Dense-choice Counter Machines revisited
Florent Bouchy, Alain Finkel, Pierluigi San Pietro
TL;DR
This paper revisits Dense-choice Counter Machines, clarifies their definition, and provides new decidability and undecidability results using logical characterizations of their configuration reachability.
Contribution
It extends the definition of Dense Counter Machines to align with discrete Counter Machines and offers new theoretical results on their computational properties.
Findings
Logical characterization of reachable configurations
Decidability results for reversal-bounded Dense-choice Counter Machines
Undecidability results for certain configurations
Abstract
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines, and we provide new undecidability and decidability results. Using the first-order additive mixed theory of reals and integers, we give a logical characterization of the sets of configurations reachable by reversal-bounded Dense-choice Counter Machines.
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