from numerous submissions. The scope of CP 2014 includes all aspects of computing with constraints, including theory, algorithms, environments, languages, models, systems, and applications such as decision making, resource allocation, schedulling, configuration, and planning.

Beyond The Horizon Of Computability

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Author : Marcella Anselmo
language : en
Publisher: Springer Nature
Release Date : 2020-06-23

Beyond The Horizon Of Computability written by Marcella Anselmo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-23 with Computers categories.

This book constitutes the proceedings of the 16th Conference on Computability in Europe, CiE 2020, which was planned to be held in Fisciano, Italy, during June 29 until July 3, 2020. The conference moved to a virtual format due to the coronavirus pandemic. The 30 full and 5 short papers presented in this volume were carefully reviewed and selected from 72 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2020 had as its motto Beyond the Horizon of Computability, reflecting the interest of CiE in research transgressing the traditional boundaries of computability theory.

Relational And Algebraic Methods In Computer Science

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Author : Jules Desharnais
language : en
Publisher: Springer
Release Date : 2018-10-22

Relational And Algebraic Methods In Computer Science written by Jules Desharnais and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-22 with Mathematics categories.

This book constitutes the proceedings of the 17th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2018, held in Groningen, The Netherlands, in October/November 2018. The 21 full papers and 1 invited paper presented together with 2 invited abstracts and 1 abstract of a tutorial were carefully selected from 31 submissions. The papers are organized in the following topics: Theoretical foundations; reasoning about computations and programs; and applications and tools.

Theory And Applications Of Models Of Computation

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Author : Ding-Zhu Du
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

Theory And Applications Of Models Of Computation written by Ding-Zhu Du and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Computers categories.

This book constitutes the refereed proceedings of the 17th Annual Conference on Theory and Applications of Models of Computation, TAMC 2022, held as a virtual event, in September 2022. The 33 full papers were carefully reviewed and selected from 75 submissions. The main themes of the selected papers are computability, complexity, algorithms, information theory and their extensions to machine learning theory, and foundations of artificial intelligence.