# Some positive results for boundedness of multiple recursive rules

## 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.

## Keywords

Conjunctive Query Recursive Rule Datalog Program Persistent Variable Target Link## Preview

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## References

- [Ab]Abiteboul, S.: Boundedness is undecidable for Datalog programs with a single recursive rules. IPL 32 (1989), pp. 281–287Google Scholar
- [AP]Afrati, F., Papadimitriou, C.H.: The parallel complexity of simple chain queries. ACM PODS, 1987, pp. 210–213Google Scholar
- [BKBR]Beeri, C., Kanellakis, P.C., Bancilhon, F., Ramakrishnan, R.: Bounds on the propagation of selection into logic programs. ACM PODS, 1987, pp. 214–226Google Scholar
- [CGKV]Cosmadakis, S., Gaifman, H., Kanellakis, P.C., Vardi, M.Y.: Decidable optimizations for datalog logic programs. ACM Symp. on Theory of Computing, 1988, pp. 477–490Google Scholar
- [CM]Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational databases. ACM Symp. on Theory of Computing, 1977, pp. 77–90Google Scholar
- [GMSV]Gaifman, H., Mairson, H., Sagiv, Y., Vardi, M.Y.: Undecidable optimization problems for database logic programs. Proc. of 2nd IEEE Symposium on Logic in Computer Science, 1987, pp. 106–115Google Scholar
- [Gu]Guessarian, I.: Deciding boundedness for uniformly connected Datalog programs. Lecture Notes in Computer Science 470, ICDT 1990, pp. 395–405Google Scholar
- [HKMV]Hillebrand, G.G., Kanellakis, P.C., Mairson, H.G., Vardi, M.Y.: Tools for datalog boundedness. ACM PODS, 1991, pp. 1–12Google Scholar
- [Io]Ioanidis, Y.E.: A time bound on the materialization of some recursively defined views. VLDB, 1985, pp. 219–226Google Scholar
- [NS]Naughton, J., Sagiv, Y.: A decidable class of bounded recursions. ACM PODS, 1986, pp. 227–236Google Scholar
- [Na]Naughton, J.: Data independent recursion in deductive databases. JCSS 38 (1989), pp. 259–289Google Scholar
- [S]Sagiv, Y.: On computing restricted projections of representative instances. ACM PODS, 1985, pp. 171–180Google Scholar
- [Va]Vardi, M.Y.: Decidability and undecidability results for boundedness of linear recursive queries. ACM PODS, 1988, pp. 341–351Google Scholar