arXiv subjects

Andrei Draghici

Publications and source records attributed to Andrei Draghici.

6 recordsLinked to original sources

arXiv2026

The Role of Semirings in Incremental View Maintenance

We study the problem of incremental view maintenance (IVM) under inserts to semiring-annotated databases. The key observation put forward in this paper is that the complexity of the IVM problem depends fundamentally on the underlying semiring. We introduce a class of conjunctive queries called p-hierarchical. For a zero-sum free and zero-divisor free commutative semiring $K$, we show that for any p-hierarchical query with fractional hypertree width fhtw and any insert-only update sequence of length N to an initially empty K-database, we can construct a data structure that can be updated in O(N^{fhtw-1}) amortized time and supports the enumeration of the query result with constant delay. In particular, the amortized update time for any p-hierarchical alpha-acyclic query is constant. For a class of semirings used to model a wide range of computational problems, we give conditional lower bounds showing that any conjunctive query without self-joins that is not p-hierarchical cannot be maintained with constant amortized update time and constant enumeration delay under inserts. This class includes the natural semiring and its generalizations to the provenance and covariance semirings, as well as idempotent and strictly ordered semirings such as the tropical semiring. When put together, our upper and lower bounds imply a dichotomy for the insert-only maintenance of conjunctive queries without self-joins over every semiring in our class: such a query can be maintained with constant amortized update time and constant enumeration delay if and only if it is p-hierarchical alpha-acyclic.

cs.DB↗

arXiv2026

Numerical Stability of Linear Algebra Operations over Relational Databases

A large body of work in the database literature develops efficient algorithms for linear algebra and machine learning over matrices defined by relational joins, yet the numerical stability of such computations has so far received no attention. This is a practical concern: a join matrix can be much larger than the input database, and the repeated copies of input values it contains compound the floating-point errors incurred by the numerical operations performed over it. This paper initiates a formal investigation of numerical stability for linear algebra over database joins. We first show that backward stability, the standard yardstick of numerical stability, loses its effectiveness in this setting: join matrices form a structured subspace of the ambient matrix space, so a perturbation explaining a computed result need not correspond to any perturbed input database. This failure already occurs for operations as simple as matrix-vector multiplication. To overcome this limitation, we introduce projected backward stability, a generalization of backward stability from the computation of one function to that of a composition of two functions, and establish its connection to classical backward stability. In our database setting, the two functions are the join query and the numerical operation. We further introduce the database condition number as the square root of the ratio of maximal to minimal number of copies of input data values into the join matrix, and show that it quantifies how a perturbation of the join matrix is amplified into a perturbation of the input database, independently of the computation used. The database condition number coincides with the classical condition number of the expansion matrix that replicates input values into the join matrix.

cs.DB↗

arXiv2026

Maintaining Queries under Updates Using Heavy-Light Partitioning of the Input Relations

We study the classical incremental view maintenance problem: Given a query and a database, maintain the query output under single-tuple updates (inserts or deletes) to the database such that the tuples in the query output can be enumerated with constant delay after any update. We introduce a maintenance approach whose update time matches or improves the best update time reported in prior work. Whereas prior approaches are manually tailored to each of a handful of queries, our approach generalizes to arbitrary join queries. It combines three techniques: delta queries, trees of materialized views, and heavy-light data partitioning. The overall update time incurred by our approach for a given join query is characterized by the maintenance width, a new measure that is parameterized by the heavy-light threshold for data partitioning. We show how to find the threshold that minimizes the maintenance width.

cs.DB↗

arXiv2023

Reachability in Fixed VASS: Expressiveness and Lower Bounds

The recent years have seen remarkable progress in establishing the complexity of the reachability problem for vector addition systems with states (VASS), equivalently known as Petri nets. Existing work primarily considers the case in which both the VASS as well as the initial and target configurations are part of the input. In this paper, we investigate the reachability problem in the setting where the VASS is fixed and only the initial configuration is variable. We show that fixed VASS fully express arithmetic on initial segments of the natural numbers. It follows that there is a very weak reduction from any fixed such number-theoretic predicate (e.g. primality or square-freeness) to reachability in fixed VASS where configurations are presented in unary. If configurations are given in binary, we show that there is a fixed VASS with five counters whose reachability problem is PSPACE-hard.

cs.FL↗

arXiv2023

Semënov Arithmetic, Affine VASS, and String Constraints

We study extensions of Semënov arithmetic, the first-order theory of the structure $(\mathbb{N}, +, 2^x)$. It is well-knonw that this theory becomes undecidable when extended with regular predicates over tuples of number strings, such as the Büchi $V_2$-predicate. We therefore restrict ourselves to the existential theory of Semënov arithmetic and show that this theory is decidable in EXPSPACE when extended with arbitrary regular predicates over tuples of number strings. Our approach relies on a reduction to the language emptiness problem for a restricted class of affine vector addition systems with states, which we show decidable in EXPSPACE. As an application of our results, we settle an open problem from the literature and show decidability of a class of string constraints involving length constraints.

cs.LO↗

arXiv2021

On the Complexity of Inductively Learning Guarded Rules

We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the $σ^P_2$-complete task of learning Horn clauses on the polynomial hierarchy. Motivated by practical applications on large datasets we identify a natural tractable fragment of the problem. Finally, we also generalise all of our results to $k$-guarded clauses for constant $k$.

cs.CC↗