Coalgebraic semantics for component systems
We propose a novel approach for defining the semantics of component systems coinductively. In particular, we formalize a framework for component systems within the theorem prover Isabelle/HOL. Using this formalization, we are able to formally reason about and verify aspects of component composition and interaction. Furthermore, we discuss strategies for adaptor code generation from a given component system specification. We demonstrate the applicability of our approach by a case study.
One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.