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Key research themes
1. How do logical systems and cognitive models relate to computational tractability in mathematics and cognition?
This research theme explores the connection between descriptive complexity theory—linking logical expressiveness to computational complexity classes—and models of human cognitive capacities, especially in mathematical cognition. The significance lies in assessing whether the traditional computational complexity cutoff at class P (polynomial-time tractability) adequately characterizes the feasibility of computational models for human reasoning, and in examining the limitations of such strict classifications for capturing the nuances of cognition and mathematical problem solving.
Key finding: This work advances the critique of the P-cognition thesis, which restricts feasible cognitive functions to those in complexity class P, by arguing that computational complexity measures are too coarse to serve as strict... Read more
2. What methods best capture and quantify computational complexity in quantum field theories and holography?
Research in this area investigates various approaches to defining and measuring complexity in quantum field theory (QFT), often motivated by holographic duality (AdS/CFT correspondence), and how complexity evolves over time. Distinguishing among these approaches, especially circuit complexity derived from wave functions versus geometric proposals like complexity=volume or complexity=action conjectures, has strong implications for understanding quantum computational resources, black hole physics, and quantum information theory. This work also probes the applicability and limitations of bounds such as Lloyd's bound within these contexts.
Key finding: This paper proposes a novel testing procedure employing information-theoretic measures (Loschmidt echo and Fidelity) to discriminate among definitions of complexity in QFT, avoiding issues like gate or basis dependence. It... Read more
Key finding: Analyzing Lloyd's computational speed bound in the context of holographic complexity, this work identifies that standard assumptions about orthogonalizing quantum gates are violated for large AdS black holes, which involve... Read more
3. How can cognitive complexity of computer programs be formally modeled and assessed to reflect human comprehension challenges?
This research strand focuses on defining, quantifying, and validating complexity metrics for computer programs from cognitive perspectives, emphasizing the subjective human effort in understanding programs. Methods draw on cognitive load theory, schema theory, and hierarchical models of task complexity, aiming to develop frameworks that capture the interplay of programming constructs, plan complexity, and inter-schema interactions. Such frameworks are instrumental for computing education research, instructional design, and improving curriculum sequencing based on objective yet cognitively grounded measures.
Key finding: This article proposes the Cognitive Complexity of Computer Programs (CCCP) framework, which evaluates program complexity by measuring plan depth and maximal plan interactivity, reflecting the complexity of requisite cognitive... Read more
Key finding: Building upon cognitive psychology and educational research, this work introduces "Rules of Program Behavior" to better characterize program semantics for learners’ mental models and proposes a theoretical framework that... Read more
Key finding: This study argues that cognitive complexity should not be confined to fixed quantitative metrics but expressed as subjective ratings incorporating human factor variability. Using divisive hierarchical clustering and user... Read more
Key finding: The paper introduces a measure of software complexity grounded on cognitive weights assigned to basic control structures (BCS) reflecting the mental effort during comprehension. It proposes aggregating these weights through... Read more