A closed-form evaluation for Datalog queries with integer (gap)-order constraints
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We address termination analysis for the class of gap-order constraint systems (GCS), an (infinitely-branching) abstract model of counter machines recently introduced in [8], in which constraints (over ℤ) between the variables of the source state and the target state of a transition are gap-order constraints (GC) [18]. GCS extend monotonicity constraint systems [4], integral relation automata [9], and constraint automata in [12]. Since GCS are infinitely-branching, termination does not imply strong termination, i.e. the existence of an upper bound on the lengths of the runs from a given state. We show the following: (1) checking strong termination for GCS is decidable and Pspace-complete, and (2) for each control location of the given GCS, one can build a GC representation of the set of variable valuations from which strong termination does not hold.