Related papers: The Covering Problem
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…
Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Formal logic enables computers to reason in natural language by representing sentences in symbolic forms and applying rules to derive conclusions. However, in what our study characterizes as "rulebreaker" scenarios, this method can lead to…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
Membership (membership query / membership testing) is a fundamental problem across databases, networks and security. However, previous research has primarily focused on either approximate solutions, such as Bloom Filters, or exact methods,…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…
The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular…
Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results…
To precisely evaluate a language model's capability for logical reading comprehension, we present a dataset for testing the understanding of the rationale behind critical reasoning. For questions taken from an existing multiplechoice…
In the text processing context, most ML models are built on word embeddings. These embeddings are themselves trained on some datasets, potentially containing sensitive data. In some cases this training is done independently, in other cases,…