Turing-Complete Subclasses of CHR

Sneyers, Jon

doi:10.1007/978-3-540-89982-2_72

Cited by 10 publications

(17 citation statements)

References 8 publications

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“…On the other hand, when allowing mul-tiple heads, even restricting to a host language which allows only constants does not allow to obtain any decidability property, since also with this limitation CHR is still Turing complete [116,32]. The only (implicit) decidability results concern…”

Section: Chr With Prioritiesmentioning

confidence: 99%

“…is strictly less expressive than CHR ωa (C): in fact there exists a termination preserving encoding of Turing Machines into CHR ωa (C) [116,32].…”

Section: Definition 52 Given Two Configurations Smentioning

confidence: 99%

“…As mentioned in the introduction, while CHR ωa (C) and CHR ωa 1 (F ) are Turing complete languages [116,32], the question of the expressive power of CHR ωa 1 (C) is open. Here we answer to this question by proving that the existence of a terminating computation is decidable for this language, thus showing that CHR ωa 1 (C) is less expressive than Turing machines.…”

Section: Single-headed Chr ω a (C)mentioning

confidence: 99%

“…These results are not immediate. Indeed, CHR ωa (C), without further restrictions and with any of the two semantics, is a Turing complete language [116,32]. It remains quite expressive also with our restrictions: for example, CHR ωa 1 (C), the second fragment that we have considered, allows an infinite number of different states, hence, for example, it can not be translated to Petri Nets.…”

Section: Summary and Related Workmentioning

confidence: 99%

“…In particular, [116] showed that a further restriction of CHR ωa 1 (C), which does not allow built-ins in the body of rules (and which therefore does not allow unification of terms) is not Turing complete. This result is obtained by translating CHR ωa 1 (C) programs (without unification) into propositional CHR and using the encoding of propositional CHR intro Petri Nets provided in [13].…”

Section: Summary and Related Workmentioning

confidence: 99%

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Constraints meet concurrency

Mauro

2015

Constraints

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We investigate the benefits that emerge when the fields of constraint programming and concurrency meet. On one hand, constraints can be use in concurrency theory to increase the conciseness and the expressive power of concurrent languages from a pragmatic point of view. On the other hand, problems modeled by using constraints can be solved faster and more efficiently using a concurrent system. We explore both directions providing two separate lines of contribution. Firstly we study the expressive power of a concurrent language, namely Constraint Handling Rules, that supports constraints as a primitive construct. We show what features of this language make it Turing powerful. Then we propose a framework to solve constraint problems that is intended to be deployed on a concurrent system. For the development of this framework we used the concurrent language Jolie following the Service Oriented paradigm. Based on this experience, we also propose an extension to Service Oriented Languages to overcome some of their limitations and to improve the development of concurrent applications. Needless to say, I am also in debt with my coauthors:

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Section: Chr With Prioritiesmentioning

confidence: 99%

“…is strictly less expressive than CHR ωa (C): in fact there exists a termination preserving encoding of Turing Machines into CHR ωa (C) [116,32].…”

Section: Definition 52 Given Two Configurations Smentioning

confidence: 99%

Section: Single-headed Chr ω a (C)mentioning

confidence: 99%

Section: Summary and Related Workmentioning

confidence: 99%

Section: Summary and Related Workmentioning

confidence: 99%

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Constraints meet concurrency

Mauro

2015

Constraints

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Constraint Handling Rules - What Else?

Frühwirth

2015

Rule Technologies: Foundations, Tools, and Applications

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Abstract. Constraint Handling Rules (CHR) is both an effective concurrent declarative constraint-based programming language and a versatile computational formalism. While conceptually simple, CHR is distinguished by a remarkable combination of desirable features:-a semantic foundation in classical and linear logic, -an effective and efficient sequential and parallel execution model -guaranteed properties like the anytime online algorithm properties -powerful analysis methods for deciding essential program properties. This overview of some CHR-related research and applications is by no means meant to be complete. Essential introductory reading for CHR provide the survey article [125] and the books [56,63]. Up-to-date information on CHR can be found online at the CHR web-page www. constraint-handling-rules.org, including the slides of the keynote talk associated with this article. In addition, the CHR website dtai. cs.kuleuven.be/CHR/ offers everything you want to know about CHR, including online demo versions and free downloads of the language. Executive SummaryConstraint Handling Rules (CHR) [56] tries to bridge the gap between theory and practice, between logical specification and executable program by abstraction through constraints and the concepts of computational logic. CHR has its roots in constraint logic programming and concurrent constraint programming, but also integrates ideas from multiset transformation and rewriting systems as well as automated reasoning and theorem proving. It seamlessly blends multi-headed rewriting and concurrent constraint logic programming into a compact userfriendly rule-based programming language. CHR consists of guarded reactive rules that transform multisets of relations called constraints until no more change occurs. By the notion of constraint, CHR does not need to distinguish between data and operations, and its rules are both descriptive and executable.In CHR, one distinguishes two main kinds of rules: Simplification rules replace constraints by simpler constraints while preserving logical equivalence, e.g., X≤Y∧Y≤X ⇔ X=Y. Propagation rules add new constraints that are logically redundant but may cause further simplification, e.g., X≤Y∧Y≤Z ⇒ X≤Z. Together with X≤X ⇔ true, these rules encode the axioms of a partial order relation. The rules compute its transitive closure and replace inequalities ≤ by equalities = whenever possible. For example, A≤B∧B≤C∧C≤A becomes A=B∧B=C. More program examples can be found in Section 2. Semantics of CHR are discussed in Section 3.

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Decidability properties for fragments of CHR

Gabbrielli¹,

Mauro²,

Meo³

et al. 2010

Theory and Practice of Logic Programming

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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 expressive than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines

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Turing-Complete Subclasses of CHR

Cited by 10 publications

References 8 publications

Constraints meet concurrency

Constraints meet concurrency

Constraint Handling Rules - What Else?

Decidability properties for fragments of CHR

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