Related papers: Kleene Algebra
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
We introduce the notion of clone algebra, intended to found a one-sorted, purely algebraic theory of clones. Clone algebras are defined by true identities and thus form a variety in the sense of universal algebra. The most natural clone…
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
Higher-dimensional automata (HDA) are a formalism to faithfully model the behaviour of concurrent systems. For ordinary automata, there is a correspondence between regular expressions, regular languages and finite automata, which provides a…
Presentations of Kan extensions of category actions provide a natural framework for expressing induced actions, and therefore a range of different combinatorial problems. Rewrite systems for Kan extensions have been defined and a variation…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
Guarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with Tests (KAT) that was recently introduced to reason efficiently about imperative programs. In contrast to KAT, GKAT does not have an algebraic axiomatization, but…
We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…
We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model…
Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far.…
Kozen and Tiuryn have introduced the substructural logic $\mathsf{S}$ for reasoning about correctness of while programs (ACM TOCL, 2003). The logic $\mathsf{S}$ distinguishes between tests and partial correctness assertions, representing…
Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…