Related papers: Partial Redundancy in Saturation
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
The support for higher-order reasoning in the Vampire theorem prover has recently been completely reworked. This rework consists of new theoretical ideas, a new implementation, and a dedicated strategy schedule. The theoretical ideas are…
We investigate the computational complexity of minimizing the source side-effect in order to remove a given number of tuples from the output of a conjunctive query. This is a variant of the well-studied {\em deletion propagation} problem,…
We extend the semantics and type system of a lambda calculus equipped with common constructs to be "resource-aware". That is, the semantics keeps track of the usage of resources, and is stuck, besides in case of type errors, if either a…
Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no…
The resource calculus is an extension of the lambda-calculus allowing to model resource consumption. It is intrinsically non-deterministic and has two general notions of reduction - one parallel, preserving all the possible results as a…
Functional dependencies (FDs) are basic constraints in relational databases and are used for many data management tasks. Most FD discovery algorithms find all valid dependencies, but this causes two problems. First, the computational cost…
We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux…
Large Reasoning Models (LRMs) employ reasoning to address complex tasks. Such explicit reasoning requires extended context lengths, resulting in substantially higher resource consumption. Prior work has shown that adversarially crafted…
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…
Existing QA benchmarks typically assume distinct documents with minimal overlap, yet real-world retrieval-augmented generation (RAG) systems operate on corpora such as financial reports, legal codes, and patents, where information is highly…
Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed.…
Redundancy is related to the amount of functionality that the structure can sustain in the worst-case scenario of structural degradation. This paper proposes a widely-applicable concept of redundancy optimization of finite-dimensional…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into…
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…
Clause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to…
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…