# Some positive results for boundedness of multiple recursive rules

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## Abstract

Following results are sketched in this extended abstract: (1) Datalog recursive programs where each rule has at most one subgoal called *unit recursions* are shown to be bounded, with an effective construction of equivalent non-recursive programs. (2) A *generalized chain program*, which allow IDB predicates of arbitrary arity and remove the uniqueness condition of chain variables, is bounded if and only if it is a unit recursion. (3) The characterization of uniform unboundedness for linear sirups in [NS] is extended to a substantial superclass called class *C*^{+}. (4) Boundedness for class *C*^{+} with multiple exit rules is decidable in polynomial space. (5) Predicate boundedness is decidable in doubly exponential time for a large class of Datalog programs that properly contains all connected monadic programs. (6) For binary linear programs, program boundedness is decidable if each recursive predicate is defined by at most one recursive rule; predicate boundedness is also decidable if each recursive predicate is mutually recursive with one another.

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