# CPO Semantics of Timed Interactive Actor Networks

### Xiaojun Liu and Edward A. Lee

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-67

May 18, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-67.pdf

We give a denotational framework for composing interactive components into closed or open systems and show how to adapt classical domain-theoretic approaches to open systems and to timed systems. For timed systems, instead of the usual metric-space-based approaches, we show that existence and uniqueness of behaviors are ensured by continuity with respect to a simply defined prefix order. Existence and uniqueness of behaviors, however, does not imply that a composition of components yields a useful behavior. The unique behavior could be empty or smaller than expected. We define liveness and show that appropriately defined causality conditions ensure liveness and freedom from Zeno conditions. In our formulation, causality does not require a metric and can embrace a wide variety of models of time.

**Author Comments:** A revised version of this paper is at
http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-131.html.

BibTeX citation:

@techreport{Liu:EECS-2006-67, Author = {Liu, Xiaojun and Lee, Edward A.}, Title = {CPO Semantics of Timed Interactive Actor Networks}, Institution = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {May}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-67.html}, Number = {UCB/EECS-2006-67}, Note = {A revised version of this paper is at <a href="http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-131.html"> http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-131.html</a>.}, Abstract = {We give a denotational framework for composing interactive components into closed or open systems and show how to adapt classical domain-theoretic approaches to open systems and to timed systems. For timed systems, instead of the usual metric-space-based approaches, we show that existence and uniqueness of behaviors are ensured by continuity with respect to a simply defined prefix order. Existence and uniqueness of behaviors, however, does not imply that a composition of components yields a useful behavior. The unique behavior could be empty or smaller than expected. We define liveness and show that appropriately defined causality conditions ensure liveness and freedom from Zeno conditions. In our formulation, causality does not require a metric and can embrace a wide variety of models of time.} }

EndNote citation:

%0 Report %A Liu, Xiaojun %A Lee, Edward A. %T CPO Semantics of Timed Interactive Actor Networks %I EECS Department, University of California, Berkeley %D 2006 %8 May 18 %@ UCB/EECS-2006-67 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-67.html %F Liu:EECS-2006-67