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In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
LLMs often exhibit Aha moments such as self-correction after tokens like "Wait," yet the underlying mechanism remains unclear. Standard LLMs collapse mainly through silent divergence, where trajectories drift from the correct answer yet…
Gaze event detection is fundamental to vision science, human-computer interaction, and applied analytics. However, current workflows often require specialized programming knowledge and careful handling of heterogeneous raw data formats.…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
The size of a data structure (i.e., the number of elements in it) is a widely used property of a data set. However, for concurrent programs, obtaining a correct size efficiently is non-trivial. In fact, the literature does not offer a…
The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
Proof nets for MLL (unit-free Multiplicative Linear Logic) are concise graphical representations of proofs which are canonical in the sense that they abstract away syntactic redundancy such as the order of non-interacting rules. We argue…
Multi-threaded programs are challenging to write. Developers often need to reason about a prohibitively large number of thread interleavings to reason about the behavior of software. A non-interference property like atomicity can reduce…
Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that…
For over a decade, researchers in formal methods tried to create formalisms that permit natural specification of systems and allow mathematical reasoning about their correctness. The availability of fully-automated reasoning tools enables…
Formal reasoning about the time complexity of algorithms and data structures is usually done in interactive theorem provers like Isabelle/HOL. This includes reasoning about amortized time complexity which looks at the worst case performance…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Runtime verification is an effective automated method for specification-based offline testing and analysis as well as online monitoring of complex systems. The specification language is often a variant of regular expressions or a popular…
Proving linear inequalities and identities of Shannon's information measures, possibly with linear constraints on the information measures, is an important problem in information theory. For this purpose, ITIP and other variant algorithms…
Recently, data abstraction has been studied in the context of separation logic, with noticeable practical successes: the developed logics have enabled clean proofs of tricky challenging programs, such as subject-observer patterns, and they…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…