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Counter machines and verification problems. (English) Zbl 1061.68095
Summary: We study various generalizations of reversal-bounded multicounter machines and show that they have decidable emptiness, infiniteness, 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 verification/debugging of safety properties in infinite-state transition systems. For example, we show that (binary, forward, and backward) reachability and safety are solvable for these machines.

##### MSC:
 68Q45 Formal languages and automata 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68Q60 Specification and verification (program logics, model checking, etc.)
ALGOL 60
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##### References:
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