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Bounds in the propagation of selection into logic programs. (English) Zbl 0796.68054

Summary: We consider the problem of propagating selections into logic programs (i.e., recursive Horn clause programs). In particular, we study the class of chain programs and formalize selection propagation on such a logic programs as: the task of finding an equivalent program containing only monadic derived predicates. Selection propagation is always possible for database programs (i.e., first-order formula programs) and is often a desirable optimization. We show that the situation is qualitatively different for logic programs. We associate a context-free language \(L(H)\) with every chain program \(H\). We show that, given \(H\), propagating a selection involving some constant is possible iff \(L(H)\) is regular and therefore undecidable. We also show that propagating a selection of the form \(p(X,X)\) is possible iff \(L(H)\) is finite and therefore decidable. We demonstrate the connection of these two cases, respectively, with the weak monadic second-order theory of one successor and with monadic generalized spectra. We further clarify the analogy between chain programs and context-free languages from the point of view of program equivalence, first-order expressibility over finite structures, and selection propagation heuristics.

MSC:

68N17 Logic programming
68P15 Database theory
68Q45 Formal languages and automata
68N01 General topics in the theory of software
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[1] Afrati, F.; Papadimitridu, C., The parallel complexity of simple chain queries, (Proceedings, 6th PODS (1987), ACM), 210-214
[2] Aho, A. V.; Ullman, J. D., Universality of data retrieval languages, (Proceedings, 6th POPL (1979), ACM), 110-117
[3] Ajtai, M.; Fagin, R., Reachability is harder for directed than for undirected graphs, (Proceedings, 29th FOCS. Proceedings, 29th FOCS, IEEE (1988)), 358-367 · Zbl 0708.03016
[4] Apt, K. R.; van Emden, M. H., Contributions to the theory of logic programming, Assoc. Comput. Mach., 29, No. 4, 841-862 (1982) · Zbl 0483.68004
[5] Bancilhon, F.; Maier, D.; Sagiv, Y.; Ullman, J. D., Magic sets and other strange ways to implement logic programs, (Proceedings, 5th PODS (1986), ACM), 1-14
[6] Bancilhon, F.; Ramakrishnan, R., An amateur’s introduction to recursive query processing strategies, (Proceedings, 86 Sigmod (1986), ACM), 16-52
[7] Beeri, C.; Ramakrishnan, R., On the power of magic, (Proceedings, 6th PODS (1987), ACM), 269-283
[8] Blattner, M., The unsolvability of the equality problem for sentential forms of context free grammars, J. Comput. System Sci., 7, No. 5, 463-468 (1973) · Zbl 0273.68054
[9] Buchi, J. T., Weak second order arithmetic and finite automata, Z. Math. Logik, 6, 66-92 (1960) · Zbl 0103.24705
[10] Chandra, A. K.; Harel, D., Horn clause programs and generalizations, J. Logic Programm., 2, 1-15 (1985) · Zbl 0583.68058
[11] Chandra, A. K.; Harel, D., Structure and complexity of relational queries, J. Comput. System Sci., 25, No. 1, 99-128 (1982) · Zbl 0511.68073
[12] Cosmadakis, S.; Kanellakis, P., Parallel evaluation of recursive rule queries, (Proceedings, 5th PODS (1986), ACM), 280-293
[13] Cosmadakis, S. S.; Gaifman, H.; Kanellakis, P. C.; Vardi, M. Y., Decidable optimization problems for database logic programs, (Proceedings, 20th STOC (1988), ACM), 477-490
[14] Derougemont, M., Uniform definability of finite structures with successor, (Proceedings, 16th STOC (1984), ACM), 409-417
[15] Elgot, C., Decision problems of finite automaton design and related arithmetics, Trans. Amer. Math. Soc., 98, 21-51 (1961) · Zbl 0111.01102
[16] Fagin, R., Monadic generalized spectra, Z. Math. Logik, 21, 89-96 (1975) · Zbl 0317.02054
[17] Gaifman, H.; Mairson, H.; Sagiv, Y.; Vardi, M. Y., Undecidable optimization problems for database logic programs, (Proceedings, 2nd LICS (1987), IEEE), 106-115 · Zbl 0785.68021
[18] Gaifman, H.; Vardi, M. Y., A simple proof that connectivity of finite graphs is not first order definable, Bulletin EATCS, 26, 44-45 (1985)
[19] Henschen, L. J.; Naqvi, S. A., On compiling queries in recursive first-order databases, Assoc. Comput. Mach., 31, No. 1, 47-85 (1984) · Zbl 0629.68095
[20] Hopcroft, J. E.; Ullman, J. D., Introduction to Automata Theory, Languages, and Computation (1979), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0196.01701
[21] Moschovakis, Y. N., Elementary Induction on Abstract Structures (1974), North-Holland: North-Holland Amsterdam · Zbl 0307.02003
[22] Naughton, J. F., One-sided recursions, (Proceedings, 6th PODS (1987), ACM), 340-349
[23] Sacca, D.; Zaniolo, C., On the implementation of a simple class of logic queries for databases, (Proceedings, 5th PODS (1986), ACM), 16-23
[24] Sagiv, Y., Optimizing datalog programs, (Proceedings, 6th PODS (1987), ACM), 349-362
[25] Shmueli, O., Decidability and expressiveness aspects of logic queries, (Proceedings, 6th PODS (1987), ACM), 237-249
[26] Thatcher, J. W.; Wright, J. B., Generalized finite automata theory with an application to a decision problem of second order logic, Math. Systems Theory, 2, No. 1, 57-81 (1968) · Zbl 0157.02201
[27] Ullman, J. D., Principles of Database Systems (1983), Cpmput. Sci. Press: Cpmput. Sci. Press Rockville, MD
[28] Ullman, J. D., Implementation of logical query languages for databases, ACM Trans. Database Systems, 10, 289-321 (1985) · Zbl 0573.68060
[29] Ullman, J. D.; Van Gelder, A., Parallel complexity of logical query programs, Algorithmica, 3, No. 1, 5-42 (1988) · Zbl 0646.68062
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