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Iteration Algebras are not Finitely Axiomatizable (Extended Abstract) (2000)  (Make Corrections)  (2 citations)
Stephen L. Bloom, Zoltan Esik
Latin American Theoretical INformatics



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Abstract: Stephen L. Bloom and Zoltan Esik # 1 Stevens Institute of Technology Department of Computer Science Hoboken, NJ 07030 bloom@cs.stevens-tech.edu 2 A. Jozsef University Department of Computer Science Szeged, Hungary esik@inf.u-szeged.hu Abstract. Algebras whose underlying set is a complete partial order and whose termoperations are continuous may be equipped with a least fixed point operation x.t. The set of all equations involving the -operation which hold in all continuous ... (Update)

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.... is known that in the presence of cycles, a finite number of axioms cannot capture interesting notions of equivalence (see e.g. Sew94,BE00] This implies that traditional rewriting cannot produce normal forms of interesting cyclic structures (note, though, that there is a...

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BibTeX entry:   (Update)

Stephen L. Bloom and Zoltan Esik. Iteration algebras are not finitely axiomatizable. In Latin American Theoretical INformatics (Theory), pages 367--376, 2000. http://citeseer.ist.psu.edu/bloom00iteration.html   More

@inproceedings{ bloom00iteration,
    author = "Stephen L. Bloom and Zoltan Esik",
    title = "Iteration Algebras Are Not Finitely Axiomatizable. Extended Abstract",
    booktitle = "Latin American Theoretical {INformatics}",
    number = "Theory",
    pages = "367-376",
    year = "2000",
    url = "citeseer.ist.psu.edu/bloom00iteration.html" }
Citations (may not include all citations):
162   Data types as lattices (context) - Scott - 1976
112   Initial algebra semantics and continuous algebras (context) - Goguen, Thatcher et al. - 1977
18   Iteration Theories: The Equational Logic of Iterative Proces.. (context) - Bloom, Esik - 1993
13   Theoretical Computer Science (context) - Krob, of - 1991
11   Mathematical Structures in Computer Science (context) - Bloom, Esik et al. - 1993
11   An algebraic theory for regular languages of finite and infi.. (context) - Wilke - 1993
9   Theoretical Computer Science (context) - Tiuryn, points et al. - 1980
9   Lecture Notes in Computer Science (context) - Guessarian - 1981
9   Independence of the equational axioms of iteration theories (context) - Esik - 1988
5   Information and Computation (context) - Esik, for - 1999
5   Theoretical Informatics and Applications (context) - Bloom, Esik et al. - 1998
4   Hyperidentities and hypervarieties (context) - Taylor - 1981
4   Semigroups and automata on infinite words - Perrin, Pin - 1995
4   Fixed points and algebras with infinitely long expressions (context) - Tiuryn - 1978
3   Iteration theories of synchronization trees (context) - Bloom, Esik et al. - 1993
2   Theoretical Computer Science (context) - Nelson - 1983
1   International Journal of Foundations of Computer Science (context) - Bloom, Esik
1   An Eilenberg Theorem for #-languages (context) - Wilke - 1991
1   Equational mu-calculus (context) - Niwinski

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