A Modified Completeness Theorem of KAT and Decidability of Term Reducibility

  title={A Modified Completeness Theorem of KAT and Decidability of Term Reducibility},
  author={Takeo Uramoto},
Kleene algebra with tests (KAT) was introduced by Kozen as an extension of Kleene algebra (KA). The decidability of equational formulas p = q and Horn formulas ∧ i p i = q i → p = q in KAT has been studied so far by several researchers. Continuing this line of research, this paper studies the decidability of existentially quantified equational formulas ∃ q ∈ P. (p = q) in KAT, where P is a fixed collection of KAT terms. A new completeness theorem of KAT is proved, and via the completeness… 
1 Citations
Canonical finite models of Kleene algebra with tests


Kleene Algebra with Tests and Program Schematology
A purely algebraic approach to scheme equivalence using Kleene algebra with tests (KAT), where instead of transforming schemes directly using combinatorial graph manipulation, they are regarded as a certain kind of automaton on abstract traces.
Nonlocal Flow of Control and Kleene Algebra with Tests
  • D. Kozen
  • Mathematics
    2008 23rd Annual IEEE Symposium on Logic in Computer Science
  • 2008
This paper shows how KAT can be used to give a rigorous equational treatment of control constructs involving nonlocal transfer of control such as unconditional jumps, loop statements with multi-level breaks, and exception handlers, and develops a compositional semantics and a complete equational axiomatization.
Hypotheses in kleene algebra
Kleene algebra (an Horn axiomatization of Kleene's algebra of regular events) has proved to be an eeective tool for reasoning about programs. Within the algebra, we can reason succinctly about both
The Böhm-Jacopini Theorem Is False, Propositionally
A purely propositional account of the Bohm---Jacopini theorem, which states that any deterministic flowchart program is equivalent to a while program, and reformulate the problems at the propositional level in terms of automata on guarded strings, the automata-theoretic counterpart to Kleene algebra with tests.
Kleene Algebra with Tests: Completeness and Decidability
The completeness of the equational theory of Kleene algebras with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models is proved.
The Complexity of Kleene Algebra with Tests
The equational theory of Kleene algebras with tests has been shown to be decidable in at most exponential time by an efficient reduction to Propositional Dynamic Logic.
A coalgebraic approach to Kleene algebra with tests
A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events
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
Computational Adequacy in an Elementary Topos
It is proved that computational adequacy holds if and only if the topos is 1-consistent (i.e. its internal logic validates only true Σ\(^{\rm 0}_{\rm 1}\)-sentences).
KAT-ML: an interactive theorem prover for Kleene algebra with tests
KAT-ML is described, an implementation of an interactive theorem prover for Kleene algebra with tests (KAT) designed to reflect the natural style of reasoning with KAT that one finds in the literature.