Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances1

Abstract. This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CNF formulas hard for resolution, which is a central task of Proof-Complexity theory, but also propose models with both many hard instances and exact phase transitions. Then, the implications of such models are addressed. It is shown both theoretically and experimentally that an application of Model RB/RD might be in the generation of hard satisfiable instances, which is not only of practical importance but also related to some open problems in cryptography such as generating one-way functions. Subsequently, a further theoretical support for the generation method is shown by establishing exponential lower bounds on the complexity of solving random satisfiable and forced satisfiable instances of RB/RD near the threshold. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems. 1

Soundserver: Data Sonification On-Demand For Computational

The rapid accumulation of large collections of data has created the need for efficient and intelligent schemes for knowledge extraction and results analysis. The resulting information is typically visualized, but it may also be presented through audio techniques such as sonification. Sonification techniques become especially interesting when the client application runs on graphically limited devices such as mobile phones or PDAs (Personal Digital Assistants). In this paper we present an architecture for a sonification server that will be used in the Sound Data Mining project. In this project sound will be used to increase perception and present information extracted by spatial data mining techniques. The server is based on an audio synthesis engine and will relieve clients with little audio synthesis capabilities from the burden of sound processing. By providing sonification modules, this server can potentially be used on a variety of applications where sonification techniques are required