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Given a foliation, there is a well-known notion of holonomy, which can be understood as an action that differentiates to the Bott connection on the normal bundle. We present an analogous notion for Lie subalgebroids, consisting of an…
A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Holographic algorithms are a recent breakthrough in computer science and has found applications in information theory. This paper provides a proof to the central component of holographic algorithms, namely, the Holant theorem. Compared with…
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…
We prove that if S is a set of functions from a set A to itself, S is closed under composition, and S contains all transpositions of A, then the action of S on Acan be recovered from the semigroup consisting of S together with its…
We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount- ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear…
In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse…
This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…
We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear…
For simple theories with a strong version of amalgamation we obtain the canonical hyperdefinable group from the group configuration. This provides a generalization to simple theories of the group configuration theorem for stable theories.
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…