Iteration Theories of Boolean Functions
A systematic study of the fixed point (or dagger) operation in Lawvere algebraic theories was initiated by Elgot and the ADJ group. Their work led to the introduction of iteration theories in 1980, which capture the equational properties of fixed points in the models proposed by Elgot and the ADJ group. The book  and the survey paper  provide ample evidence that the axioms of iteration theories have a general scope and constitute a complete description of the equational properties of the fixed point operation.
KeywordsBoolean Function Monotonic Function Point Identity Complete Lattice Point Operation
Unable to display preview. Download preview PDF.
- 1.H. Bekić, Definable operations in general algebras, and the theory of automata and flowcharts, Technical Report, IBM Laboratory, Vienna, 1969.Google Scholar
- 2.S. L. Bloom and Z. Ésik, Iteration Theories: The Equational Logic of Iterative Processes, Springer, 1993.Google Scholar
- 4.S. L. Bloom and Z. Ésik, There is no finite axiomatization of iteration theories, in: proc. LATIN 2000, LNCS 1776, Springer, 2000, 367–376.Google Scholar
- 5.J. W. de Bakker and D. Scott, A theory of programs. IBM, Vienna, 1969.Google Scholar
- 7.D. Niwinski, Equational μ-calculus, Computation Theory, Zaborów, 1984, LNCS 208, Springer, 1985, 169–176.Google Scholar
- 8.E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Princeton University Press, 1941.Google Scholar