Algebraic structure theory of sequential machinesJuris Hartmanis
Algebraic structure theory of sequential machines
by Juris Hartmanis · first published 1966
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You may be interested in: Hartmanis & Stearns, Algebraic Structure Theory of Sequential Machines (1966)
on “The topos theory of computing: introduction to the mathematics of dataflow [pdf]” ↗Upon review, Hartmanis and Stearns appear to have come closest to my work. I would recommend readers take a look at Algebraic Structure Theory of Sequential Machines (1966) prior to my paper to get a background motivation for my treatment of the subject. The idea of partition pairs in that textbook coincides with epimorphism classes in the Sierpinski topos. So basically,…
on “The topos theory of computing: introduction to the mathematics of dataflow [pdf]” ↗The basic idea of an information flow was introduced by Hartmanis and Stearns in the algebraic structure theory of sequential machines. This is a beautiful and elegant formalism for describing how information flows in sequential machines. Now using new mathematics I have put this theory on its highest level of generality. But its not…
on “A new way of programming with information flows” ↗…has an incredibly remarkable logic of quotients. It has been shown that the dual logic of quotients in Sets^(->) is intuitively similar to the partition pairs construction of Hartmanis and Stearns in Algebraic Structure Theory of Sequential Machines (1966). So the immense power of the topos Sets^(->) is enough to capture their central construction for creating a computational structure theory, and mine. All this demonstrates that Sets^(->) by itself…
on “The Logic of Functional Programming” ↗Love the autobio. Noise and the differential reminds me of Hartmanis & Stearns, Algebraic Structure Theory of Sequential Machines (1966), in that the latter roughly studied how our knowledge of what state an automaton is in diffuses over repeated transitions.
on “Quantum Won't Replace Your Computer” ↗