Journal of Logic Programming
Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Fractals everywhere
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
Negation as failure using tight derivations for general logic programs
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
Unsolvable problems for SLDF resolution
Journal of Logic Programming
Logic for applications
Handbook of logic in computer science (vol. 3): semantic structures
Handbook of logic in computer science (vol. 3): semantic structures
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Learning from interpretation transition
Machine Learning
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We show how to regard covered logic programs as cellular automata. Covered logic programs are ones for which every variable occurring in the body of a given clause also occurs in the head of the same clause. We generalize the class of register machine programs to permit negative literals and characterize the members of this class of programs as n‐state 2‐dimensional cellular automata. We show how monadic covered programs, the class of which is computationally universal, can be regarded as 1‐dimensional cellular automata. We show how to continuously (and differentiably) deform 1‐dimensional cellular automata from one to another and understand the arrangement of these cellular automata in a separable Hilbert space over the real numbers. The embedding of the cellular automata of fixed radius r is a linear mapping into {\mathbf{R}}^{2^{2r+1}} in which a cellular automaton’s transition function is the attractor of a state‐governed iterated function system of affine contraction mappings. The class of covered monadic programs having a particular fixed point has a uniform arrangement in an affine subspace of the Hilbert space \ell^2. Furthermore, these programs are construable as almost everywhere continuous functions from the unit interval \{x\mid 0 \leq x \leq 1\} to the real numbers {\mathbf{R}}. As one consequence, in particular, we can define a variety of natural metrics on the class of these programs. Moreover, for each program in this class, the set of initial segments of the program’s fixed points, with respect to an ordering induced by the program’s dependency relation, is a regular set.