Semirings and Formal Power Series (original) (raw)
References
J. Adámek, E. Nelson, and J. Reiterman. Tree constructions of free continuous algebras. Journal of Computer and System Sciences, 24:114–146, 1982. ArticleMathSciNet Google Scholar
J. Berstel, editor. Séries formelles en variables non commutatives et applications. Laboratoire d’Informatique Théorique et Programmation, Ecole Nationale Supérieure de Techniques Avancées, Paris, 1978. MATH Google Scholar
J. Berstel and C. Reutenauer. Les séries rationelles et leurs langages. Masson, Paris, 1984. English translation: Rational Series and Their Languages, volume 12 of Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, 1988. Google Scholar
S.L. Bloom and Z. Ésik. Iteration Theories, Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, 1993. MATH Google Scholar
J.H. Conway. Regular Algebra and Finite Machines. Chapman & Hall, London, 1971. MATH Google Scholar
M. Droste and P. Gastin. On aperiodic and star-free formal power series in partially commuting variables. Theory of Computing Systems, 42:608–631, 2008. Extended abstract in: D. Krob, A.A. Milchalev, and A.V. Milchalev, editors, Formal Power Series and Algebraic Combinatorics, 12th Int. Conf., Moscow, pages 158–169. Springer, Berlin, 2000. ArticleMATHMathSciNet Google Scholar
S. Eilenberg. Automata, Languages and Machines, volume A. Academic Press, San Diego, 1974. Google Scholar
Z. Ésik and W. Kuich. Locally closed semirings. Monatshefte für Mathematik, 137:21–29, 2002. ArticleMATH Google Scholar
Z. Ésik and W. Kuich. Equational axioms for a theory of automata. In C. Martin-Vide, V. Mitrana, and G. Paun, editors, Formal Languages and Applications, volume 148 of Studies in Fuzziness and Soft Computing, pages 183–196. Springer, Berlin, 2004. Google Scholar
Z. Ésik and W. Kuich. Finite automata. In M. Droste, W. Kuich, and H. Vogler, editors, Handbook of Weighted Automata. Chapter 3. Springer, Berlin, 2009. Google Scholar
K. Głazek. A Guide to the Literature on Semirings and Their Applications in Mathematics and Information Science. Kluwer Academic, Dordrecht, 2002. Google Scholar
J.A. Goguen, J.W. Thatcher, E.G. Wagner, and J.B. Wright. Initial algebra semantics and continuous algebras. Journal of the Association for Computing Machinery, 24:68–95, 1977. MATHMathSciNet Google Scholar
J. Golan. Semirings and Their Applications. Kluwer Academic, Dordrecht, 1999. MATH Google Scholar
M. Goldstern. Vervollständigung von Halbringen. Diplomarbeit, Technische Universität Wien, 1985. Google Scholar
I. Guessarian. Algebraic Semantics, volume 99 of Lecture Notes in Computer Science. Springer, Berlin, 1981. MATH Google Scholar
P. Hájek. Metamathematics of Fuzzy Logic. Kluwer Academic, Dordrecht, 1998. MATH Google Scholar
U. Hebisch. The Kleene theorem in countably complete semirings. Bayreuther Mathematische Schriften, 31:55–66, 1990. MATHMathSciNet Google Scholar
U. Hebisch and H.J. Weinert. Halbringe—Algebraische Theorie und Anwendungen in der Informatik. Teubner, Leipzig, 1993. English translation: Semirings—Algebraic Theory and Applications in Computer Science. World Scientific, Singapore, 1998. MATH Google Scholar
B. Heidergott, G.J. Olsder, and J. van der Woude. Max Plus at Work. Princeton University Press, Princeton, 2006. MATH Google Scholar
D. Kozen. A completeness theorem for Kleene algebras and the algebra of regular events. Information and Computation, 110:366–390, 1994. ArticleMATHMathSciNet Google Scholar
W. Kuich. The Kleene and the Parikh theorem in complete semirings. In ICALP’87, volume 267 of Lecture Notes in Computer Science, pages 212–225. Springer, Berlin, 1987. Google Scholar
W. Kuich. Semirings and formal power series: Their relevance to formal languages and automata theory. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 1, Chapter 9, pages 609–677. Springer, Berlin, 1997. Google Scholar
W. Kuich and A. Salomaa. Semirings, Automata, Languages, volume 5 of Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, 1986. MATH Google Scholar
E.G. Manes and M.A. Arbib. Algebraic Approaches to Program Semantics. Springer, Berlin, 1986. MATH Google Scholar
G. Markowsky. Chain-complete posets and directed sets with applications. Algebra Universalis, 6:53–68, 1976. ArticleMATHMathSciNet Google Scholar
M. Mohri. Semiring frameworks and algorithms for shortest-distance problems. Journal of Automata, Languages and Combinatorics, 7:321–350, 2002. MATHMathSciNet Google Scholar
I. Petre and A. Salomaa. Algebraic systems and pushdown automata. In M. Droste, W. Kuich, and H. Vogler, editors, Handbook of Weighted Automata. Chapter 7. Springer, Berlin, 2009. Google Scholar
G. Rahonis. Fuzzy languages. In M. Droste, W. Kuich, and H. Vogler, editors, Handbook of Weighted Automata. Chapter 12. Springer, Berlin, 2009. Google Scholar
J. Sakarovitch. Kleene’s theorem revisited. In Trends, Techniques, and Problems in Theoretical Computer Science, 4th International Meeting of Young Computer Scientists, volume 281 of Lecture Notes in Computer Science, pages 39–50. Springer, Berlin, 1987. Google Scholar
J. Sakarovitch. Éléments de Théorie des Automates. Vuibert, Paris, 2003. Google Scholar
J. Sakarovitch. Rational and recognisable power series. In M. Droste, W. Kuich, and H. Vogler, editors, Handbook of Weighted Automata. Chapter 4. Springer, Berlin, 2009. Google Scholar
A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin, 1978. MATH Google Scholar
W. Wechler. The Concept of Fuzziness in Automata and Language Theory. Akademie Verlag, Berlin, 1978. MATH Google Scholar
X. Zhao. Locally closed semirings and iteration semirings. Monatshefte für Mathematik, 144:157–167, 2005. ArticleMATH Google Scholar
U. Zimmermann. Linear and Combinatorial Optimization in Ordered Algebraic Structures, volume 10 of Annals of Discrete Mathematics. North-Holland, Amsterdam, 1981. MATH Google Scholar