Remarks on blind and partially blind one-way multicounter machines

Abstract

We consider one-way nondeterministic machines which have counters allowed to hold positive or negative integers and which accept by final state with all counters zero. Such machines are called blind if their action depends on state and input alone and not on the counter configuration. They are partially blind if they block when any counter is negative (i.e., only nonnegative counter contents are permissible) but do not know whether or not any of the counters contain zero. Blind multicounter machines are equivalent in power to the reversal bounded multicounter machines of Baker and Book [1], and for both blind and reversal bounded multicounter machines, the quasirealtime family is as powerful as the full family. The family of languages accepted by blind multicounter machines is the least intersection closed semiAFL containing { a n b n | n⩾0} and also the least intersection closed semiAFL containing the two-sided Dyck set on one letter. Blind multicounter machines are strictly less powerful than quasirealtime partially blind multicounter machines. Quasirealtime partially blind multicounter machines accept the family of computation state sequences or Petri net languages which is equal to the least intersection closed semiAFL containing the one-sided Dyck set on one letter but is not a principal semiAFL. For partially blind multicounter machines, as opposed to blind machines, linear time is more powerful than quasirealtime. Assuming that the reachability problem for vector addition systems is decidable [16], partially blind multicounter machines accept only recursive sets and do not accept even {a nb n|n⩾0 ∗ , and quasirealtime partially blind multicounter machines are less powerful than general quasirealtime multicounter machines.