Universal Hypergraphic Automata Representation by Autonomous Input Symbols

Hypergraphic automata are automata with state sets and input symbol sets being hypergraphs which are invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are automata Atm(H1,H2). Here,H1is a state hypergraph,H2is classified as an output symbol hypergraph, andS= EndH1× Hom(H1,H2) is an input symbol semigroup. Such automata are called universal hypergraphic automata. The input symbol semigroupSof such an automaton Atm(H1,H2) is an algebra of mappings for such an automaton. Semigroup properties are interconnected with properties of the algebraic structure of the automaton. Thus, we can study universal hypergraphic automata with the help of their input symbol semigroups. In this paper, we investigated a representation problem of universal hypergraphic automata in their input symbol semigroup. The main result of the current study describes a universal hypergraphic automaton as a multiple-set algebraic structure canonically constructed from autonomous input automaton symbols. Such a structure is one of the major tools for proving relatively elementary definability of considered universal hypergraphic automata in a class of semigroups in order to analyze interrelation of elementary characteristics of universal hypergraphic automata and their input symbol semigroups. The main result of the paper is the solution of this problem for universal hypergraphic automata for effective hypergraphs withp-definable edges. It is an important class of automata because such an algebraic structure variety includes automata with state sets and output symbol sets represented by projective or affine planes, along with automata with state sets and output symbol sets divided into equivalence classes. The article is published in the authors' wording.

Tool Operation Recognition Based on Robust Optical Flow and HMM from Short-Time Sequential Image Data

This paper discusses a method to precisely recognize which tool is to be used based on the optical flow and HMM from short-time sequential images that operate a variety of hand-operated carpenter tools in the real environment. Operation recognition from a single-eye camera includes problems on differences in the difficulty of fixing the shape of the tool and poor motion periodicity due to occlusion of the fingers, back of the hand, and arm of the operator. This paper models operation without separating the integrated motions of the hand and tool and recognizes it with four tools divided into different categories from these motions. The optical flow method via the nonlinear robust function is used to suppress possible error caused by discontinuous motion components, HMM with a flexible time axis is applied to implement learning and recognition. The average vector of the optical flow mapped into the conversion diagram was designed to output symbol numbers for the generation of symbol time series. The three subjects have been asked to operate given tools for conducting learning recognition experiments. The number of input and output symbol has been varied for comparison. This results in a maximum of 100% recognition on the average for learning and recognition by the same person and in a maximum of 88.6% for learning and recognition by different persons. This method has been proven robust and effective because an average of 79.4% or higher recognition rate has been obtained even for short data of input symbol 5 (equivalent to 0.2 seconds) difficult to recognize.