Abstract
A new model of computation called VH-system is introduced. It is a formalization of domino tilings. We show how the semantics of nondeterminism on VH-systems, being a natural counterpart of the machinery of tilings, can be modified to cover both deterministic and alternating computations. As a by-product we present a new proof of the fact that the satisfiability problem of boolean Horn formulas is complete in PTIME.
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References
Chandra, A.K., D.C. Kozen, and L.J. Stockmeyer, Alternation, J. ACM 28 (1981) 114–133.
Chlebus, B.S., Domino-tiling games, submitted to J. Comput. Syst. Sci.
Chlebus, B.S., Subclasses of boolean formulas and their satisfiability problems, to appear.
van Emde Boas, P., Dominoes are forever, 1-st GTI Workshop, Paderborn, 75–95, 1983.
Garey, M.R., and D.S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness", H. Freeman, San Francisco, 1979.
Harel, D., A simple highly undecidable domino problem (or, a lemma on infinite trees, with applications), Proc. Logic and Computation Conference, Clayton, Victoria, Australia, 1984.
Harel, D., Recurring dominoes: making the highly undecidable highly understandable, in M. Karpinski (ed.), Foundations of Computing Theory, Proc. 1983 FCT Conf. Borgholm Sweden, Springer LNCS 158 (1983) 177–194; also to appear in Annals of Discrete Math.
Hopcroft, J.E., and J.D. Ullman, "Introduction to Automata Theory, Languages and Computation", Addison-Wesley, Reading, MA, 1979.
Jones, N.D., and W.T. Laaser, Complete problems for deterministic polynomial time, Theor. Comput. Sci. 3 (1976) 105–117.
Levin, L.A., Universal sequential search problems, (translation), Problems in Information Transmission 9 (1973) 265–266.
Lewis, H.R., Complexity of solvable cases of the decision problem for the predicate calculus, 19th FOCS, 35–47, 1978.
Lewis, H.R., "Unsolvable Classes of Quantificational Formulas", Addison-Wesley, Reading, 1979.
Lewis, H.R., and C.H. Papadimitriou, "Elements of the Theory of Computation", Prentice-Hall, 1981.
Savelsberg, M.P.W., and P. van Emde Boas, BOUNDED TILING, an alternative to SATISFIABILITY?, in G. Wechsung ed. Proc. 2nd Frege Conference, Schwerin 1984, Akademie Verlag, Mathematische Forschung 20 (1984) 354–363.
Stockmeyer, L.J., The polynomial-time hierarchy, Theor. Comput. Sci. 3 (1976) 1–22.
Wang, H., Proving theorems by pattern recognition II, Bell System Tech. J. 40 (1961) 1–4.
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© 1985 Springer-Verlag Berlin Heidelberg
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Chlebus, B.S. (1985). From domino tilings to a new model of computation. In: Skowron, A. (eds) Computation Theory. SCT 1984. Lecture Notes in Computer Science, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16066-3_4
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DOI: https://doi.org/10.1007/3-540-16066-3_4
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