Dagstuhl-Seminar — Semirings in Databases, Automata, and Logic

Semirings are fundamental algebraic structures that in recent times have found a number of applications to computer science, especially in the areas of databases and automata. On the side of databases, commercial query languages, such as SQL, use bag semantics, instead of set semantics, to evaluate relational database queries, which means that the semiring of the natural numbers is used to annotate tuples in the input and output relations. More generally, the annotations can be values in some fixed semiring; this gives a common generalization of both set semantics and bag semantics of database queries, and also makes it possible to model other situations in which one is interested, e.g., in the probability or the reliability of an answer. Furthermore, semirings of polynomials have been successfully used to carry out a rigorous study of provenance in databases. On the side of automata, semirings are used to define weighted automata, which are nondeterministic finite automata augmented with values from a semiring as weights on the transitions. These weights may model, e.g., the cost involved when executing a transition, the amount of resources or time needed for this, or the probability or reliability of its successful execution. Weighted automata have found numerous applications to natural language processing, speech recognition, and algorithms for digital image compression. These applications have inspired numerous investigations in the logic-in-computer-science community.