Related papers: Undecidability Results and Their Relevance in Mode…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Recent approaches in music generation rely on disentangled representations, often labeled as structure and timbre or local and global, to enable controllable synthesis. Yet the underlying properties of these embeddings remain underexplored.…
Much like most of cognition research, music cognition is an interdisciplinary field, which attempts to apply methods of cognitive science (neurological, computational and experimental) to understand the perception and process of composition…
Nowadays, humans are constantly exposed to music, whether through voluntary streaming services or incidental encounters during commercial breaks. Despite the abundance of music, certain pieces remain more memorable and often gain greater…
Correlations between quantum theory and music theory - specifically between principles of quantum computing and musical harmony - can lead to new understandings and new methodologies for music theorists and composers. The quantum principle…
The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical…
Advancements in the digital technologies have enabled researchers to develop a variety of Computational Music applications. Such applications are required to capture, process, and generate data related to music. Therefore, it is important…
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
This paper presents the Computoser hybrid probability/rule based algorithm for music composition (http://computoser.com) and provides a reference implementation. It addresses the issues of unpleasantness and lack of variation exhibited by…
The task of a music recommender system is to predict what music item a particular user would like to listen to next. This position paper discusses the main challenges of the music preference prediction task: the lack of information on the…
Music similarity is an essential aspect of music retrieval, recommendation systems, and music analysis. Moreover, similarity is of vital interest for music experts, as it allows studying analogies and influences among composers and…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…
These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers…
This article presents a formal model demonstrating that genuine autonomy, the ability of a system to self-regulate and pursue objectives, fundamentally implies computational unpredictability from an external perspective. we establish…
The development of artificial intelligent composition has resulted in the increasing popularity of machine-generated pieces, with frequent copyright disputes consequently emerging. There is an insufficient amount of research on the…
This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on…