Download or read book Complexity of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky and published by Cambridge University Press. This book was released on 2021-06-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.

Download or read book Complexity of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky and published by Cambridge University Press. This book was released on 2021-06-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Complexity Classifications of Boolean Constraint Satisfaction Problems written by Nadia Creignou and published by SIAM. This book was released on 2001-01-01 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a novel form of a compendium that classifies an infinite number of problems by using a rule-based approach.

Download or read book Complexity of Constraints written by Nadia Creignou and published by Springer. This book was released on 2008-12-23 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book On Infinite Domain CSPs Parameterized by Solution Cost written by George Osipov and published by Linköping University Electronic Press. This book was released on 2024-04-24 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Applications of Partial Polymorphisms in Fine Grained Complexity of Constraint Satisfaction Problems written by Biman Roy and published by Linköping University Electronic Press. This book was released on 2020-03-23 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study the worst-case complexity ofconstraint satisfaction problems and some of its variants. We use methods from universal algebra: in particular, algebras of total functions and partial functions that are respectively known as clones and strong partial clones. The constraint satisfactionproblem parameterized by a set of relations ? (CSP(?)) is the following problem: given a set of variables restricted by a set of constraints based on the relations ?, is there an assignment to thevariables that satisfies all constraints? We refer to the set ? as aconstraint language. The inverse CSPproblem over ? (Inv-CSP(?)) asks the opposite: given a relation R, does there exist a CSP(?) instance with R as its set of models? When ? is a Boolean language, then we use the term SAT(?) instead of CSP(?) and Inv-SAT(?) instead of Inv-CSP(?). Fine-grained complexity is an approach in which we zoom inside a complexity class and classify theproblems in it based on their worst-case time complexities. We start by investigating the fine-grained complexity of NP-complete CSP(?) problems. An NP-complete CSP(?) problem is said to be easier than an NP-complete CSP(?) problem if the worst-case time complexity of CSP(?) is not higher thanthe worst-case time complexity of CSP(?). We first analyze the NP-complete SAT problems that are easier than monotone 1-in-3-SAT (which can be represented by SAT(R) for a certain relation R), and find out that there exists a continuum of such problems. For this, we use the connection between constraint languages and strong partial clones and exploit the fact that CSP(?) is easier than CSP(?) when the strong partial clone corresponding to ? contains the strong partial clone of ?. An NP-complete CSP(?) problem is said to be the easiest with respect to a variable domain D if it is easier than any other NP-complete CSP(?) problem of that domain. We show that for every finite domain there exists an easiest NP-complete problem for the ultraconservative CSP(?) problems. An ultraconservative CSP(?) is a special class of CSP problems where the constraint language containsall unary relations. We additionally show that no NP-complete CSP(?) problem can be solved insub-exponential time (i.e. in2^o(n) time where n is the number of variables) given that theexponentialtime hypothesisis true. Moving to classical complexity, we show that for any Boolean constraint language ?, Inv-SAT(?) is either in P or it is coNP-complete. This is a generalization of an earlier dichotomy result, which was only known to be true for ultraconservative constraint languages. We show that Inv-SAT(?) is coNP-complete if and only if the clone corresponding to ? contains essentially unary functions only. For arbitrary finite domains our results are not conclusive, but we manage to prove that theinversek-coloring problem is coNP-complete for each k>2. We exploit weak bases to prove many of theseresults. A weak base of a clone C is a constraint language that corresponds to the largest strong partia clone that contains C. It is known that for many decision problems X(?) that are parameterized bya constraint language ?(such as Inv-SAT), there are strong connections between the complexity of X(?) and weak bases. This fact can be exploited to achieve general complexity results. The Boolean domain is well-suited for this approach since we have a fairly good understanding of Boolean weak bases. In the final result of this thesis, we investigate the relationships between the weak bases in the Boolean domain based on their strong partial clones and completely classify them according to the setinclusion. To avoid a tedious case analysis, we introduce a technique that allows us to discard a largenumber of cases from further investigation.

Download or read book Relational and Algebraic Methods in Computer Science written by Jules Desharnais and published by Springer. This book was released on 2018-10-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Automated Reasoning written by Didier Galmiche and published by Springer. This book was released on 2018-07-06 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Principles and Practice of Constraint Programming written by Gilles Pesant and published by Springer. This book was released on 2015-08-12 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Principles and Practice of Constraint Programing CP 2013 written by Christian Schulte and published by Springer. This book was released on 2013-09-07 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Constraint Satisfaction with Infinite Domains written by Manuel Bodirsky and published by . This book was released on 2004 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Beyond the Horizon of Computability written by Marcella Anselmo and published by Springer Nature. This book was released on 2020-06-23 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Theory and Applications of Models of Computation written by Ding-Zhu Du and published by Springer Nature. This book was released on 2023-01-01 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Automata Languages and Programming written by Susanne Albers and published by Springer Science & Business Media. This book was released on 2009-07-06 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICALP 2009, the 36th edition of the International Colloquium on Automata, Languages and Programming, was held on the island of Rhodes, July 6–10, 2009. ICALP is a series of annual conferences of the European Association for Theoretical Computer Science (EATCS) which ?rst took place in 1972. This year, the ICALP program consisted of the established track A (focusing on algorithms, complexity and games) and track B (focusing on logic, automata, semantics and theory of programming), and of the recently introduced track C (in 2009 focusing on foundations of networked computation). In response to the call for papers, the Program Committee received 370 s- missions: 223 for track A, 84 for track B and 63 for track C. Out of these, 108 papers were selected for inclusion in the scienti?c program: 62 papers for track A, 24 for track B and 22 for track C. The selection was made by the Program Committees based on originality, quality, and relevance to theoretical computer science. The quality of the manuscripts was very high indeed, and many dese- ing papers could not be selected. ICALP 2009 consisted of ?ve invited lectures and the contributed papers.

Download or read book The Complexity of Valued Constraint Satisfaction Problems written by Springer and published by . This book was released on 2012-10-20 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algorithms and Complexity of Constraint Satisfaction Problems written by Marko Samer and published by . This book was released on 2009 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Homogeneous Ordered Graphs Metrically Homogeneous Graphs and Beyond written by Gregory Cherlin and published by Cambridge University Press. This book was released on 2022-07-07 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of two volumes presenting the state of the art in the classification of homogeneous structures and related problems in the intersection of model theory and combinatorics. It extends the results of the first volume to generalizations of graphs and tournaments with additional binary relations. An appendix explores open problems.