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We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…

In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…

Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time…

In this paper, we study the complexity of answering conjunctive queries (CQ) with inequalities). In particular, we are interested in comparing the complexity of the query with and without inequalities. The main contribution of our work is a…

The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size $n$ into smaller subproblems (say, $a$ copies of size $n/b$ each), along with some auxiliary work of cost…

Extractive Question Answering (EQA) in Machine Reading Comprehension (MRC) often faces the challenge of dealing with semantically identical but format-variant inputs. Our work introduces a novel approach, called the ``Query Latent Semantic…

The problem of checking whether a recursive query can be rewritten as query without recursion is a fundamental reasoning task, known as the boundedness problem. Here we study the boundedness problem for Unions of Conjunctive Regular Path…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming…

We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…

The formalism of RPQs (regular path queries) is an important building block of most query languages for graph databases. RPQs are generally evaluated under homomorphism semantics; in particular only the endpoints of the matched walks are…

Most data analytical pipelines often encounter the problem of querying inconsistent data that violate pre-determined integrity constraints. Data cleaning is an extensively studied paradigm that singles out a consistent repair of the…

Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge representation tool. Though existing ASP variants enjoy efficient implementations, generating an answer set remains intractable. The goal of this research is to define…

Connectionist Temporal Classification has recently attracted a lot of interest as it offers an elegant approach to building acoustic models (AMs) for speech recognition. The CTC loss function maps an input sequence of observable feature…

Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…

Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit…

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…

Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and…