Conway Numbers and Iteration Theory

Conway and iteration hemirings

Conway hemirings are Conway semirings without a multiplicative unit. We also define iteration hemirings as Conway hemirings satisfying certain identities associated with the finite groups. Iteration hemirings are iteration semirings without a multiplicative unit. We provide an analysis of the relationship between Conway hemirings and (partial) Conway semirings and describe several free construc...

Partial Conway and Iteration Semirings

A Conway semiring is a semiring S equipped with a unary operation * : S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or N rat Σ * of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conw...

Some Remarks on Conway and Iteration Theories

We present an axiomatization of Conway theories which yields, as a corollary, a very concise axiomatization of iteration theories satisfying the functorial implication for base morphisms. It has been shown that most fixed point operations in computer science share the same equational properties. These equational properties are captured by the notion of iteration theories [1, 3]. Several axiomat...

Conway and iteration hemirings Part 2

Conway and iteration hemirings Part 1