N. Immermann. Languages that capture complexity classes. SIAM J. Comput., 16(4), 1988. Home/Search Document Not in Database Summary Related Articles Check |
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The Monadic Quantifier Alternation Hierarchy over Graphs is.. - Matz, Thomas (1998) (12 citations) (Correct)
....formulas over grids are also studied in [BM92] The authors establish a close connection to multihead automata over a two dimensional input tape. The arity of transitive closure operators corresponds in a way to the number of heads of an automaton. This gives more insight into the results of [Imm88], where it is shown that first order transitive closure formulas of unbounded arity have the same power as non deterministic logarithmic space bounded Turing machines. Both [BM92] and [Imm88] show that the results are also true in the situation where determinism is requested for TC operators and ....
....corresponds in a way to the number of heads of an automaton. This gives more insight into the results of [Imm88] where it is shown that first order transitive closure formulas of unbounded arity have the same power as non deterministic logarithmic space bounded Turing machines. Both [BM92] and [Imm88] show that the results are also true in the situation where determinism is requested for TC operators and machines. In [MP94] the authors study formulas of bounded arity (instead of monadic as in our case) in a more general context of arbitrary finite structures (instead of just graphs and grids ....
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N. Immermann. Languages that capture complexity classes. SIAM J. Comput., 16(4), 1988.
First-Order Closure and the Monadic Second-Order Alternation.. - Matz (1998) (1 citation) (Correct)
.... is strict was raised in [Fag95] After that question had been answered affirmatively in [MT97] the authors of [AFS97,AFS98] noted the drawback that the levels of the monadic hierarchy are not closed under first order quantifications, whereas the levels of the polynomial hierarchy (or, by [Imm88] equivalently, of the full second order quantifier alternation hierarchy) are. They raised the question whether also the closed hierarchy is 4 2 DEFINITIONS AND RESULTS strict. A formula on the k th level of this closed hierarchy is obtained from a formula of the k th level of the ordinary ....
N. Immermann. Languages that capture complexity classes. SIAM J. Comput., 16(4), 1988.
A More Expressive Deterministic Query Language With Efficient.. - Gire, Hoang (1996) (Correct)
....one proposed in the previous section, and is based on the use of the so called logical reduction operator. Logical reductions between problems mean reductions that can be expressed in a logical language. The notion is derived from the idea of interpretations between theories and was used in [End] [Imm87] and [Daw] In this section, we use this notion under the form of a constructor integrated in the language itself. We begin the presentation of this reduction constructor by a simple example Let R be an unary relation, the query R has an even cardinality can be expressed by the formula ....
N. Immermann. Languages that capture complexity classes. SIAM Journal on Computing, 16:760-778, 1987.
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