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Data analytics often involves hypothetical reasoning: repeatedly modifying the data and observing the induced effect on the computation result of a data-centric application. Previous work has shown that fine-grained data provenance can help…
This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes…
We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…
If $\mathcal{C}$ is a cocomplete monoidal category in which tensoring from both sides preserves coequalizers, then the category of monoids over $\mathcal{C}$ is cocomplete. The same holds if $\mathcal{C}$ has regular factorizations and…
We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
We explore the relationship between the category of MV-algebras and its full subcategories of perfect and semisimple algebras, showing that this pair of subcategories defines a pretorsion theory. We study the Galois structure associated…
Three reasonable hypotheses lead to the thesis that physical phenomena can be described and simulated with cellular automata. In this work, we attempt to describe the motion of a particle upon which a constant force is applied, with a…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field…
The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the…
A conjecture due to Y. Han asks whether that Hochschild homology groups of a finite dimensional algebra vanish for sufficiently large degrees would imply that the algebra is of finite global dimension. We investigate this conjecture from…
We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of finitely-generated…
Given a simple Lie algebra $\mathfrak{g}$ and an element $\mu\in\mathfrak{g}^*$, the corresponding shift of argument subalgebra of $\text{S}(\mathfrak{g})$ is Poisson commutative. In the case where $\mu$ is regular, this subalgebra is known…
Stochastic automata over monoids as input sets are studied. The well-definedness of these automata requires an extension postulate that replaces the inherent universal property of free monoids. As a generalization of Turakainen's result, it…
The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…
In the sl\_n case, A. Berenstein and A. Zelevinsky studied the Sch\"{u}tzenberger involution in terms of Lusztig's canonical basis, [3]. We generalize their construction and formulas for any semisimple Lie algebra. We use for this the…
Esparza and Reiter have recently conducted a systematic comparative study of weak asynchronous models of distributed computing, in which a network of identical finite-state machines acts cooperatively to decide properties of the network's…