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In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…
Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of…
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…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
We present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}$-classes for this…
The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and…
A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Computational devices combining two or more different parts, one controlling the operation of the other, for example, derive their power from the interaction, in addition to the capabilities of the parts. Non-classical computation has…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…