On Bounded Linear Codes and the Commutative Equivalence

The problem of the commutative equivalence of semigroups generated by semi-linear languages is studied. In particular conditions ensuring that the Kleene closure of a bounded semi-linear code is commutatively equivalent to a regular language are investigated

Acceptance Ambiguity for Quantum Automata

We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the distribution of acceptance probabilities of such MO-QFA, which is partly motivated by similar freeness problems for matrix semigroups and other computational models. We show that determining if the acceptance probabilities of all possible input words are unique is undecidable for 32 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial configuration is defined over real algebraic numbers. We utilize properties of the skew field of quaternions, free rotation groups, representations of tuples of rationals as a linear sum of radicals and a reduction of the mixed modification Post\u27s correspondence problem

On the Commutative Equivalence of Algebraic Formal Series and Languages

The problem of the commutative equivalence of context-free and regular languages is studied. Conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

The Weight of (Im)possibility: Exploring body weight and shape with trans and gender non-conforming people

In recent decades, theorising around trans embodiment has sought to move away from narratives of the ‘wrong’ and pathological trans body. Emergent analytical and theoretical frameworks have instead highlighted the ways in which particular bodies become designated as trans, and what this means for the kinds of possibilities for embodiment that are opened up and closed down at the levels of both individual relationships and contexts, and structural and systemic constraints. The significance of weight and shape in relation to these embodied possibilities has not yet been fully explored within sociology. Drawing upon qualitative interviews with 21 participants who identified as trans and/or gender non-conforming, this thesis examines the intersection of body weight and shape with trans and gender non-conforming positionality in order to address gaps in existing knowledge around the meaning and significance of weight and shape for trans and gender non-conforming people and communities in the UK. Phenomenological epistemology informs this thesis and the thematic analysis (TA) undertaken, centring participants’ experiential claims. In discussion of the findings presented, I argue that weight and shape are enmeshed with the constraints and possibilities of gendered positionality in ways that indicate the need for wide-reaching and profound transformation in order for relationships with the body based on connection, acceptance, and pleasure to be more consistently and widely possible for trans and gender non-conforming people. Relationships with weight and shape, as I illustrate in this thesis, were not simply shaped by the conditions and possibilities for embodiment in which they were situated, but represented sites of agentic engagement within and through conditions of embodied possibility

Freeness Properties of Weighted and Probabilistic Automata over Bounded Languages

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, such as the dimensions of the generator matrices and the semiring over which the matrices are defined. Most freeness problems have been shown to be undecidable starting from dimension three, even for upper-triangular matrices over the natural numbers. There are many open problems still remaining in dimension two. A recent paper has also investigated freeness properties of bounded languages of matrices. We consider a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set of scalar values computable from multiplying a fixed row vector by a matrix from a finately generated semigroup and then multiplying by a fixed column vector, of appropriate size. Ambiguity and freeness problems are defined in terms of the uniqueness of factorizations for each scalar. Such problems have also been studied in connection to formal power series. We show various undecidability results and their connections to weighted and probabilistic finite automata

On injectivity of quantum finite automata

We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the injectivity problem of determining if the acceptance probability function of a MO-QFA is injective over all input words, i.e., giving a distinct probability for each input word. We show that the injectivity problem is undecidable for 8 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial state vector is real algebraic. We also show undecidability of this problem when the initial vector is rational, although with a huge increase in the number of states. We utilize properties of quaternions, free rotation groups, representations of tuples of rationals as linear sums of radicals and a reduction of the mixed modification of Post's correspondence problem, as well as a new result on rational polynomial packing functions which may be of independent interest.</div