A survey of topological work at CEOL

We present an overview of ongoing work at the Centre for Efficiency-Oriented languages (CEOL), with a focus on topological aspects. CEOL researchers are engaged in designing a new Real-Time Language to improve software timing. The centre broadly focuses on bridging Semantics and Complexity and unites researchers with expertise in Semantics of Programming Languages, Real-Time Languages, Compiler Design and Graph Based Algorithms. CEOL aims to narrow the gap between Worst Case Execution Time analysis and Average Case Execution Time analysis for Real-Time languages and its longer term goal is the development of ACETT, an Average Case Execution Time Tool. This research work is of crucial interest to industry, given that real-time software is widely used in a variety of applications, such as chemical plants, satellite communications, the space industry, telephone exchanges, medical equipment, the motor industry, etc. Topological work at CEOL focuses on the exploration of quantitative Domains, semivaluations, partial metrics and their applications. We give an overview of prior results obtained at CEOL in this area and of current work on relating the notion of balance of algorithms to running time and of an exploration of semivaluations in relation to algorithmic running time.