Counter Machines and Veri cation

We study various generalizations of reversal-bounded multicounter machines and show that they have decidable emptiness, innniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linear-relation tests among the counters and parameterized constants (e.g., \Is 3x?5y?2D 1 +9D 2 < 12?", where x; y are counters, and D 1 ; D 2 are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the veriica-tion/debugging of safety properties in innnite-state transition systems. For example, we show that (binary, forward, and backward) reachability and safety are solvable for these machines.