Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning

Does the solar system compute the laws of motion?

The counterfactual account of physical computation is simple and, for the most part, very attractive. However, it is usually thought to trivialize the notion of physical computation insofar as it implies ‘limited pancomputationalism’, this being the doctrine that every deterministic physical system computes some function. Should we bite the bullet and accept limited pancomputationalism, or reject the counterfactual account as untenable? Jack Copeland would have us do neither of the above. He attempts to thread a path between the two horns of the dilemma by buttressing the counterfactual account with extra conditions intended to block certain classes of deterministic physical systems from qualifying as physical computers. His theory is called the ‘algorithm execution account’. Here we show that the algorithm execution account entails limited pancomputationalism, despite Copeland’s argument to the contrary. We suggest, partly on this basis, that the counterfactual account should be accepted as it stands, pancomputationalist warts and all

A Review of Verbal and Non-Verbal Human-Robot Interactive Communication

In this paper, an overview of human-robot interactive communication is presented, covering verbal as well as non-verbal aspects of human-robot interaction. Following a historical introduction, and motivation towards fluid human-robot communication, ten desiderata are proposed, which provide an organizational axis both of recent as well as of future research on human-robot communication. Then, the ten desiderata are examined in detail, culminating to a unifying discussion, and a forward-looking conclusion

Computer simulations, mathematics and economics

Economists lise different kinds of computer simulation. However, there is little attention on the theory of simulation, which is considered either a technology or an extension of mathematical theory or, else, a way of modelling that is alternative to verbal description and mathematical models. The paper suggests a systematisation of the relationship between simulations, mathematics and economics. In particular, it traces the evolution of simulation techniques, comments some of the contributions that deal with their nature, and, finally, illustrates with some examples their influence on economie theory. Keywords: Computer simulation, economie methodology, multi-agent programming techniques.

Connectionist natural language parsing

The key developments of two decades of connectionist parsing are reviewed. Connectionist parsers are assessed according to their ability to learn to represent syntactic structures from examples automatically, without being presented with symbolic grammar rules. This review also considers the extent to which connectionist parsers offer computational models of human sentence processing and provide plausible accounts of psycholinguistic data. In considering these issues, special attention is paid to the level of realism, the nature of the modularity, and the type of processing that is to be found in a wide range of parsers

Decidability and Universality in Symbolic Dynamical Systems

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2: minor orthographic changes v3: section 5.2 (collatz functions) mathematically improved v4: orthographic corrections, one reference added v5:27 pages. Important modifications. The formalism is strengthened: temporal logic replaced by finite automata. New results. Submitte