@inproceedings { Gutman20110701,
author = "Gutman A.E.",
title = "Prefix rewriting systems as object-oriented data models",
booktitle = "Ershov Informatics Conference 2011. Knowledge and Ontologies *ELSEWHERE* 2011. The Third Workshop (Novosibirsk, July 1, 2011): Proceedings",
address = "Novosibirsk",
publisher = "Price-Courier",
year = "2011",
pages = "5--14",
annote = "A deterministic longest-prefix rewriting system is a rewriting system such that there are no rewriting rules $X\rightarrow Y$, $X\rightarrow Z$ with $Y\ne Z$, and only longest prefixes of words are subject to rewriting. Given such a system, analogs are defined and examined of some concepts related to object-oriented data systems: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration. In particular, the algorithms are presented for answering the following questions: Are all words finitely rewritable? Do there exist recurrent words? Is the system conceptually consistent? Given two words $X$ and $Y$, does $X$ conceptually depend on $Y$? Does the type of $X$ coincide with that of $Y$? Is the type of $X$ a subtype of that of $Y$?",
keywords = "prefix rewriting, term rewriting, object-oriented data system, information system, consistency verification, ontology of a data model"
}
@inproceedings { Gutman20121115,
author = "Gutman A.E.",
howpublished = "Electronic",
title = "Representation and analysis of object-oriented data by means of rewriting systems",
booktitle = "Mal'tsev Meeting. International Conference (Novosibirsk, November 12--16, 2012)",
address = "Novosibirsk",
year = "2012",
pages = "26",
language = "russian",
annote = "In the framework of deterministic prefix rewriting systems, the notions are introduced and studied which are typical for the object-oriented approach to data organization: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration."
}
@inproceedings { Gutman20140610,
author = "Gutman A.E.",
title = "Object-oriented data as prefix rewriting systems",
booktitle = "Advanced mathematics, computations and applications -- 2014. International conference (Novosibirsk, June 8--11, 2014): Abstracts",
address = "Novosibirsk",
publisher = "Academizdat",
year = "2014",
isbn = "978-5-9904865-8-4",
pages = "48",
annote = "A new approach is suggested for representing and analysing object-oriented data by means of rewriting systems."
}
@article { Gutman20131017,
author = "Gutman A.E.",
title = "Object-oriented data as prefix rewriting systems",
journal = "Vladikavk. Math. J.",
year = "2015",
volume = "17",
number = "3",
pages = "23--35",
doi = "10.23671/VNC.2017.3.7260",
annote = "A deterministic longest-prefix rewriting system is a rewriting system such that there are no rewriting rules $X\rightarrow Y$, $X\rightarrow Z$ with $Y\ne Z$, and only longest prefixes of words are subject to rewriting. Given such a system, analogs are defined and examined of some concepts related to object-oriented data systems: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration. In particular, algorithms are presented for answering the following questions: Are all words finitely rewritable? Do there exist recurrent words? Is the system conceptually consistent? Given two words $X$ and $Y$, does $X$ conceptually depend on $Y$? Does the type of $X$ coincide with that of $Y$? Is the type of $X$ a subtype of that of $Y$?",
keywords = "prefix rewriting, term rewriting, object-oriented data system, information system, consistency verification, ontology of a data model"
}