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Dynamic logic
TLDR
This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events
  • D. Kozen
  • Mathematics
    Inf. Comput.
  • 15 July 1991
A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given. Axioms for Kleene
A completeness theorem for Kleene algebras and the algebra of regular events
  • D. Kozen
  • Mathematics
    [] Proceedings Sixth Annual IEEE Symposium on…
  • 15 July 1991
A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given. Axioms for Kleene
Kleene algebra with tests
TLDR
A purely equational proof is given, using Kleene algebra with tests and commutativity conditions, of the following classical result: every while program can be simulated by a while program with at most one while loop.
Lower bounds for natural proof systems
  • D. Kozen
  • Computer Science
    18th Annual Symposium on Foundations of Computer…
  • 30 September 1977
TLDR
A lower space bound of n/log(n) is shown for the proof system for the PTIME complete theory and a lower length bound of 2cn/log('n'): length of polynomial space for the PSPACE complete theory.
Semantics of probabilistic programs
  • D. Kozen
  • Computer Science
    20th Annual Symposium on Foundations of Computer…
  • 29 October 1979
Results on the Propositional µ-Calculus
TLDR
A propositional version of the Μ-calculus is defined, and an exponential-time decision procedure, small model property, and complete deductive system is given, and it is shown that it is strictly more expressive than PDL.
NetKAT: semantic foundations for networks
TLDR
It is shown that NetKAT is an instance of a canonical and well-studied mathematical structure called a Kleene algebra with tests (KAT) and proved that its equational theory is sound and complete with respect to its denotational semantics.
A probabilistic PDL
  • D. Kozen
  • Mathematics
    J. Comput. Syst. Sci.
  • 1 December 1983
TLDR
A probabilistic analog PPDL of Propositional Dynamic Logic is given and a small model property is proved and a polynomial space decision procedure for formulas involving well-structured programs is given.
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