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Algebraic Ordinals

100%

Bloom S. L. , Ésik Z.

2010

tom Vol. 99, nr 4

383-407

An algebraic tree T is one determined by a finite system of fixed point equations. The frontier Fr(T ) of an algebraic tree T is linearly ordered by the lexicographic order

Partial Conway and Iteration Semirings

80%

Bloom S. L. , Ésik Z. , Kuich W.

2008

tom Vol. 86, nr 1-2

19-40

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 Conway identities. We introduce here partial Conway semirings, which are semirings S which have a star operation defined only on an ideal of S; when the arguments are appropriate, the operation satisfies the above identities. We develop the general theory of partial Conway semirings and prove a Kleene theorem for this generalization.