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Complexity of a CHR Solver for Existentially Quantified Conjunctions of Equations over Trees [chapter]

Marc Meister, Khalil Djelloul, Thom Frühwirth
Lecture Notes in Computer Science  
We then present an extended CHR solver for solving existentially quantified conjunctions of non-flat equations in the theory of finite or infinite trees.  ...  One of the first CHR programs is the classic constraint solver for syntactic equality of rational trees that performs unification.  ...  We thank the anonymous reviewers for their comments which helped us to improve this paper.  ... 
doi:10.1007/978-3-540-73817-6_9 dblp:conf/csclp/MeisterDF06 fatcat:vf2nppa2dnghnkt5i2a4zde56a

Toward a first-order extension of Prolog's unification using CHR

Khalil Djelloul, Thi-Bich-Hanh Dao, Thom Fruehwirth
2007 Proceedings of the 2007 ACM symposium on Applied computing - SAC '07  
It represents the mechanism of binding the contents of variables and can be seen as solving conjunctions of equations over finite or infinite trees.  ...  CHR (Constraint Handling Rules) has originally been developed for writing constraint solvers, but the constraints here go much beyond implicitly quantified conjunctions of atomic constraints and are considered  ...  Particular thanks also to Marc Meister and Hariolf Betz for their kind reviews of this article.  ... 
doi:10.1145/1244002.1244016 dblp:conf/sac/DjelloulDF07 fatcat:louwfm4vebehllbhgvikchwjdq

Constraint Systems and Constraint Solvers [chapter]

Thom Frühwirth, Slim Abdennadher
2003 Cognitive Technologies  
Constraint systems are the result of taking a data type together with its operations and interpreting the resulting expressions as constraints.  ...  These constraint systems use the universal data types of numbers (integers or reals) to represent scalar data or terms to represent structured data.  ...  In constraint programming, we are mainly concerned with conjunctions of atomic constraints whose variables are (implicitly) existentially quantified.  ... 
doi:10.1007/978-3-662-05138-2_8 fatcat:n3j7gzn5wbburmcbzjtg3ezjgy

A Framework for Extended Algebraic Data Types [chapter]

Martin Sulzmann, Jeremy Wazny, Peter J. Stuckey
2006 Lecture Notes in Computer Science  
Extended forms of algebraic data types allow for sophisticated type extensions. A number of proposals exists and its often hard to understand what has been achieved.  ...  Here, we present a unifying framework which subsumes previous systems such as guarded recursive data types, the combination of type classes and existential types etc.  ...  We use common notation for Boolean conjunction (∧), implication (⊃) and universal (∀) and existential quantifiers (∃). Often, we abbreviate ∧ by "," and use set notation for conjunction of formulae.  ... 
doi:10.1007/11737414_5 fatcat:4e6agnz4dvflzil5rq7aeciqr4

As time goes by: Constraint Handling Rules - A survey of CHR research from 1998 to 2007 [article]

Jon Sneyers, Peter Van Weert, Tom Schrijvers, Leslie De Koninck
2009 arXiv   pre-print
Originally designed for writing user-defined constraint solvers, it is now recognized as an elegant general purpose language.  ...  Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules.  ...  A language for experimenting with declarative paradigms. In  ... 
arXiv:0906.4474v2 fatcat:pmadjyra3vdublffzz5pjzlbxa

As time goes by: Constraint Handling Rules

JON SNEYERS, PETER VAN WEERT, TOM SCHRIJVERS, LESLIE DE KONINCK
2009 Theory and Practice of Logic Programming  
Originally designed for writing user-defined constraint solvers, it is now recognized as an elegant general purpose language.  ...  AbstractConstraint Handling Rules (CHR) is a high-level programming language based on multiheaded multiset rewrite rules.  ...  Meister, Djelloul et al. (2006) presented a solver for existentially quantified conjunctions of non-flat equations over rational trees.  ... 
doi:10.1017/s1471068409990123 fatcat:jlx6gexqqzht5blkoxzzelst6e

Theory of finite or infinite trees revisited

KHALIL DJELLOUL, THI-BICH-HANH DAO, THOM FRÜHWIRTH
2008 Theory and Practice of Logic Programming  
We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable  ...  AbstractWe present in this paper a first-order axiomatization of an extended theoryTof finite or infinite trees, built on a signature containing an infinite set of function symbols and a relationfinite  ...  Acknowledgments We thank Alain Colmerauer for our very long discussions about the theory of finite or infinite trees and its models.  ... 
doi:10.1017/s1471068407003171 fatcat:dsmrs7hgbba4tfeic5ztz2sqbq

Theory of Finite or Infinite Trees Revisited [article]

Khalil Djelloul, Thi-bich-hanh Dao, Thom Fruehwirth
2007 arXiv   pre-print
We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable  ...  We present in this paper a first-order axiomatization of an extended theory T of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation (t) which enables  ...  Acknowledgments We thank Alain Colmerauer for our very long discussions about the theory of finite or infinite trees and its models.  ... 
arXiv:0706.4323v1 fatcat:pc6loiiimzf7bm3olewrqzj6te

QBF Modeling: Exploiting Player Symmetry for Simplicity and Efficiency [chapter]

Ashish Sabharwal, Carlos Ansotegui, Carla P. Gomes, Justin W. Hart, Bart Selman
2006 Lecture Notes in Computer Science  
We argue that while CNF is well suited to "existential reasoning" as demonstrated by the success of modern SAT solvers, it is far from ideal for "universal reasoning" needed by QBF.  ...  In particular, they use the standard conjunctive normal form (CNF) augmented with layers of variable quantification for modeling tasks as QBF.  ...  Acknowledgments We thank the anonymous reviewers for helpful comments.  ... 
doi:10.1007/11814948_35 fatcat:4vmbgbjjzrf3fm4tse2chmntly

Beyond NP: Arc-Consistency for Quantified Constraints [chapter]

Lucas Bordeaux, Eric Monfroy
2002 Lecture Notes in Computer Science  
Our main result is to propose quantified arc-consistency as a natural extension of the classical CSP notion. 1 As for CSPs, this name shall be used both for particular instances ("a QCP") and for the general  ...  Effective SAT-based solvers have been designed very recently for the special case of boolean constraints.  ...  Information provided by A. G. D. Rowley is also gratefully acknowledged. Last, we are indebted to the authors of [13] , whose title we somewhat plagiarized.  ... 
doi:10.1007/3-540-46135-3_25 fatcat:dnu3pusclzg47dto26o5e2vc5q

Meaning in Context [chapter]

Henning Christiansen, Veronica Dahl
2005 Lecture Notes in Computer Science  
The model fits well with a "flat" semantic representation as first proposed by Hobbs (1985) , consisting basically of a conjunction of atomic predications in which all variables are existentially quantified  ...  Discourse analysis is clearly a process of abduction in this framework, and it is shown that the mentioned constraint solvers serve as effective and efficient abductive engines for the purpose.  ...  In general, our methodology is applicable to "flat" meaning representations (e.g., those involving a conjunction of atomic predications in which all variables are existentially quantified with the widest  ... 
doi:10.1007/11508373_8 fatcat:uhyqzusgcncvhimatgishk7cue

The SOCS Computational Logic Approach to the Specification and Verification of Agent Societies [chapter]

Marco Alberti, Federico Chesani, Marco Gavanelli, Evelina Lamma, Paola Mello, Paolo Torroni
2005 Lecture Notes in Computer Science  
The operational counterpart of the proposed framework has been implemented and integrated in SOCS-SI, a tool that can be used for on-the-fly verification of agent compliance with respect to specified protocols  ...  It describes the SOCS social model: an agent interaction specification and verification framework equipped with a declarative and operational semantics, expressed in terms of abduction.  ...  Acknowledgements This work is partially funded by the Information Society Technologies programme of the European Commission under the IST-2001-32530 SOCS Project [3] , and by the MIUR COFIN 2003 projects  ... 
doi:10.1007/978-3-540-31794-4_17 fatcat:kjxvrk7tczce5kvzp3stjlcboa

Constraints meet concurrency

Jacopo Mauro
2015 Constraints  
For the development of this framework we used the concurrent language Jolie following the Service Oriented paradigm.  ...  Firstly we study the expressive power of a concurrent language, namely Constraint Handling Rules, that supports constraints as a primitive construct.  ...  For this reason my first thanks goes to all the professors, assistants, colleagues and friends with whom I have had the pleasure to interact with in these years.  ... 
doi:10.1007/s10601-015-9218-6 fatcat:7cjwl2p4anfkvbpahjnklrs7my

A Survey on String Constraint Solving [article]

Roberto Amadini
2021 arXiv   pre-print
This paper reports a comprehensive survey on string constraint solving by exploring the large number of approaches that have been proposed over the last decades to solve string constraints.  ...  String solving approaches have become popular over the last years given the massive use of strings in different application domains like formal analysis, automated testing, database query processing, and  ...  decidability of quantifier-free formulas over word equations in solved form and length constraints; (iii) the decidability of quantifierfree formulas over word equations in regular solved form, length  ... 
arXiv:2002.02376v8 fatcat:why6oeufmrbozbl22jlf7yivea

Optimizing Compilation and Computational Complexity of Constraint Handling Rules [chapter]

Jon Sneyers
2009 Lecture Notes in Computer Science  
Originally designed in the early 1990s as a specialpurpose programming language for adding user-defined constraint solvers to a host language, CHR has evolved over the last decade into a powerful and elegant  ...  In this dissertation we investigate the CHR programming language from the point of view of computational complexity theory. The first part introduces complexity theory, CHR, and CHR compilation.  ...  Rational trees. presented a solver for existentially quantified conjunctions of non-flat equations over rational trees.  ... 
doi:10.1007/978-3-642-02846-5_41 fatcat:ywwhwcnysbea3alkxbrz7ppfxe
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