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Abstract: We give a finitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa 's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 Introduction Kleene algebras are algebraic structures with operators +, \Delta, , 0, and 1 satisfying certain axioms. They arise in various guises in a number of settings: relational algebra [22, 23], semantics and logics of programs [14, 24], automata... (Update)
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The Algebra of - Finite State Processes (Correct)
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1.7: Dynamic Logic - Harel, Kozen, Tiuryn (1984) (Correct)
1.5: Kleene Algebra with Tests - Kozen (1999) (Correct)
1.4: On the Complexity of Reasoning in Kleene Algebra - Kozen (1997) (Correct)
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0.4: Parikh's Theorem in Commutative Kleene Algebra - Hopkins, Kozen (1999) (Correct)
0.4: The Complexity of Kleene Algebra with Tests - Cohen, Kozen, Smith (1996) (Correct)
0.4: On Action Algebras - Kozen (1993) (Correct)
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43: Two complete axiom systems for the algebras of regular events (context) - Salomaa - 1966
42: Representation of Events in Nerve Nets and Finite Automata (context) - Kleene - 1956
37: Chapman and Hall (context) - Conway, Finite - 1971
BibTeX entry: (Update)
Dexter Kozen. A completeness theorem for Kleene algebras and the algebra of regular events. Information and Computation, 110:366--390, 1994. http://citeseer.ist.psu.edu/kozen94completeness.html More
@inproceedings{ kozen91completeness,
author = "Dexter Kozen",
title = "A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events",
booktitle = "Logic in Computer Science",
pages = "214-225",
year = "1991",
url = "citeseer.ist.psu.edu/kozen94completeness.html" }
Citations (may not include all citations):1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1975
259 Elements of the Theory of Computation (context) - Lewis, Papadimitriou - 1981
192 Representation of events in nerve nets and finite automata (context) - Kleene - 1956
121 and Machines (context) - Eilenberg, Languages - 1974
107 Rational Series and Their Languages (context) - Berstel, Reutenauer - 1984
104 Automata Theoretic Aspects of Formal Power Series (context) - Salomaa, Soittola - 1978
84 A completeness theorem for Kleene algebras and the algebra o.. - Kozen - 1991
59 Two complete axiom systems for the algebra of regular events (context) - Salomaa - 1966
34 Springer-Verlag (context) - Kuich, Salomaa et al. - 1986
33 On defining relations for the algebra of regular events (context) - Redko - 1964
33 Relation algebras with transitive closure (context) - Ng, Tarski - 1977
33 Relation Algebras with Transitive Closure (context) - Ng - 1984
27 Data Structures and Algorithms 2: Graph Algorithms and NP-Co.. (context) - Mehlhorn - 1984
21 Dynamic algebras as a well-behaved fragment of relation alge.. - Pratt - 1988
17 The Kleene and Parikh theorem in complete semirings (context) - Kuich - 1987
16 Chapman and Hall (context) - Conway, Algebra et al. - 1971
13 On induction vs (context) - Kozen - 1981
13 Theoretical Computer Science (context) - Krob, system et al. - 1991
13 A semiring on convex polygons and zero-sum cycle problems (context) - Iwano, Steiglitz - 1990
12 On Kleene algebras and closed semirings - Kozen - 1990
10 Equational axioms for regular sets (context) - Bloom, 'Esik - 1991
8 emes complets d (context) - Boffa, sur - 1990
4 Kleene's Theorem revisited: a formal path from Kleene to Cho.. (context) - Sakarovitch - 1987
4 A new finite complete solvable quasiequational calculus for .. (context) - Archangelsky - 1992
3 Algebraic Theory of Automata (context) - G'ecseg, Pe'ak - 1972
3 the algebra of regular expressions (context) - Anderaa - 1965
2 Completeness of calculi for axiomatically defined classes of.. (context) - Selman - 1972
2 Closure algorithms and the star-height problem of regular la.. (context) - Backhouse - 1975
1 Completeness result for the propositional ¯-calculus (context) - Walukiewicz - 1993
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.cornell.edu/Kozen/papers/papers.html): More
Efficient Algorithms for Optimal Video Transmission - Dexter Kozen (1995) (Correct)
Parikh's Theorem in Commutative Kleene Algebra - Hopkins, Kozen (1999) (Correct)
Partial Automata and Finitely Generated Congruences: An Extension.. - Kozen (1992) (Correct)
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