Some Aspects of Linear Space Automata

Linear space automaton is introduced as a generalization of probabilistic automaton and its various properties are investigated. Linear space automaton has the abilities equivalent to probabilistic automaton but we can treat the former more easily than the latter because we can make use of properties of the linear space, successfully. First the solutions are given for the problems of connectivity, state equivalence, reduction and identification of linear space automata. Second, the matrix representation of linear space automaton is investigated and the relations between linear space automaton and probabilistic automaton are shown. Third, we discuss the closure properties of the family of all real functions on a free semigroup Σ* which are defined by linear space automata and then give a solution to the synthesis problem of linear space automata. Finally, some considerations are given to the problems of sets of tapes accepted by l.a.'s and also of operations under which the family of all the output functions of l.a.'s is not closed.