It is known that the set of powers of two is recognizable by a finite automaton if the notational base used for representing numbers is itself a power of two but is unrecognizable in all other bases.â€¦ (More)

An infinite sequence over a finite alphabet is regular if the indices of those positions at which each given symbol occurs in the sequence constitute a set of numbers which in suitable base isâ€¦ (More)

Lower bound~ on the capacity and on the product of capacity and computation time are obtained for machines which recognize the set of squares. The bound on capacity is approached to within a factorâ€¦ (More)

We establish an algebraic condition which is necessary and sufficient for a word function of finite rank to be expressible as the sum of two functions, each of rank lower than that of the givenâ€¦ (More)

We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than oneâ€¦ (More)

This paper discusses some of the origins of Computational Complexity. It is shown that they can be traced back to the late 1950â€™s and early 1960â€™s. In particular, it is investigated to what extentâ€¦ (More)