Abstract—We give a denotational framework (a “meta model”) within which certain properties of models of computation can be compared. It describes concurrent processes in general terms as sets of possible behaviors. A process is determinate if, given the constraints imposed by the inputs, there are exactly one or exactly zero behaviors. Compositions of processes are processes with behaviors in the intersection of the behaviors of the component processes. The interaction between processes is through signals, which are collections of events. Each event is a value-tag pair, where the tags can come from a partially ordered or totally ordered set. Timed models are where the set of tags is totally ordered. Synchronous events share the same tag, and synchronous signals contain events with the same set of tags. Synchronous processes have only synchronous signals as behaviors. Strict causality (in timed tag systems) and continuity (in untimed tag systems) ensure determinacy under certain technical conditions. The framework is used to compare certain essential features of various models of computation, including Kahn process networks, dataflow, sequential processes, concurrent sequential processes with rendezvous, Petri nets, and discrete-event systems. I.

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This document describes Ptolemy II version 0.3. It contains three parts. The first part is a user's guide, which begins with an overview of the objectives of the software, then explains how to construct applets and applications, then reviews the actor libraries, and then concludes with a tutorial on writing actors. The second part documents the software infrastructure. It is meant to complement, not replace, the code documentation. The third part documents the domains that have been written so far. Ptolemy II supports heterogeneous modeling and design of concurrent systems. It is component technology, in that the models are built by interconnecting components. Executable models are constructed under a model of computation, which is the set of "laws of physics" that govern the interaction of components in the model. If the model is describing a mechanical system, then the model of computation may literally be the laws of physics. More commonly, however, it is a set of rules that are more abstract, and provide a framework within which a designer builds models. A set of rules that govern the interaction of components is called the semantics of the model of computation. Each domain implements such a set of rules. Ptolemy II is written entirely in Java, and aims to support the construction of applets, servlets, migrating code, and embedded Java.

Abstract. This paper extends the application of the Cantor metric as a mathematical tool for defining causalities from pure discrete models to mixed-signal and hybrid models. Using the Cantor metric, which maps timed signals, continuous or discrete, into a metric space, we define causality as contractive properties of processes operating on these signals. Thus, the Banach fixed point theorem can be applies to establish conditions for the existence, uniqueness, and liveness of the behaviors for mixed-signal and hybrid systems. The results also provide theoretical foundations for the simulation technologies for such systems, including the time-marching strategy, evaluation of feedback loops, and the necessity of supporting rollback. 1

Memorandum UCB/ERL M05/22 Earlier versions: • UCB/ERL M04/16 UCB/ERL M03/28 UCB/ERL M02/23 UCB/ERL M99/40 UCB/ERL M01/12

The composite signal flow model of computation targets systems with significant control and data processing parts. It builds on the data flow and synchronous data flow models and extends them to include three signal types: non-periodic signals, sampled signals, and vectorized sampled signals. Vectorized sampled signals are used to represent vectors and computations on vectors. Several conversion processes are introduced to facilitate synchronization and communication with these signals. We discuss the severe implications, that these processes have on the causal behaviour of the system. We illustrate the model and its usefulness with three applications. A co-modelling and co-simulation environment combining Matlab and SDL; a high level timing analysis as a consequence of the operations on vectors; conditions for a parallel, distributed simulation. 1. Introduction Current approaches to system modelling can be divided into two groups, homogeneous and heterogeneous models...

Multi-agent systems where the members are developed by parties with competing interests, and where there is no access to a member’s internal state, are often classified as ‘open’. The specification of protocols for open agent systems of this sort is largely seen as a design-time activity. Moreover, there is no support for run-time specification modification. Due to environmental, social, or other conditions, however, it is often required to revise the specification during the protocol execution. To address this requirement, we present an infrastructure for ‘dynamic ’ protocol specifications, that is, specifications that may be modified at runtime by agents. The infrastructure consists of well-defined procedures for proposing a modification of the ‘rules of the game ’ as well as decision-making over and enactment of proposed modifications. We evaluate proposals for rule modification by modelling dynamic specifications as metric spaces. Furthermore, we constrain the enactment of proposals that do not meet the evaluation criteria. We illustrate our infrastructure by presenting a dynamic specification of a resourcesharing protocol, and an execution of this protocol in which the participating agents modify the protocol specification.

This document describes the design and implementation of Ptolemy II 2.0.1. Ptolemy II is a set of Java packages supporting heterogeneous, concurrent modeling and design. The focus is on assembly of concurrent components. The key underlying principle in the Ptolemy II is the use of well-defined models of computation that govern the interaction between components. A major problem area that is addressed is the use of heterogeneous mixtures of models of computation. The kernel package in Ptolemy II supports clustered hierarchical graphs, which are collections of entities and relations between those entities. Its actor package extends the kernel so that entities have functionality and can communicate via the relations. Its domains extend the actor package by imposing models of computation on the interaction between entities. Examples of models of computation include discrete-event systems, dataflow, process networks, continuous-time models, synchronous/reactive systems, and communicating sequential processes. Ptolemy II includes a number of support packages, providing for example graph-theoretic manipulations, matrix and vector math and signal processing functions, visual display of data, a sophisticated type system, data encapsulation and an expression language and parser.

Based on Memorandum UCB/ERL M01/12 Originally published as Memorandum UCB/ERL M99/40

In 1938 Morse and Hedlund proved that a functions f : ZZ ! f0; 1g is periodic if the number jP f (n)j of dierent n-blocks (f(x + 1); : : : ; f(x + n)) with x 2 ZZ does not exceed n for some n. In 1940 they studied such functions f with jP f (n)j = n + 1 for all positive integers n. These are closely related to Sturmian sequences, which occur in many branches of mathematics, computer science and physics. Recently the authors studied k-dimensional functions f : ZZ k ! f0; 1g with jP f (A)j jAj, where P f (A) is the set of dierent vectors (f(~x+~a 1 ); : : : ; f(~x+ ~a n )) with ~x 2 ZZ k for a given conguration A = f~a 1 ; : : : ; ~a n g ZZ k . In this paper, we characterize functions satisfying jP f (A)j jAj + 1 for all congurations A ZZ k . Our proof requires a separation theorem for convex sets of lattice points, which may be of independent interest. This work was done at the University of Leiden, made possible by grants from NUFFIC and the Hannoversche Hochschulgemeinschaft. The rst author is very grateful to these institutions for their help and support. 1 1.