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Decidability properties for fragments of CHR

Published online by Cambridge University Press:  09 July 2010

MAURIZIO GABBRIELLI ,
JACOPO MAURO ,
MARIA CHIARA MEO  and
JON SNEYERS
MAURIZIO GABBRIELLI
Affiliation:
Dipartimento di Scienze dell'Informazione and Lab. Focus INRIA, Università di Bologna, Italy (e-mail: gabbri@cs.unibo.it)
JACOPO MAURO
Affiliation:
Dipartimento di Scienze dell'Informazione, Università di Bologna, Italy (e-mail: jmauro@cs.unibo.it)
MARIA CHIARA MEO
Affiliation:
Dipartimento di Scienze, Università di Chieti Pescara, Italy (e-mail: cmeo@unich.it)
JON SNEYERS
Affiliation:
Departement Computerwetenschappen, K.U. Leuven, Belgium (e-mail: jon.sneyers@cs.kuleuven.be)
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Abstract

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity > 0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive1 than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines.

Keywords

constraint programmingexpressivitywell-structured transition systems
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 10 , Special Issue 4-6: 26th International Conference on Logic Programming , July 2010 , pp. 611 - 626
Copyright
Copyright © Cambridge University Press 2010

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