Related papers: Concurrent Kleene Algebra: Free Model and Complete…

Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…

We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable…

Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on…

Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics…

This paper introduces the first, open source software library for Constraint Consistent Learning (CCL). It implements a family of data-driven methods that are capable of (i) learning state-independent and -dependent constraints, (ii)…

Foundation models for vision have transformed visual recognition with powerful pretrained representations and strong zero-shot capabilities, yet their potential for data-efficient learning remains largely untapped. Active Learning (AL) aims…

For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…

We provided (PNSE'2014) expressions for free choice nets having "distributed choice property" which makes the nets "direct product" representable. In a recent work (PNSE'2016), we gave equivalent syntax for a larger class of free choice…

Nowadays, real-world applications often face streaming data, which requires the learning system to absorb new knowledge as data evolves. Continual Learning (CL) aims to achieve this goal and meanwhile overcome the catastrophic forgetting of…

In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier…

We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter…

We have implemented Kima, an automated error correction system for concurrent logic programs. Kima corrects near-misses such as wrong variable occurrences in the absence of explicit declarations of program properties. Strong moding/typing…

In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…

This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…

We introduce Probabilistic Regular Expressions (PRE), a probabilistic analogue of regular expressions denoting probabilistic languages in which every word is assigned a probability of being generated. We present and prove the completeness…

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…

Constraint Handling Rules is an effective concurrent declarative programming language and a versatile computational logic formalism. CHR programs consist of guarded reactive rules that transform multisets of constraints. One of the main…

We show that Csanky's fast parallel algorithm for computing the characteristic polynomial of a matrix can be formalized in the logical theory LAP, and can be proved correct in LAP from the principle of linear independence. LAP is a natural…

We give a decision procedure and proof of correctness for the equational theory of probabilistic Kleene algebra with angelic nondeterminism introduced in Ong, Ma, and Kozen (2025).

A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always…