arXiv subjects

Sara Cohen

Publications and source records attributed to Sara Cohen.

7 recordsLinked to original sources

arXiv2026

Few Rows Tell Them Apart: Equivalence of Queries Mixing Set and Bag Semantics

Bounded SQL equivalence checkers search for a counter-example database of bounded size, and a search that comes back empty proves nothing. We supply missing theory: computable bounds $B$ such that agreement on all databases with at most $B$ tuples per relation implies equivalence. We work in the combined-semantics framework, which captures SQL's mix of duplicate-eliminating (DISTINCT) and duplicate-preserving computation over set-valued relations. For conjunctive queries we prove a bound linear in the query size for fixed multiset width: inequivalent queries already disagree on a database with at most $2^w |Q|$ tuples, where the width $w$ counts only the columns the queries actually read, independently of the total number of multiset variables. Declared keys shrink the bound to $2^{kw} |Q|$ for the smaller key-width $kw$, acyclic foreign keys leave it unchanged, and the result extends to several classes of queries with comparisons, for which equivalence had not previously been characterized. For these fragments, bounded search becomes a terminating, complete decision procedure.

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arXiv2018

Database Perspectives on Blockchains

Modern blockchain systems are a fresh look at the paradigm of distributed computing, applied under assumptions of large-scale public networks. They can be used to store and share information without a trusted central party. There has been much effort to develop blockchain systems for a myriad of uses, ranging from cryptocurrencies to identity control, supply chain management, etc. None of this work has directly studied the fundamental database issues that arise when using blockchains as the underlying infrastructure to manage data. The key difference between using blockchains to store data and centrally controlled databases is that transactions are accepted to a blockchain via a consensus mechanism. Hence, once a user has issued a transaction, she cannot be certain if it will be accepted. Moreover, a yet unaccepted transaction cannot be retracted by the user, and may be appended to the blockchain in the future. This causes difficulties as the user may wish to reissue a transaction, if it was not accepted. Yet this data may then become appended twice to the blockchain. In this paper we present a database perspective on blockchains by introducing formal foundations for blockchains as a storage layer that underlies a database. The main issue that we tackle is uncertainty in transaction appending that is a result of the consensus mechanism. We study two flavors of transaction appending problems: (1) the complexity of determining whether it is possible for a denial constraint to be contradicted, given the state of the blockchain, pending transactions, and integrity constraints and (2) the complexity of generating transactions that are mutually (in)consistent with given subsets of pending transactions. Solving these problems is critical to ensure that users can issue transactions consistent with their intentions. Finally, we chart important directions for future work.

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arXiv2004

Generating All Maximal Induced Subgraphs for Hereditary, Connected-Hereditary and Rooted-Hereditary Properties

The problem of computing all maximal induced subgraphs of a graph G that have a graph property P, also called the maximal P-subgraphs problem, is considered. This problem is studied for hereditary, connected-hereditary and rooted-hereditary graph properties. The maximal P-subgraphs problem is reduced to restricted versions of this problem by providing algorithms that solve the general problem, assuming that an algorithm for a restricted version is given. The complexity of the algorithms are analyzed in terms of total polynomial time, incremental polynomial time and the complexity class P-enumerable. The general results presented allow simple proofs that the maximal P-subgraphs problem can be solved efficiently (in terms of the input and output) for many different properties.

cs.DS↗

arXiv2002

Equivalences Among Aggregate Queries with Negation

Query equivalence is investigated for disjunctive aggregate queries with negated subgoals, constants and comparisons. A full characterization of equivalence is given for the aggregation functions count, max, sum, prod, toptwo and parity. A related problem is that of determining, for a given natural number N, whether two given queries are equivalent over all databases with at most N constants. We call this problem bounded equivalence. A complete characterization of decidability of bounded equivalence is given. In particular, it is shown that this problem is decidable for all the above aggregation functions as well as for count distinct and average. For quasilinear queries (i.e., queries where predicates that occur positively are not repeated) it is shown that equivalence can be decided in polynomial time for the aggregation functions count, max, sum, parity, prod, toptwo and average. A similar result holds for count distinct provided that a few additional conditions hold. The results are couched in terms of abstract characteristics of aggregation functions, and new proof techniques are used. Finally, the results above also imply that equivalence, under bag-set semantics, is decidable for non-aggregate queries with negation.

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arXiv2001

EquiX--A Search and Query Language for XML

EquiX is a search language for XML that combines the power of querying with the simplicity of searching. Requirements for such languages are discussed and it is shown that EquiX meets the necessary criteria. Both a graph-based abstract syntax and a formal concrete syntax are presented for EquiX queries. In addition, the semantics is defined and an evaluation algorithm is presented. The evaluation algorithm is polynomial under combined complexity. EquiX combines pattern matching, quantification and logical expressions to query both the data and meta-data of XML documents. The result of a query in EquiX is a set of XML documents. A DTD describing the result documents is derived automatically from the query.

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arXiv2000

EquiX---A Search and Query Language for XML

EquiX is a search language for XML that combines the power of querying with the simplicity of searching. Requirements for such languages are discussed and it is shown that EquiX meets the necessary criteria. Both a graphical abstract syntax and a formal concrete syntax are presented for EquiX queries. In addition, the semantics is defined and an evaluation algorithm is presented. The evaluation algorithm is polynomial under combined complexity. EquiX combines pattern matching, quantification and logical expressions to query both the data and meta-data of XML documents. The result of a query in EquiX is a set of XML documents. A DTD describing the result documents is derived automatically from the query.

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arXiv2000

Algorithms for Rewriting Aggregate Queries Using Views

Queries involving aggregation are typical in database applications. One of the main ideas to optimize the execution of an aggregate query is to reuse results of previously answered queries. This leads to the problem of rewriting aggregate queries using views. Due to a lack of theory, algorithms for this problem were rather ad-hoc. They were sound, but were not proven to be complete. Recently we have given syntactic characterizations for the equivalence of aggregate queries and applied them to decide when there exist rewritings. However, these decision procedures do not lend themselves immediately to an implementation. In this paper, we present practical algorithms for rewriting queries with $\COUNT$ and $\SUM$. Our algorithms are sound. They are also complete for important cases. Our techniques can be used to improve well-known procedures for rewriting non-aggregate queries. These procedures can then be adapted to obtain algorithms for rewriting queries with $\MIN$ and $\MAX$. The algorithms presented are a basis for realizing optimizers that rewrite queries using views.

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