Reset machines

AbstractA reset tape has one read-write head which moves only left-to-right except that the head can be reset once to the left end and the tape rescanned; a multiple-reset machine has reset tapes as auxiliary storage and a one-way input tape. Linear time is no more powerful than real time for nondeterministic multiple-reset machines and so the family MULTI-RESET of languages accepted in real time by nondeterministic multiple-reset machines is closed under linear erasing. MULTI-RESET is closed under Kleene. It can be characterized as the smallest family of languages containing the regular sets and closed under intersection and linear-erasing homomorphic duplication or as the smallest intersection-closed semiAFL containing COPY = {ww | w in {a, b}∗}. A circular tape is read full-sweep from left-to-right only and then reset to the left, any number of times; a nonwriting circular tape cannot be altered after the first sweep. For nondeterministic machines operating in real time, multiple reset tapes, circular tapes or nonwriting circular tapes have the same power. Languages in MULTI-RESET can be accepted in real time by nondeterministic machines using only three reset tapes or using only one reset tape and one nonwriting circular tape

Effective Theories for Circuits and Automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure

Cascade synthesis of finite-state machines

One can construct any finite-state machine as a cascade interconnection of machines whose inputs either permute the states or reset them all to one state. Each permutation group needed in the construction is a homomorphic image of a group generated by the action of a set of input sequences on a state subset of the original machine. Proofs of these facts will be given and their application to the Krohn-Rhodes theory described

Manufacturing: the new case for vertical integration

The article argues that the solid corporation will continue to view vertical integration as a critical part of manufacturing reform. Manufacturing reform and backward integration are related in insidious ways to the three stages of production over which the big manufacturers preside. Without integration, technology-based corporations may wind up pauperizing upstream components producers in order to earn premiums for downstream assembly and distribution operations, businesses that are comparatively flush. The authors elaborate on the production process which are divided into three stages: the assembly stage, the sub-assembly stage, and the component stage; at each there is a separate tier of factories and businesses. They also discuss the implications of the Western companies' leaning toward less integration