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Completion of Rewrite Systems with Membership Constraints Part II: Constraint Solving

H. Comon
1998 Journal of symbolic computation  
We consider a constraint system involving equations and membership constraints. Membership constraints are interpreted as the membership to some recognizable tree languages.  ...  The terms may contain a restricted kind of context variables. We give a set of constraint solving rules which is proved to be complete and terminating.  ...  Werner and two anonymous referees for their valuable comments on earlier versions of this paper.  ... 
doi:10.1006/jsco.1997.0186 fatcat:fngauclqh5c5rbptiirqta65vy

Completion of Rewrite Systems with Membership Constraints Part I: Deduction Rules

H. Comon
1998 Journal of symbolic computation  
Computing critical pairs requires, however, to solve some constraints in a second-order logic with membership constraints.  ...  We consider a constrained equational logic where the constraints are membership conditions t 2 s where s is interpreted as a regular tree language.  ...  Ackowledgments I thank Andreas Werner who found an important oversight (the rule Deduce 4) and a mistake (the WT-property was a property of terms instead of equations) in an earlier version of this paper  ... 
doi:10.1006/jsco.1997.0185 fatcat:4hgvpheipzawzpajypupquym7y

Automated Induction for Complex Data Structures [article]

Adel Bouhoula, Florent Jacquemard
2008 arXiv   pre-print
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints.  ...  Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating).  ...  We are also grateful to Jared Davis and Sorin Stratulat for having processed the example on sorted lists with respectively ACL2 and SPIKE.  ... 
arXiv:0811.4720v1 fatcat:l6esx2n64jcofdkuiwpk6ifmye

Page 4216 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
Wilkerson (1-MOR-C; Rolla, MO) 99f:68115 68Q42 Comon, Hubert (F-ENSET-SV; Cachan) Completion of rewrite systems with membership constraints. II. Constraint solving. (English summary) J.  ...  Trotter (Princeton, NJ) 99f:68114 68Q42 Comon, Hubert (F-ENSET-SV; Cachan) Completion of rewrite systems with membership constraints. I. Deduction rules. (English summary) J.  ... 

Solving Binary CSP Using Computational Systems

Carlos Castro
1996 Electronical Notes in Theoretical Computer Science  
Based on the notion of Computational Systems we associate actions with rewriting rules and control with strategies that establish the order of application of the inferences.  ...  The main contribution of this work is to lead the way to the design of a formalism allowing to better understand constraint solving and to apply in the domain of CSP the knowledge already developed in  ...  Formally, this is the combination of a rewrite theory in rewriting logic 19], together with a notion of strategy to e ciently compute with given rewriting rules.  ... 
doi:10.1016/s1571-0661(04)00042-8 fatcat:syov7eejhjagfcmwacwlj6ucxi

A uniform approach to constraint-solving for lists, multisets, compact lists, and sets

Agostino Dovier, Carla Piazza, Gianfranco Rossi
2008 ACM Transactions on Computational Logic  
In this paper we extend these results considering more general constraints, namely equality and membership constraints and their negative counterparts.  ...  They have been analyzed from an axiomatic point of view with a parametric approach in [20] where the relevant unification algorithms have been developed.  ...  Membership and Not-Membership Constraints The rewriting procedures for membership and not-membership constraints on a specific aggregate are obtained from the general schema of Figure 2 , using the rewriting  ... 
doi:10.1145/1352582.1352583 fatcat:c6q6kwtwcreunfpuhphcfcrlky

Sufficient completeness verification for conditional and constrained TRS

Adel Bouhoula, Florent Jacquemard
2012 Journal of Applied Logic  
We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities  ...  Our approach is integrated into a framework for inductive theorem proving based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms  ...  Acknowledgements We wish to sincerely thank Joe Hendrix for having processed the above examples of Sections 5 and 9 with the Sufficient Completeness Checker for Maude, and the reviewers whose useful remarks  ... 
doi:10.1016/j.jal.2011.09.001 fatcat:6ujglk45dra4pctmvfmzus7wba

Conditional Narrowing Modulo in Rewriting Logic and Maude [chapter]

Luis Aguirre, Narciso Martí-Oliet, Miguel Palomino, Isabel Pita
2014 Lecture Notes in Computer Science  
This work studies the relationship between verifiable and computable answers for reachability problems in rewrite theories with an underlying membership equational logic.  ...  These problems have the form withx some variables, or a conjunction of several of these subgoals. A calculus that solves this kind of problems has been developed and proved correct.  ...  Another topic addressed by the present work, membership equational logic, is defined by Meseguer [Mes97] . An equivalent rewrite system for Mel theories is presented by Durán, Lucas et al.  ... 
doi:10.1007/978-3-319-12904-4_4 fatcat:mieify6evjfi3b7djcr43gjoci

Hippo: A System for Computing Consistent Answers to a Class of SQL Queries [chapter]

Jan Chomicki, Jerzy Marcinkowski, Slawomir Staworko
2004 Lecture Notes in Computer Science  
The only output of this system is the Answer Set consisting of the consistent answers to the input Query in the database instance DB with respect to a set of integrity constraints IC.  ...  In the base version of the system this is done by simply executing the appropriate membership queries on the database.  ... 
doi:10.1007/978-3-540-24741-8_53 fatcat:xw4isbziczaozlzne2if6uxc7a

Imposing assertions in Maude via program transformation

María Alpuente, Demis Ballis, Julia Sapiña
2019 MethodsX  
This paper describes an automated correction methodology for Maude programs that is based on program transformation and can be used to enforce a safety policy, given by a set A of system assertions, in  ...  •A simple logical notation to declaratively express invariant properties and other safety constraints through assertions.  ...  An assertion S | f holds in a system state s iff, for every subterm of s that matches (modulo E) the algebraic structure of the state template S with substitution s, the constraints given by the instantiated  ... 
doi:10.1016/j.mex.2019.10.035 pmid:31763189 pmcid:PMC6861556 fatcat:khq25ufekfc3xh7hhz6zzkgvey

A uniform approach to constraint-solving for lists, multisets, compact lists, and sets [article]

Agostino Dovier, Carla Piazza, Gianfranco Rossi
2003 arXiv   pre-print
In this paper we extend these results considering more general constraints including not only equality but also membership constraints as well as their negative counterparts. (*) A. Dovier, A.  ...  These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*) where the relevant unification algorithms have been developed.  ...  The anonymous referee greatly helped us in improving the presentation of the paper.  ... 
arXiv:cs/0309045v1 fatcat:3es5wm3xtzgfbdt2mggyp3hgx4

Query rewriting and answering under constraints in data integration systems

Andrea Calì, Domenico Lembo, Riccardo Rosati
2003 International Joint Conference on Artificial Intelligence  
Then, we introduce a semantics which is able to cope with violations of constraints, and present a sound and complete rewriting technique for the same dec idable class of constraints.  ...  In the case of sound views, we provide sound and complete rewriting techniques for a maximal class of constraints for which decidability holds.  ...  fect rewriting of a UCQ query in GAV integration systems with KDs and IDs.  ... 
dblp:conf/ijcai/CaliLR03 fatcat:hzpf3pw4k5cj7ay74j5dcpjy5i

Twenty Years Later [chapter]

Jean-Pierre Jouannaud
2005 Lecture Notes in Computer Science  
Back in the late 80s, many of us feared that this would soon be the case, that research in rewrite systems was deepening the gap with everyday's computer science practice, and that we should develop rewrite-based  ...  powerful provers that would make a difference with the state of art and help address real applications such as software verification.  ...  The main difference with the case of ground completion is that the rewrite system may be infinite, and therefore no decidability result can be obtained in general.  ... 
doi:10.1007/978-3-540-32033-3_27 fatcat:6xggpx3i7ve7rfewekdb4vfiv4

On the Classification of Visual Languages by Grammar Hierarchies

KIM MARRIOTT, BERND MEYER
1997 Journal of Visual Languages and Computing  
Although the hierarchy is based on the constraint multiset grammar formalism, we sketch how other visual language specification formalisms can be mapped into constraint multiset grammars so that a comparison  ...  of context-sensitivity.  ...  The top-left production generates the start symbol, the top-right production swaps the representation of tokens in the string, the bottom-left production encodes XPaX  ... 
doi:10.1006/jvlc.1997.0053 fatcat:m4vgn7ckeresvi42abbqruxmpi

Computing consistent query answers using conflict hypergraphs

Jan Chomicki, Jerzy Marcinkowski, Slawomir Staworko
2004 Proceedings of the Thirteenth ACM conference on Information and knowledge management - CIKM '04  
The work presented here addresses the issue of computing consistent query answers for projection-free queries and denial integrity constraints.  ...  In [2], the notion of consistent query answer was proposed to achieve that objective. [2] introduced the notion of repair: a database that satisfies the integrity constraints and is minimally different  ...  The flow of data in Hippo is shown in Figure 2 output of this system is the Answer Set consisting of the consistent answers to the input query E with respect to a set of integrity constraints IC in the  ... 
doi:10.1145/1031171.1031254 dblp:conf/cikm/ChomickiMS04 fatcat:qxslo55dcfe4dju6ym4xqiyypm
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