0-1 laws and decision problems for fragments of second-order logic
Kolaitis, P.G.
Vardi, M.Y.
IBM Almaden Res. Center, San Jose, CA;
This paper appears in: Logic in Computer Science, 1988. LICS '88., Proceedings of the Third Annual Symposium on
Publication Date: 5-8 Jul 1988
On page(s): 2-11
Meeting Date: 07/05/1988 - 07/08/1988
Location: Edinburgh, UK
ISBN: 0-8186-0853-6
References Cited: 32
INSPEC Accession Number: 3248141
Digital Object Identifier: 10.1109/LICS.1988.5095
Current Version Published: 2002-08-06
Abstract
Fragments of existential second-order logic are investigated in
which the patterns of first order quantifiers are restricted. The focus
is on the class Σ11 (Ackermann) of
existential second-order sentences in which the first-order part belongs
to the Ackermann class, i.e. it contains at most one universal
first-order quantifier. All properties expressible by
Σ11 (Ackermann) sentences are NP-computable,
and there are natural NP-complete properties, such as satisfiability,
that are expressible by such sentences. It is established that the 0-1
law holds for the class Σ11 (Ackermann), and
it is shown that the associated decision problem is NEXPTIME-complete.
It is also shown that the 0-1 law fails for other fragments of
existential second-order logic in which first-order part belongs to
certain prefix classes with an unsolvable decision problem
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