In general, constructing a locally-optimal structure is a little harder than constructing an arbitrary structure, but significantly easier than constructing a globally-optimal structure. A similar situation arises in listing. In counting, most problems are #P-complete, but in approximate counting we observe an interesting reversal of the pattern. Assuming that #BIS is not equivalent to #SAT und...

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model’s symmetries, which can preempt standard lifting te...

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O∗(3ns(n)) upper bound for this problem f...

Epistemic protocol specifications allow programs, for settings in which multiple agents act with incomplete information, to be described in terms of how actions are related to what the agents know. They are a variant of the knowledge-based programs of Fagin et al [Distributed Computing, 1997], motivated by the complexity of synthesizing implementations in that framework. The paper proposes an a...