# A Domain Equation for Bisimulation

@article{Abramsky1991ADE, title={A Domain Equation for Bisimulation}, author={Samson Abramsky}, journal={Inf. Comput.}, year={1991}, volume={92}, pages={161-218} }

Some basic topics in the theory of concurrency are studied from the point of view of denotational semantics, and particularly the ''domain theory in logical form'' developed by the author. A domain of synchronization trees is defined by means of a recursive domain equation involving the Plotkin powerdomain. The logical counterpart of this domain is described, and shown to be related to it by Stone duality. The relationship of this domain logic to the standard Hennessy-Milner logic for…

## 205 Citations

A coinduction principle for recursive data types based on bisimulation

- Computer Science[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science
- 1993

An internal full abstraction result for the canonical model of the untyped call-by-value lambda -calculus is proved from two strong-extensionality theorems stating that the equality relation is maximal among all bisimulations.

Pi-Calculus in Logical Form

- Mathematics, Computer Science22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
- 2007

It is shown that initial algebras of functors defined in terms of categorical constructions give rise to a logic that is sound, complete, and characterises bisimilarity.

Gamma and the Logic of Transition Traces

- Computer Science
- 1997

This paper systematically develops a program logic for Gamma from a denotational semantics, a domain-theoretic reformulation of the transition trace semantics, which was deened for Gamma by Sands and based on earlier work by Brookes.

Deriving Denotational Models for Bisimulation from Struc- Tured Operational Semantics

- Computer Science
- 2007

The deened an order theoretic interpretation for L and it is proved that it is a complete model for the equational theory of ACP, which is an interesting question which kind of structure to use in order to model this.

CPO Models for a Class of GSOS Languages

- Computer ScienceTAPSOFT
- 1995

This paper presents a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail and Meyer, and gets several general results on the bisimulation preorder.

A fully abstract denotational semantics for the calculus of higher-order communicating systems

- Computer ScienceTheor. Comput. Sci.
- 2001

Non-determinism in a functional setting

- Computer Science[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science
- 1993

This work identifies the denotational type that captures the computational situation delta =P(( delta to delta ) perpendicular to ), where P(-) is the Plotkin power-domain functor and carries out a systematic programme that hinges on three distinct interpretations of delta, namely process-theoretic, Denotational, and logical.

Volume 92 Number 2 ( 1991 ) , in the article “ A Domain Equation for Bisimulation

- Computer Science
- 2001

The researchers who wish to apply Abramsky’s domain logic for transition systems in their work should use the version presented in [1, Chap. 5] in lieu of that offered in the journal paper, because there is a subtle error in the proof of Theorem 5.5.8.

A Fully Abstract Model for the [pi]-calculus

- Computer ScienceInf. Comput.
- 2002

A central role is played by the description of non-determinism as a free construction and by the equational theory of the metalanguage in this proof of full abstraction for the finite /spl pi/-calculus in the set-theoretic model.

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