TY - GEN

T1 - A dichotomy for the generalized model counting problem for unions of conjunctive queries

AU - Kenig, Batya

AU - Suciu, Dan

N1 - Publisher Copyright: © 2021 ACM.

PY - 2021/6/20

Y1 - 2021/6/20

N2 - We study the generalized model counting problem, defined as follows: given a database, and a set of deterministic tuples, count the number of subsets of the database that include all deterministic tuples and satisfy the query. This problem is computationally equivalent to the evaluation of the query over a tuple-independent probabilistic database where all tuples have probabilities in set0, 1 2, 1 . Previous work has established a dichotomy for Unions of Conjunctive Queries (UCQ) when the probabilities are arbitrary rational numbers, showing that, for each query, its complexity is either in polynomial time or #P-hard. The query is called safe in the first case, and unsafe in the second case. Here, we strengthen the hardness proof, by proving that an unsafe UCQ query remains #P-hard even if the probabilities are restricted to set0, 1 2, 1 . This requires a complete redesign of the hardness proof, using new techniques. A related problem is the model counting problem, which asks for the probability of the query when the input probabilities are restricted to set0, 1 2 . While our result does not extend to model counting for all unsafe UCQs, we prove that model counting is #P-hard for a class of unsafe queries called Type-I forbidden queries.

AB - We study the generalized model counting problem, defined as follows: given a database, and a set of deterministic tuples, count the number of subsets of the database that include all deterministic tuples and satisfy the query. This problem is computationally equivalent to the evaluation of the query over a tuple-independent probabilistic database where all tuples have probabilities in set0, 1 2, 1 . Previous work has established a dichotomy for Unions of Conjunctive Queries (UCQ) when the probabilities are arbitrary rational numbers, showing that, for each query, its complexity is either in polynomial time or #P-hard. The query is called safe in the first case, and unsafe in the second case. Here, we strengthen the hardness proof, by proving that an unsafe UCQ query remains #P-hard even if the probabilities are restricted to set0, 1 2, 1 . This requires a complete redesign of the hardness proof, using new techniques. A related problem is the model counting problem, which asks for the probability of the query when the input probabilities are restricted to set0, 1 2 . While our result does not extend to model counting for all unsafe UCQs, we prove that model counting is #P-hard for a class of unsafe queries called Type-I forbidden queries.

KW - #p-hardness

KW - Model counting

KW - Tuple-independent databases

UR - http://www.scopus.com/inward/record.url?scp=85109217326&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/3452021.3458313

DO - https://doi.org/10.1145/3452021.3458313

M3 - منشور من مؤتمر

T3 - Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

SP - 312

EP - 324

BT - PODS 2021 - Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

T2 - 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2021

Y2 - 20 June 2021 through 25 June 2021

ER -