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Coalgebraic modal logic and games

   Department of Computer Science

  , Prof Georg Struth  Monday, June 27, 2022  Funded PhD Project (Students Worldwide)

About the Project

A fully funded PhD studentship at the intersection of logic, category theory, and program semantics. Master's students in mathematics or computer science with strong interests on fundamental research are especially encouraged to apply.

About the Supervisor

Dr. Harsh Beohar is a lecturer in the verification group at Dept. of Computer Science, University of Sheffield. His main research interests are behavioural equivalences/distances, coalgebras and their modal logic, process algebra and comparative concurrency semantics.

Project Description

Coalgebras are mathematical structures that can be seen as a 'categorical' generalisation of an automaton/a state machine. Various forms of behavioural conformances (like bisimulation equivalence/distance, trace equivalence/distance) can be defined on the states of such coalgebras. In this project, we would like to study modal logic and corresponding 2-player games on coalgebras with side effects. The research will be part of a project called "Quantitative verification of software families based on coalgebraic modal logic and games". Some preliminary result on behavioural equivalence can be found here:


In addition, the candidate will have the opportunity to collaborate with researchers both domestically from the verification group in Sheffield and internationally with researchers from Germany working on coalgebras and related topics.

About the Department

99 percent of our research is rated in the highest two categories in the REF 2021, meaning it is classed as world-leading or internationally excellent. We are rated as 8th nationally for the quality of our research environment, showing that the Department of Computer Science is a vibrant and progressive place to undertake research.

The overall aim of the verification group is to develop (automated) techniques to reason about behaviour of complex software systems based on sound theory. Research areas include: semantics of concurrent and distributed systems; logics in computer science; algebraic and categorical approaches to program semantics; verification of multi-core programs and weak memory models; security verification; interactive and automated theorem proving.

Entry Requirements

Applicants should hold an MSc (or equivalent graduate) degree in Mathematics or Computer Science. If English is not your first language, you must have an IELTS score of 6.5 overall, with no less than 6.0 in each component.

How to Apply

To apply for a PhD studentship, applications must be made directly to the University of Sheffield using the Postgraduate Online Application Form. Make sure you name Dr Harsh Beohar and Professor Georg Struth as your proposed supervisors.

Information on what documents are required and a link to the application form can be found here - https://www.sheffield.ac.uk/postgraduate/phd/apply/applying 

The form has comprehensive instructions for you to follow, and pop-up help is available. 

Your research proposal should:

-be no longer than 4 A4 pages, include references

-outline your reasons for applying for this studentship

-explain how you would approach the research, including details of your skills and experience in the topic area

Funding Notes

This studentship will cover tuition fees at the UK rate and provide a tax-free stipend at the standard UK rate (currently £15,609 for 2021/22), for three and a half years. International students are eligible to apply, however, will have to pay the difference between the UK and Overseas tuition fee.

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