The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and non-deterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a denotational semantics for the strongest-postcondition of ntcc processes and, based on this semantics, we develop a proof system for linear-temporal properties of these processes. The expressiveness of ntcc is illustrated by modeling cells, timed systems such as RCX controllers, multi-agent systems such as the Predator /Prey game, and musical applications such as generation of rhythms patterns and controlled improvisation. 1

Systems biology is a new area in biology that aims at achieving a systems-level understanding of biological systems. While current genome projects provide a huge amount of data on genes or proteins, lots of research is still necessary to understand how the dierent parts of a biological system interact in order to perform complex biological functions.

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This paper presents a probabilistic language, called λ○, whose expressive power is beyond discrete distributions. Rich expressiveness of λ ○ is due to its use of sampling functions, i.e., mappings from the unit interval (0.0, 1.0] to probability domains, in specifying probability distributions. As such, λ ○ enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of λ ○ is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

Motivated by many practical applications that have to compute in the presence of uncertainty, we propose a monadic probabilistic language based upon the mathematical notion of sampling function. Our language provides a unified representation scheme for probability distributions, enjoys rich expressiveness, and o#ers high versatility in encoding probability distributions. We also develop a novel style of operational semantics called a horizontal operational semantics, under which an evaluation returns not a single outcome but multiple outcomes. We have preliminary evidence that the horizontal operational semantics improves the ordinary operational semantics with respect to both execution time and accuracy in representing probability distributions.

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...

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This article presents a probabilistic language, called λ○, whose expressive power is beyond discrete distributions. Rich expressiveness of λ ○ is due to its use of sampling functions, that is, mappings from the unit interval (0.0, 1.0] to probability domains, in specifying probability distributions. As such, λ ○ enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of λ ○ is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

We investigate the construction of linear operators representing the semantics of probabilistic programming languages expressed via probabilistic transition systems. Finite transition relations, corresponding to finite automata, can easily be represented by finite dimensional matrices; for the infinite case we need to consider an appropriate generalisation of matrix algebras. We argue that C∗-algebras, or more precisely Approximately Finite (or AF) algebras, provide a sufficiently rich mathematical structure for modelling probabilistic processes. We show how to construct for a given probabilistic language a unique AF algebra A and how to represent the operational semantics of processes within this framework: finite computations correspond directly to operators in A, while infinite processes are represented by elements in the so-called strong closure of this algebra.

Abstract Concurrent constraint programming (ccp) is a model of concurrency for systems in which agents (also called processes) interact with one another by telling and asking information in a shared medium. Timed (or temporal) ccp extends ccp by allowing agents to be constrained by time requirements. The novelty of timed ccp is that it combines in one framework an operational and algebraic view based upon process calculi with a declarative view based upon temporal logic. This allows the model to benefit from two well-established theories used in the study of concurrency. This essay offers an overview of timed ccp covering its basic background and central developments. The essay also includes an introduction to a temporal ccp formalism called thentcc calculus. 1

Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higher-order logic formalization of the Standard Uniform random variable. We show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover and the proof steps have been summarized. This formalized Standard Uniform random variable can be transformed to formalize other continuous random variables, such as Uniform, Exponential, Normal, etc., by using various Non-uniform random number generation techniques. The formalization of these continuous random variables will enable us to perform error free probabilistic analysis of systems within the framework of a higher-order-logic theorem prover. For illustration purposes, we present the formalization of the Continuous Uniform random variable based on our Standard Uniform random variable and then utilize it to perform a simple probabilistic analysis of roundoff error in HOL. 1 1

Abstract. Probabilistic Choice Operators (PCOs) are convenient tools to model uncertainty in CP. They are useful to implement randomized algorithms and stochastic processes in the concurrent constraint framework. Their implementation is based on the random selection of a value inside a finite domain according to a given probability distribution. Unfortunately, the probabilistic choice of a PCO is usually delayed until the probability distribution is completely known. This is inefficient and penalizes their broader adoption in real-world applications. In this paper, we associate to PCO a filtering algorithm that prunes the variation domain of its random variable during constraint propagation. Our algorithm runs in O(n) where n denotes the size of the domain of the probabilistic choice. Experimental results show the practical interest of this approach. 1