Key research themes
1. How can recursive grammar-based methods enable efficient and uniform generation of combinatorial objects with complex properties?
This theme focuses on the development of systematic, grammar-driven algorithms that enable the uniform random generation of combinatorial objects, particularly addressing multiple and non-algebraic parameters. It explores the extension of context-free grammar ideas into object grammars, and the valuation techniques that allow parameterized enumeration and probabilistic generation, which is critical for both theoretical combinatorics and practical applications in property generation.
2. How can property specifications be systematically represented and made accessible to improve the accuracy and usability of formal verification?
This research area investigates techniques for supporting the elicitation, formal representation, and comprehension of property specifications. It addresses the challenges of bridging the gap between mathematically precise property definitions and their accessibility to engineers, emphasizing the use of structured templates, natural language representations, user-guided decision processes, and their formal counterparts to minimize ambiguity and enhance correctness in property-based verification workflows.
3. What are the ontological and conceptual challenges in defining and reasoning about properties, and how do these impact property-awareness and specification in formal and philosophical contexts?
This strand investigates the foundational nature of properties from both philosophical and formal perspectives, including the debate on whether property-awareness involves representation, the ontological underpinnings of properties (universalism, nominalism, tropism), the difficulties in property ascription and reasoning (e.g., paradoxes in property theory), and their implications for property modeling, specification, and inheritance. Understanding these issues is essential for accurately conceptualizing, representing, and reasoning about properties in computational and logical frameworks.