Section: New Results

Expressiveness of computational models

Participants : Cosimo Laneve, Maurizio Gabbrielli, Gianluigi Zavattaro.

Expressiveness refers to the study of the expressive power of computational models.

We have studied [46] the expressiveness of an actor-based language similar to the language ABS developed in Hats. We have identified the presence/absence of fields as a relevant feature: the dynamic creation of names in combination with fields gives rise to Turing completeness. On the other hand, restricting to stateless actors gives rise to systems for which properties such as termination are decidable. Such decidability result holds in actors with states when the number of actors is finite and the state is read-only.

Our other study of expressiveness has been made on Constraint Handling Rules (CHR), a committed-choice declarative language originally designed for writing constraint solvers and that is nowadays a general purpose language. The study of CHR is interesting within Focus as this kind of languages, having both constraint solving and concurrency features, allow us to express in a natural way quantitative aspects related to resources. Moreover, constraints may be used to describe dynamic adaptation and evolution of systems. CHR programs consist of multi-headed guarded rules which allow one to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expressive power of the language (somehow, it can be considered similar to multiple synchronization gathering $n$ processes simultaneously), however no formal result in this direction had been proved so far. We have proved [18] a number of expressiveness results to support such a claim. First, we have analyzed the Turing completeness of CHR with respect to the underlying constraint theory. If the constraint theory is powerful enough then restricting to single head rules does not affect Turing completeness. On the other hand, differently from the case of the multi-headed language, the single head CHR language is not Turing powerful when the underlying signature (for the constraint theory) does not contain function symbols. Then we have proved that, no matter which constraint theory is considered, under some reasonable assumptions it is not possible to encode the CHR language (with multi-headed rules) into a single headed language while preserving the semantics of the programs. Moreover, under some stronger assumptions, considering an increasing number of atoms in the head of a rule augments the expressive power of the language.