Generation of heuristics by transforming the problem representation

This paper formally defines the idea of transforming one problem representation into another. The power of changing the problem representation is demonstrated in the context of heuristic generation. We prove that each problem transformation induces an admissible and monotonic heuristic on the original problem. Furthermore we show that every admissible and monotonic heuristic is induced by some problem transformation. This result generalizes and unifies several approaches for heuristic formation reported on in the literature. We give four techniques for generating problem transformations and we apply these techniques to generate several heuristics found in the literature. We also show that changing the problem representation can prove (automatically) that some problems are unsolvable

Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)

Givental graphs and inversion symmetry

Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.Comment: 26 pages; revised according to the referees' remark