Abstract
We propose a novel technique that maps decision problems in WS1S (weak monadic second-order logic with n successors) to the problem of query evaluation of Complex-value Datalog queries. We then show how the use of advanced implementation techniques for Logic Programs, in particular the use of tabling in the XSB system, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique based on variants of tabling and goal reordering. Although our primary focus is on WS1S, it is straightforward to adapt our approach for other logics with existing automata-theoretic decision procedures, for example WS2S.
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References
Abiteoul, S., Beeri, C.: The power of languages for the manipulation of complex values. VLDB Journal 4(4), 727–794 (1995)
Beeri, C., Naqvi, S., Shmueli, O., Tsur, S.: Set construction in a logic database language. JLP 10(3&4), 181–232 (1991)
Beeri, C., Ramakrishnan, R.: On the power of Magic. JLP 10(1/2/3&4), 255–299 (1991)
Bernholtz, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 142–155. Springer, Heidelberg (1994)
Bryant, R.E.: Symbolic boolean manipulation with Ordered Binary Decision Diagrams. ACM Computing Surveys 24(3), 293–318 (1992)
Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundl. Math. 6, 66–92 (1960)
Büchi, J.R.: On a decision method in restricted second-order arithmetic. In: Proc. Int. Congr. for Logic, Methodology and Philosophy of Science, pp. 1–11 (1962)
Chaudhuri, S.: An overview of query optimization in relational systems. In: PODS, pp. 34–43 (1998)
Chen, W., Swift, T., Warren, D.S.: Efficient top-down computation of queries under the well-founded semantics. JLP 24(3), 161–199 (1995)
Chen, W., Warren, D.S.: Query evaluation under the well-founded semantics. In: PODS, pp. 168–179 (1993)
Chimenti, D., Gamboa, R., Krishnamurthy, R., Naqvi, S.A., Tsur, S., Zaniolo, C.: The LDL system prototype. IEEE Trans. Knowl. Data Eng. 2(1), 76–90 (1990)
Dawson, S., Ramakrishnan, C.R., Skiena, S., Swift, T.: Principles and practice of unification factoring. TOPLAS 18(5), 528–563 (1996)
Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc. 98, 21–52 (1961)
Freire, J., Swift, T., Warren, D.S.: Beyond depth-first strategies: Improving tabled logic programs through alternative scheduling. Journal of Functional and Logic Programming 1998(3) (1998)
Henriksen, J.G., Jensen, J.L., Jörgensen, M.E., Klarlund, N., Paige, R., Rauhe, T., Sandholm, A.: MONA: Monadic second-order logic in practice. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 89–110. Springer, Heidelberg (1995)
Janin, D., Walukiewicz, I.: Automata for the modal μ-calculus and related results. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 552–562. Springer, Heidelberg (1995)
Klarlund, N.: MONA & FIDO: The logic-automaton connection in practice. In: Computer Science Logic, pp. 311–326 (1997)
Klarlund, N., Møller, A., Schwartzbach, M.I.: MONA implementation secrets. Int. J. Found. Comput. Sci. 13(4), 571–586 (2002)
McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Information and Control 9, 521–530 (1966)
Mumick, I.S.: Query Optimization in Deductive and Relational Databases. PhD thesis, Department of Computer Science, Stanford University (1991)
Naqvi, S., Tsur, S.: A Logical Language for Data and Knowledge Bases. Computer Science Press (1989)
Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141, 1–35 (1969)
Ramakrishnan, I., Rao, P., Sagonas, K., Swift, T., Warren, D.: Efficient tabling mechanisms for logic programs. In: Proc. ICLP, pp. 697–711 (1995)
Ramakrishnan, R., Bothner, P., Srivastava, D., Sudarshan, S.: CORAL - a database programming language. In: Workshop on Deductive Databases (1990)
Ramakrishnan, R., Srivastava, D., Sudarshan, S.: Coral - control, relations and logic. In: Proc. VLDB Conference, pp. 238–250 (1992)
Ramakrishnan, R., Srivastava, D., Sudarshan, S., Seshadri, P.: The CORAL deductive system. VLDB Journal 3(2), 161–210 (1994)
Sagonas, K.F., Swift, T., Warren, D.S.: XSB as an efficient deductive database engine. In: Proc. SIGMOD, pp. 442–453 (1994)
Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages, vol. 3, Springer, Heidelberg (1997)
Ullman, J.D.: Principles of Database and Knowledge-Base Systems, vol. 1&2. Computer Science Press (1989)
Unel, G., Toman, D.: Deciding weak monadic second-order logics using complex-value datalog. In: Proc. LPAR (Short Paper) (2005)
Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. LICS, pp. 322–331 (1986)
Whaley, J., Lam, M.S.: Cloning-based context-sensitive pointer alias analysis using binary decision diagrams. In: Proc. PLDI 2004, pp. 131–144 (2004)
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Unel, G., Toman, D. (2007). Logic Programming Approach to Automata-Based Decision Procedures. In: Dahl, V., Niemelä, I. (eds) Logic Programming. ICLP 2007. Lecture Notes in Computer Science, vol 4670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74610-2_12
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DOI: https://doi.org/10.1007/978-3-540-74610-2_12
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