Related papers: Computations for symbolic substitutions
A number of novel programming languages and libraries have been proposed that offer simpler-to-use models of concurrency than threads. It is challenging, however, to devise execution models that successfully realise their abstractions…
In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework,…
We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.
The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…
We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks. Existing data generation approaches rely on open-loop pipelines and…
We study dynamics of a substitution subshift given by the substitution a->aca, b->d, c->b, d->c that is related to the Grigorchuk group. This dynamical system is shown to be, up to a countable set, conjugated to the binary odometer.
We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
While there exist many methods in machine learning for comparison of letter string data, most are better equipped to handle strings that represent natural language, and their performance will not hold up when presented with strings that…
In this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the $i$-th (rational) Betti number and Euler characteristic of the real toric variety associated to a graph…
The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…
Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite…
There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles.…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Program invariants are important for defect detection, program verification, and program repair. However, existing techniques have limited support for important classes of invariants such as disjunctions, which express the semantics of…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…