Synchronous programming (Berry (1989)) is a powerful approach to programming reactive systems. Following the idea that "processes are relations extended over time" (Abramsky (1993)), we propose a simple but powerful model for timed, determinate computation, extending the closure-operator model for untimed concurrent constraint programming (CCP). In (Saraswat et al. 1994a) we had proposed a model for this called tcc--- here we extend the model of tcc to express strong time-outs: if an event A does not happen through time t, cause event B to happen at time t. Such constructs arise naturally in practice (e.g. in modeling transistors) and are supported in synchronous programming languages. The fundamental conceptual difficulty posed by these operations is that they are nonmonotonic. We provide a compositional semantics to the non-monotonic version of concurrent constraint programming (Default cc) obtained by changing the underlying logic from intuitionistic logic to Reiter's default logic...

This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...

) Vineet Gupta Radha Jagadeesan Prakash Panangaden y vgupta@mail.arc.nasa.gov radha@cs.luc.edu prakash@cs.mcgill.ca Caelum Research Corporation Dept. of Math. and Computer Sciences School of Computer Science NASA Ames Research Center Loyola University--Lake Shore Campus McGill University Moffett Field CA 94035, USA Chicago IL 60626, USA Montreal, Quebec, Canada Abstract This paper describes a stochastic concurrent constraint language for the description and programming of concurrent probabilistic systems. The language can be viewed both as a calculus for describing and reasoning about stochastic processes and as an executable language for simulating stochastic processes. In this language programs encode probability distributions over (potentially infinite) sets of objects. We illustrate the subtleties that arise from the interaction of constraints, random choice and recursion. We describe operational semantics of these programs (programs are run by sampling random choices), deno...

. We present a language, Hybrid cc, for modeling hybrid systems compositionally. This language is declarative, with programs being understood as logical formulas that place constraints upon the temporal evolution of a system. We show the expressiveness of our language by presenting several examples, including a model for the paperpath of a photocopier. We describe an interpreter for our language, and provide traces for some of the example programs. 1 Introduction and Motivation The constant marketplace demand of ever greater functionality at ever lower price is forcing the artifacts our industrial society designs to become ever more complex. Before the advent of silicon, this complexity would have been unmanageable. Now, the economics and power of digital computation make it the medium of choice for gluing together and controlling complex systems composed of electro-mechanical and computationally realized elements. As a result, the construction of the software to implement, monitor, c...

. We extend cc to allow the specification of a discrete probability distribution for random variables. We demonstrate the expressiveness of pcc by synthesizing combinators for default reasoning. We extend pcc uniformly over time, to get a synchronous reactive probabilistic programming language, Timed pcc. We describe operational and denotational models for pcc (and Timed pcc). The key feature of the denotational model(s) is that parallel composition is essentially set intersection. We show that the denotational model of pcc (resp. Timed pcc) is conservative over cc (resp. tcc). We also show that the denotational models are fully abstract for an operational semantics that records probability information. 1 Introduction Concurrent constraint programming(CCP, [Sar93]) is an approach to computation which uses constraints for the compositional specification of concurrent systems. It replaces the traditional notion of a store as a valuation of variables with the notion of a store as a cons...

Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finite-state) systems are, of course, inadequate for reasoning about such systems. In this work we develop three related ideas for making such reasoning principles applicable to continuous systems. ffl We show how to approximate continuous systems by a countable family of finite-state probabilistic systems, we can reconstruct the full system from these finite approximants, ffl we define a metric between processes and show that the approximants converge in this metric to the full process, ffl we show that reasoning about properties definable in a rich logic can be carried out in terms of the approximants. The systems that we consider are Markov processes where the state space is continuous but the time steps are discrete. We allow such processes to interact with the environment by syn...

In synchronous programming, programs can be perceived as purely sequential, and parallelism is only a logical concept useful to develop programs in a modular way. Classical semantics for synchronous languages interpret programs as sequential input/output finite state machines (i/o FSMs) where concurrency disappears. We argue that semantics where concurrency is reected can be useful at least for improving hardware implementation, veri cation, and design of model-based schedulers. So, these semantics should not "compete" with the classical ones but should o er di erent, although consistent, views of programs, each supporting a particular task in their development. In order to de ne semantics reecting concurrency, well established techniques adopted to define "truly concurrent" semantics for asynchronous languages could be applied. In this paper, we consider as a prototype of the class of synchronous languages the language Esterel, which is gaining use in a wide variety of applications. Then, following a method proposed by Degano and Priami to give semantics for asynchronous process algebras, we develop a semantic framework in which one can define different, although consistent, semantics of Esterel programs. The idea is to define a very concrete model of the language from which more abstract models can be recovered by means of suitable abstraction functions. We define a proved transition system (PTS) as the most concrete model of Esterel. We show that the classical interpretation in FSMs can be recovered from the PTS by a suitable abstraction function, namely we show that our most concrete semantics is consistent with the classical one. Then, from proved trees obtained by unfolding parts of the PTS, we abstract locality trees and enabling trees. We show how locality trees c...

Hybrid cc is a constraint programming language suited for modeling, controlling and simulating hybrid systems, i.e. systems with continuous and discrete state changes. The language extends the concurrent constraint programming framework with default reasoning and combinators for programming continuous behavior. The most important constraint systems used in Hybrid cc are nonlinear equations and ordinary differential equations over intervals. The interval constraints are crucial in that many modeling problems are only partially specified. We describe the implementation of the Hybrid cc interpreter and constraint solvers, and evaluate the performance using some example programs.

Robotic assemblies are inherently hybrid systems. This paper pursues a class of multi-tiered peg-inhole assemblies that we call "peg-in-maze" assemblies. These assemblies require a force-responsive, low-level controller governing physical contacts plus a decisionmaking, strategic-level supervisor monitoring the overall progress. To capture this dichotomy we formulate hybrid automata, where each state represents a different forcecontrolled "behavior" and transitions between states encode the high-level strategy of the assembly. Our overarching goal is to produce a computational framework for the simulation, verification, and synthesis of such forceguided robotic assembly strategies. We investigate the use of three general hybrid-systems software tools (Hybrid cc, HyTech, and CEtool) for the simulation and verification of these strategies. We describe the computational environment we developed at Case to synthesize and implement real-world assembly strategies.