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**1 - 2**of**2**### Regular Expressions for Provenance

"... As noted by Green et al. several provenance analyses can be con-sidered a special case of the general problem of computing formal polynomials resp. power-series as solutions of an algebraic system. Specific provenance is then obtained by means of evaluating the formal polynomial under a suitable hom ..."

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As noted by Green et al. several provenance analyses can be con-sidered a special case of the general problem of computing formal polynomials resp. power-series as solutions of an algebraic system. Specific provenance is then obtained by means of evaluating the formal polynomial under a suitable homomorphism. Recently, we presented the idea of approximating the least so-lution of such algebraic systems by means of unfolding the system into a sequence of simpler algebraic systems. Similar ideas are at the heart of the semi-naive evaluation algorithm for datalog. We apply these results to provenance problems: Semi-naive evaluation can be seen as a particular implementation of fixed point iteration which can only be used to compute (finite) provenance polynomials. Other unfolding schemes, e.g. based on Newton’s method, allow us to compute a regular expression which yields a finite representation of (possibly infinite) provenance power series in the case of commutative and idempotent semirings. For specific semirings (e.g. Why(X)) we can then, in a second step, transform these regular expressions resp. power series into polynomials which capture the provenance. Using techniques like subterm sharing both the regular expressions and the polynomials can be succinctly represented.

### An Efficient SQL-based Implementation Unifying Why and Why-Not Provenance

"... LIMITED DISTRIBUTION NOTICE: The research presented in this report may be submitted as a whole or in parts for publication and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report for early dissemination of its contents. In view of the transfer of copyri ..."

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LIMITED DISTRIBUTION NOTICE: The research presented in this report may be submitted as a whole or in parts for publication and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IIT-DB prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g. payment of royalties).