Title: Efficient algorithms for monadic second order properties
       on $\R$-structures of bounded tree-width

Abstract: As it is the case in classical (discrete) complexity theory 
          also in algebraic models of computation there are many problems
          for which no efficient algortihms are known.
          Examples we are interested in are the computation of permanents,
          the feasibility of polynomial systems over finite and infinite fields,
          linear programming and some more. 
                    
          In this talk we deal with decision and computation problems given as 
          properties on weighted hypergraphs (a special case of $\R$-structures 
          as defined by  Graedel and Meer). These properties are expressed in 
          existential monadic second order logic, a logic to be defined. 
          We will introduce a sparsity condition (bounded tree width of the 
          related hypergraphs) and show that under this condition
          many otherwise hard problems can be solved in polynomial time
          w.r.t. the BSS model of computation.

          This is joint work with J.A. Makowsky, Technion.