Towards nominal computation

Bojańczyk, Mikołaj; Braud, Laurent; Klin, Bartek; Lasota, Sławomir

doi:10.1145/2103656.2103704

Cited by 25 publications

(30 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This was shown in [3] for least supports and Cartesian products, and in [4] for orbit refinement. For other examples of data symmetries that satisfy these properties, see [3,4].…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 77%

See 1 more Smart Citation

Nominal Monoids

Bojańczyk

2013

Theory Comput Syst

View full text Add to dashboard Cite

show abstract

“…This was shown in [3] for least supports and Cartesian products, and in [4] for orbit refinement. For other examples of data symmetries that satisfy these properties, see [3,4].…”

Section: Assumptions On the Data Symmetrymentioning

confidence: 77%

“…In particular, in Theorem 9.1, it could be that the assumption on orbit-finiteness is not necessary. 4 Example 8 Consider the total order symmetry, and the language of words with an even number of growing data values…”

Section: Lemma 92 If L Is Definable In First-order Logic Then M L Imentioning

confidence: 99%

Nominal Monoids

Bojańczyk

2013

Theory Comput Syst

View full text Add to dashboard Cite

show abstract

“…What is less obvious is that every orbit-finite subset is of this form. This follows from a key technical property of hulls, proved independently by Turner [39, Lemma 3.4.3.5] and Bojańczyk et al [6,Lemma 3]:…”

Section: Orbit-finite Subsetsmentioning

confidence: 88%

“…We observe that a key concept underlying the automata-theoretic research programme of Bojańczyk et al [6], that of being an orbit-finite subset, turns out to subsume a notion of topological compactness introduced, for quite different purposes, by Winskel and Turner in their work on nominal domain theory for concurrency [40]. We explain the connection and use it to develop a version of the classic notion of Scott domain within nominal sets.…”

Section: Introductionmentioning

confidence: 90%

Full abstraction for nominal Scott domains

Lösch

Pitts

2013

Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

View full text Add to dashboard Cite

We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojańczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and 'definite description' over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallel-or, to a programming language for recursively defined higher-order functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higher-order functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.

show abstract

“…The last missing part for the decidability of CSP-Inf(T) is the following lemma, whose proof follows general principles of equivariant computation on orbit-finite structures for arbitrary atom symmetries, studied in [22], [26].…”

Section: A General Decidabilitymentioning

confidence: 99%

Locally Finite Constraint Satisfaction Problems

Klin

Kopczyński

Ochremiak

et al. 2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract-First-order definable structures with atoms are infinite, but exhibit enough symmetry to be effectively manipulated. We study Constraint Satisfaction Problems (CSPs) where both the instance and the template are definable structures with atoms.As an initial step, we consider locally finite templates, which contain potentially infinitely many finite relations. We argue that such templates occur naturally in Descriptive Complexity Theory.We study CSPs over such templates for both finite and infinite, definable instances. In the latter case even decidability is not obvious, and to prove it we apply results from topological dynamics. For finite instances, we show that some central results from the classical algebraic theory of CSPs still hold: the complexity is determined by polymorphisms of the template, and the existence of certain polymorphisms, such as majority or Maltsev polymorphisms, guarantees the correctness of classical algorithms for solving finite CSP instances.

show abstract

Towards nominal computation

Cited by 25 publications

References 13 publications

Nominal Monoids

Nominal Monoids

Full abstraction for nominal Scott domains

Locally Finite Constraint Satisfaction Problems

Contact Info

Product

Resources

About