Abstract
We consider three sub-logics of the logic (±HP)*[FOs] (introduced in [Ste90]) and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems).
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S. R. BUSS AND L. HAY, On truth-table reducibility to SAT and the Difference Hierarchy over NP, Proc. 3rd Symp. on Structure in Complexity Theory, IEEE Press (1988), pp. 224–233.
R. FAGIN, Generalized first-order spectra and polynomial-time recognizable sets, Complexity of Computation (Ed. R.Karp), SIAM-AMS Proc, 7 (1974), pp. 27–41.
N. IMMERMAN AND S. LANDAU, The complexity of iterated multiplication, Proc. 4th Symp. on Structure in Complexity Theory, IEEE Press (1989), pp. 104–111.
N. IMMERMAN, Languages that capture complexity classes, SIAM J. Comput., 6, 4 (1987), pp. 760–778.
N. IMMERMAN, Nondeterministic space is closed under complementation, SIAM J. Comput., 17, 5 (1988), pp. 935–938.
I. A. STEWART, Using the Hamiltonian operator to capture NP, to appear, J. Comput. System Sci (extended abstract: Lecture Notes in Computer Science 468, Springer-Verlag, Berlin (1990), pp. 134–143).
I. A. STEWART, Comparing the expressibility of languages formed using NP-complete operators, J. Logic Computat., 1, No. 3 (1991), pp. 305–330 (extended abstract: Lecture Notes in Computer Science 484, Springer-Verlag, Berlin (1991), pp. 276–290).
I. A. STEWART, On completeness for NP via projection translations, to appear, Maths Systems Theory (extended abstract to appear: Proc. Computer Science Logic (1991), Lecture Notes in Computer Science, Springer-Verlag, Berlin).
I. A. STEWART, Complete problems for logspace involving lexicographic first paths in graphs, to appear, Proc. 17th International Workshop on Graph-Theoretic Concepts in Computer Science (1991), Lecture Notes in Computer Science, Springer-Verlag, Berlin.
I. A. STEWART, Complete problems for symmetric logspace involving free groups, Inform. Process. Lett., 40 (1991), pp. 263–267.
I. A. STEWART, Complete problems involving Boolean labelled structures and projection translations, to appear, J. Logic Computat.
L. J. STOCKMEYER, The polynomial-time hierarchy, Theor. Comp. Sci., 3 (1977), pp. 1–22.
P. SZELEPCSÉNYI, The method of forcing for nondeterministic automata, Bull. European Association Theor. Comp. Sci., 33 (1987), pp. 96–100.
K. W. WAGNER, Number-of-queries hierarchies, Rep. No. 158, Institute of Mathematics, Univ. of Augsburg, Germany (1987).
K. W. WAGNER, Bounded query classes, SIAM J. Comput., 19, 5 (1990), pp. 833–846.
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© 1992 Springer-Verlag Berlin Heidelberg
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Stewart, I.A. (1992). Logical characterizations of bounded query classes I: Logspace oracle machines. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023899
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DOI: https://doi.org/10.1007/BFb0023899
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