Conditional programmed automata.
Jan Mareš · Czech digital mathematics library · 1978
Automata JAN MAREŠ A conditional programmed automaton and functions computable on it are defined and, utilizing certain graphs, connections between those automata and functions are studied.DENOTATIONS N denotes the set of all positive integers, N 0 = /Vu{0}; for n e N 0 denote fi = {1,2,..., n} (thus, 6 = 0).If A, B, C are sets, write C = A u £ if (C = AuBet/4nB = 0).Let f : A -* B denote that / is a mapping of A into B. A mapping g of a nonempty set A 0 c A into a set B is called a mapping from A into B and denoted by g : A +-> B. Dom/ and Ran/ denote the domain and the range of/, respectively.Let n e N, let A u ..., A" be nonempty sets and let A = A! x ... x A" ; then for i e M define projections nf : A -» A ; by a prescription Tc^ax, ..., a") = a ; .