13,523 research outputs found
On tractability and congruence distributivity
Constraint languages that arise from finite algebras have recently been the
object of study, especially in connection with the Dichotomy Conjecture of
Feder and Vardi. An important class of algebras are those that generate
congruence distributive varieties and included among this class are lattices,
and more generally, those algebras that have near-unanimity term operations. An
algebra will generate a congruence distributive variety if and only if it has a
sequence of ternary term operations, called Jonsson terms, that satisfy certain
equations.
We prove that constraint languages consisting of relations that are invariant
under a short sequence of Jonsson terms are tractable by showing that such
languages have bounded relational width
Aggregation of Votes with Multiple Positions on Each Issue
We consider the problem of aggregating votes cast by a society on a fixed set
of issues, where each member of the society may vote for one of several
positions on each issue, but the combination of votes on the various issues is
restricted to a set of feasible voting patterns. We require the aggregation to
be supportive, i.e. for every issue the corresponding component of
every aggregator on every issue should satisfy . We prove that, in such a set-up, non-dictatorial
aggregation of votes in a society of some size is possible if and only if
either non-dictatorial aggregation is possible in a society of only two members
or a ternary aggregator exists that either on every issue is a majority
operation, i.e. the corresponding component satisfies , or on every issue is a minority operation, i.e.
the corresponding component satisfies We then introduce a notion of uniformly non-dictatorial
aggregator, which is defined to be an aggregator that on every issue, and when
restricted to an arbitrary two-element subset of the votes for that issue,
differs from all projection functions. We first give a characterization of sets
of feasible voting patterns that admit a uniformly non-dictatorial aggregator.
Then making use of Bulatov's dichotomy theorem for conservative constraint
satisfaction problems, we connect social choice theory with combinatorial
complexity by proving that if a set of feasible voting patterns has a
uniformly non-dictatorial aggregator of some arity then the multi-sorted
conservative constraint satisfaction problem on , in the sense introduced by
Bulatov and Jeavons, with each issue representing a sort, is tractable;
otherwise it is NP-complete
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
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