13,523 research outputs found

    On tractability and congruence distributivity

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    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

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    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 jj the corresponding component fjf_j of every aggregator on every issue should satisfy fj(x1,,,xn){x1,,,xn}f_j(x_1, ,\ldots, x_n) \in \{x_1, ,\ldots, x_n\}. 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 jj is a majority operation, i.e. the corresponding component satisfies fj(x,x,y)=fj(x,y,x)=fj(y,x,x)=x,x,yf_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =x, \forall x,y, or on every issue is a minority operation, i.e. the corresponding component satisfies fj(x,x,y)=fj(x,y,x)=fj(y,x,x)=y,x,y.f_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =y, \forall x,y. 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 XX has a uniformly non-dictatorial aggregator of some arity then the multi-sorted conservative constraint satisfaction problem on XX, 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

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    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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