A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in numerous and often surprising contexts in both fields But, perhaps, we should start with a few words about graphs in general They are, of course, one of the prime objects of study in Discrete Mathematics However, graphs are among the most ubiquitous models of both natural and human-made structures In the natural and social sciences they model relations among species, societies, companies, etc In computer science, they represent networks of communication, data organization, computational devices as well as the flow of computation, and more In mathematics, Cayley graphs are useful in Group Theory Graphs carry a natural metric and are therefore useful in Geometry, and though they are “just” one-dimensional complexes, they are useful in certain parts of Topology, eg Knot Theory In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems The study of these models calls, then, for the comprehension of the significant structural properties of the relevant graphs But are there nontrivial structural properties which are universally important? Expansion of a graph requires that it is simultaneously sparse and highly connected Expander graphs were first defined by Bassalygo and Pinsker, and their existence first proved by Pinsker in the early ’70s The property of being an expander seems significant in many of these mathematical, computational and physical contexts It is not surprising that expanders are useful in the design and analysis of communication networks What is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness In mathematics, we will encounter eg their role in the study of metric embeddings, and in particular in work around the Baum-Connes Conjecture Expansion is closely related to the convergence rates of Markov Chains, and so they play a key role in the study of Monte-Carlo algorithms in statistical mechanics and in a host of practical computational applications The list of such interesting and fruitful connections goes on and on with so many applications we will not even

/pdf/expander-graphs-and-their-applications-wbsb8gxfw2.pdf

Expander graphs and their applications

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.

The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.

The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.

The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.

- Covers the whole field of constraint programming
- Survey-style chapters
- Five chapters on applications

Table of Contents

Foreword (Ugo Montanari) 
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) 
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) 
Chapter 3. Constraint Propagation (Christian Bessiere) 
Chapter 4. Backtracking Search Algorithms (Peter van Beek) 
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) 
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons) 
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) 
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith) 
Part II : Extensions, Languages, and Applications

Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) 
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) 
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) 
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) 
Chapter 17. Constraints over Structured Domains
(Carmen Gervet) 
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings) 
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) 
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

/pdf/handbook-of-constraint-programming-53srutguo2.pdf

Handbook of Constraint Programming

The supplementary motor complex consists of the supplementary motor area, the supplementary eye field and the pre-supplementary motor area. In recent years, these areas have come under increasing scrutiny from cognitive neuroscientists, motor physiologists and clinicians because they seem to be crucial for linking cognition to action. However, theories regarding their function vary widely. This Review brings together the data regarding the supplementary motor regions, highlighting outstanding issues and providing new perspectives for understanding their functions.

Functional role of the supplementary and pre-supplementary motor areas

CONTENTS 7 Acknowledgments Many people gave substantial suggestions to improve the contents of this book. These are, in alphabetic order, Introduction During the past few years, several of us have been asked many times about references on finite tree automata. On one hand, this is the witness of the liveness of this field. On the other hand, it was difficult to answer. Besides several excellent survey chapters on more specific topics, there is only one monograph devoted to tree automata by Gécseg and Steinby. Unfortunately, it is now impossible to find a copy of it and a lot of work has been done on tree automata since the publication of this book. Actually using tree automata has proved to be a powerful approach to simplify and extend previously known results, and also to find new results. For instance recent works use tree automata for application in abstract interpretation using set constraints, rewriting, automated theorem proving and program verification, databases and XML schema languages. Tree automata have been designed a long time ago in the context of circuit verification. Many famous researchers contributed to this school which was headed by A. Church in the late 50's and the early 60's: B. Trakhtenbrot, Many new ideas came out of this program. For instance the connections between automata and logic. Tree automata also appeared first in this framework, following the work of Doner, Thatcher and Wright. In the 70's many new results were established concerning tree automata, which lose a bit their connections with the applications and were studied for their own. In particular, a problem was the very high complexity of decision procedures for the monadic second order logic. Applications of tree automata to program verification revived in the 80's, after the relative failure of automated deduction in this field. It is possible to verify temporal logic formulas (which are particular Monadic Second Order Formulas) on simpler (small) programs. Automata, and in particular tree automata, also appeared as an approximation of programs on which fully automated tools can be used. New results were obtained connecting properties of programs or type systems or rewrite systems with automata. Our goal is to fill in the existing gap and to provide a textbook which presents the basics of tree automata and several variants of tree automata which have been devised for applications in the aforementioned domains. We shall discuss only finite tree automata, and the …

/pdf/tree-automata-techniques-and-applications-4u4g26lfhm.pdf

Tree Automata Techniques and Applications

http://www.cse.lehigh.edu/~heflin/courses/sw-2010/lubm-wsj-final.pdf

LUBM: A benchmark for OWL knowledge base systems

This article surveys various complexity and expressiveness results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming.

/pdf/complexity-and-expressive-power-of-logic-programming-334cjkp9dg.pdf

Complexity and expressive power of logic programming

Part I. History Chapter 1. The Early History of Automated Deduction (Martin Davis). 1. Presburger's Procedure. 2. Newell, Shaw & Simon, and H. Gelernter. 3. First-Order Logic. Bibliography. Index. Part II. Classical Logic. Chapter 2. Resolution Theorem Proving (Leo Bachmair, Harald Ganzinger). 1. Introduction. 2. Preliminaries. 3. Standard Resolution. 4. A Framework for Saturation-Based Theorem Proving. 5. General Resolution. 6. Basic Resolution Strategies. 7. Refined Techniques for Defining Orderings and Selection Functions. 8. Global Theorem Proving Methods. 9. First-Order Resolution Methods. 10. Effective Saturation of First-Order Theories. 11. Concluding Remarks. Bibliography. Index. Chapter 3. Tableaux and Related Methods (Reiner Hahnle). 1. Introduction. 2. Preliminaries. 3. The Tableau Method. 4. Clause Tableaux. 5. Tableaux as a Framework. 6. Comparing Calculi. 7. Historical Remarks & Resources Bibliography. Notation. Index. Chapter 4. The Inverse Method (Anatoli Degtyarev, Andrei Voronkov). 1. Introduction. 2. Preliminaries. 3. Cooking classical logic. 4. Applying the recipe to nonclassical logics. 5. Naming and connections with resolution. 6. Season your meal: strategies and redundancies 7. Path calculi 8. Logics without the contraction rules 9. Conclusion Bibliography. Index Chapter 5. Normal Form Transformations (Matthias Baaz, Uwe Egly, Alexander Leitsch). 1. Introduction. 2. Notation and Definitions. 3. On the Concept of Normal Form. 4. Equivalence-Preserving Normal Forms. 5. Skolem Normal Form. 6. Conjunctive Normal Form. 7. Normal Forms in Nonclassical Logics. 8. Conclusion. Bibliography. Index. Chapter 6. Computing Small Clause Normal Forms (Andreas Nonnengart, Christoph Weidenbach). 1. Introduction. 2. Preliminaries. 3. Standard CNF-Translation. 4. Formula Renaming. 5. Skolemization. 6. Simplification. 7. Bibliographic Notes. 8. Implementation Notes. Bibliography. Index. Part III. Equality and other theories. Chapter 7. Paramodulation-Based Theorem Proving (Robert Nieuwenhuis, Albert Rubio). 1. About this chapter. 2. Preliminaries. 3. Paramodulation calculi. 4. Saturation procedures. 5. Paramodulation with constrained clauses. 6. Paramodulation with built-in equational theories. 7. Symbolic constraint solving. 8. Extensions. 9. Perspectives. Bibliography. Index. Chapter 8. Unification Theory (Franz Baader, Wayne Snyder). 1. Introduction. 2. Syntactic unification. 3. Equational unification. 4. Syntactic methods for E-unification. 5. Semantic approaches to E-unification. 6. Combination of unification algorithms. 7. Further topics. Bibliography. Index. Chapter 9. Rewriting (Nachum Dershowitz, David A. Plaisted). 1. Introduction. 2. Terminology. 3. Normal Forms and Validity. 4. Termination Properties. 5. Church-Rosser Properties. 6. Completion. 7. Relativized Rewriting. 8. Equational Theorem Proving. 9. Conditional Rewriting. 10. Programming. Bibliography. Index. Chapter 10. Equality Reasoning in Sequent-Based Calculi (Anatoli Degtyarev, Andrei Voronkov). 1. Introduction. 2. Translation of logic with equality into logic without equality. 3. Free variable systems. 4. Early history. 5. Simultaneous rigid E-unification. 6. Incomplete procedures for rigid E-unification. 7. Sequent-based calculi and paramodulation. 8. Equality elimination. 9. Equality reasoning in nonclassical logics. 10. Conclusion and open problems. Bibliography. Calculi and inference rules. Index. Chapter 11. Automated Reasoning in Geometry (Shang-Ching Chou, Xiao-Shan Gao). 1. A history review of automated reasoning in geometry. 2. Algebraic approaches to automated reasoning in geometry. 3. Coordinate-free approaches to automated reasoning in geometry. 4. AI approaches to automated reasoning in geometry. 5. Final remarks. Bibliography. Index. Chapter 12. Solving Numerical Constraints (Alexander Bockmayr, Volker Weispfenning). 1. Introduction. 2. Linear constraints over fields. 3. Linear diophantine constraints. 4. Non-linear constraints over continuous domains. 5. Non-linear diophantine constraints. Bibliography. Index. Part IV. Induction. Chapter 13. The Automation of Proof by Mathematical Induction (Alan Bundy). 1. Introduction. 2. Induction Rules. 3. Recursive Definitions and Datatypes. 4. Inductive Proof Techniques. 5. Theoretical Limitations of Inductive Inference. 6. Special Search Control Problems. 7. Rippling. 8. The Productive Use of Failure. 9. Existential Theorems. 10. Interactive Theorem Proving. 11. Inductive Theorem Provers. 12. Conclusion. Bibliography. Main Index. Name Index. Chapter 14. Inductionless Induction (Hubert Comon). 1. Introduction. 2. Formal background. 3. General Setting of the Inductionless Induction Method. 4. Inductive completion methods. 5. Examples of Axiomatizations A from the Literature. 6. Ground Reducibility. 7. A comparison between inductive proofs and proofs by consistency. Bibliography. Index.

Handbook of automated reasoning

In this article we describe VAMPIRE: a high-performance theorem prover for first-order logic. As our description is mostly targeted to the developers of such systems and specialists in automated reasoning, it focuses on the design of the system and some key implementation features. We also analyze the performance of the prover at CASC-JC.

The design and implementation of VAMPIRE

In this paper we give a short introduction in first-order theorem proving and the use of the theorem prover Vampire. We discuss the superposition calculus and explain the key concepts of saturation and redundancy elimination, present saturation algorithms and preprocessing, and demonstrate how these concepts are implemented in Vampire. Further, we also cover more recent topics and features of Vampire designed for advanced applications, including satisfiability checking, theory reasoning, interpolation, consequence elimination, and program analysis.

/pdf/first-order-theorem-proving-and-vampire-14tjv0vtlw.pdf

First-Order Theorem Proving and Vampire

This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

Andrei Voronkov

Papers

Complexity and expressive power of logic programming

Handbook of automated reasoning

The design and implementation of VAMPIRE

First-Order Theorem Proving and Vampire

Complexity and expressive power of logic programming