A note on real-time one-way alternating multicounter machines

Abstract

This paper investigates several properties of one-way alternating multicounter machines which operate in real time, and shows that (1) for each k⩾1, one-way alternating k-counter machines (1acm( k)'s) which operate in real time are less powerful than 1 acm( k+1)'s which operate in real time, (2) for each k⩾2, 1acm( k)'s which operate in real time are less powerful than 1acm( k)'s which operate in linear time, and (3) for each k⩾1, the class of sets accepted by 1acm( k)'s which operate in real time is not closed under concatenation with regular sets, Kleene closure, reversal and length-preserving homomorphism.