Automata

Abstract

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Resituating Cognition.

“…Theories of cognition have ranged from British associationist to British quantum mechanical (Penrose, 1994). Our formal model of cognition is that of an automaton with content-addressable memory in the form of finite rewritable stores-in particular a linear bounded automaton (Hopcroft & Ullman, 1979;Hopkins & Moss, 1976). To be clear, this assertion concerns the nature of our preferred model of cognition; it may characterize cognition, but cognition is both more, and more constrained, than such automata, as it must satisfy the other aspects of its definition.…”

“…Finite automata can distinguish only what can be represented in their memory. When that memory is augmented with push-down stores, or finite rewritable drives, or infinite tapes, increasingly powerful computations become possible that correspond, respectively, to Chomsky's (1956) context-free grammars, context-sensitive grammars, and universal Turing machines (Hopkins & Moss, 1976). The computation of very simple animals may correspond to the simplest of these automata, and be described in other words by associationist principles.…”

The Four Causes of Behavior

“…Computers can instantiate all of the associative models of conditioning, and their inverses. For the computational metaphor to become a model, it must be restricted to a proper subset of what computers can do; one way to accomplish this is via the theory of automata (Hopkins & Moss, 1976). Automata theory is a formal characterization of computational architectures.…”

The new science of complexity

“…In part, this assertion is false: note that the binary specification of a single state x n in the logistic map f(x) = 4x(1-x) requires precisely N(n) = 2 n (N o -2) + 2 bits, where N o is the number of bits in any simple initial condition x o = .ε 1 ...ε No 000... . If the string representing x n is arbitrarily truncated to m≤N(n) bits, then after on the order of m iterations the first bit (and all other bits) in x n' , where n' ≈ n + m, is completely wrong [7]. Multiplication of two finite binary strings of arbitrary length cannot be carried out on any fixed-state machine [5], and if multiplication is done incorrectly at any stage then after only a few more iterations the bits in x n cannot be known even to one-bit accuracy.…”

“…I will explain why economic and other social phenomena lie beyond the bounds of understanding from the standpoint of dynamical modelling that attempts to describe the time-evolution of systems, even if the goal is merely to extract the crudest features like coarsegrained statistics. I will give reasons why mathematical laws of economics do not exist in any empirical or computationally-effective [7] sense. In order to make my argument precise, I first review some little-known and poorly-understood facts about deterministic dynamical systems that include Newton's laws of motion for particles and rigid bodies, and also nondiffusive chemically-reacting systems.…”