Christian Mancas

Christian Mancas, Diana Christina Mancas

We present a pseudocode algorithm for translating our (Elementary) Mathematical Data Model schemes into relational ones and associated sets of non-relational constraints, used by MatBase, our intelligent data and knowledge base management system prototype. We prove that this algorithm is very fast, solid, complete, and optimal. We apply it to a Mathema tical scheme modeling the genealogical trees subuniverse. We also provide examples of SQL and VBA code for enforcing some of its non-relational constraints, as well as guidelines to develop code for enforcing such constraints.

Christian Mancas, Diana Christina Mancas

This research paper describes our research results on using ChatGPT, Gemini, and Claude AI to semantically reverse engineer legacy database software applications.

Christian Mancas

This research paper introduces two new constraint types and four subtypes of database constraints added to our (Elementary) Mathematical Data Model, which are the duals of the existence and non-existence ones. They are formally defined, characterized, and exemplified with real-life instances. The well-formedness, satisfiability, coherence, and minimality of sets of all 7 subtypes of existence constraints are studied. Corresponding SQL-embedded pseudocode algorithms for managing such sets are provided and proved to be of constant complexity, sound, complete, and optimal. Also provided are algorithms for enforcing these new types of constraints, called inexistence and anti-existence. Their characterization proves that they have linear complexity in the sum of the arities of the function (Cartesian product)s involved, and are sound, complete, and optimal as well. All these algorithms were implemented in both versions of our intelligent data and knowledge base management system prototype MatBase, which automatically generates code for enforcing all the 7 subtypes of existence constraints.

Christian Mancas, Diana Christina Mancas

This paper presents a pseudocode algorithm for translating (Elementary) Mathematical Data Model ((E)MDM) schemes into Entity-Relationship data models. We prove that this algorithm is linear, sound, complete, and semi-optimal. As an example, we apply this algorithm to an (E)MDM scheme for a genealogical tree sub-universe. We also provide the main additional features added to the implementation of this data science reverse engineering algorithm in MatBase, our intelligent knowledge and database management system prototype based on both the Entity-Relationship, (E)MDM, and Relational Data Models.

Christian Mancas, Diana Christina Mancas

This research paper mainly describes how to develop MS Blazor safe web applications with Claude AI, version Sonnet 4.5, starting from (Elementary) Mathematical Data Model schemas. In the sequel, it also provides a list of general software engineering best practice rules, as well as issues of the MS Blazor Server platform.