Full abstraction for fair testing in CCS

In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the 'rule of the game'. From any playground, two languages, equipped with labelled transition systems, are derived, as well as a strong, functional bisimulation between them.Comment: 15 pages, to appear in CALCO '13. To appear Lecture notes in computer science (2013

Data types with symmetries and polynomial functors over groupoids

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect is often prominent and justifies the terminology. For example, Tambara's theorem states that the category of finite polynomial functors is the Lawvere theory for commutative semirings. In this talk I will explain how an upgrade of the theory from sets to groupoids is useful to deal with data types with symmetries, and provides a common generalisation of and a clean unifying framework for quotient containers (cf. Abbott et al.), species and analytic functors (Joyal 1985), as well as the stuff types of Baez-Dolan. The multi-variate setting also includes relations and spans, multispans, and stuff operators. An attractive feature of this theory is that with the correct homotopical approach - homotopy slices, homotopy pullbacks, homotopy colimits, etc. - the groupoid case looks exactly like the set case. After some standard examples, I will illustrate the notion of data-types-with-symmetries with examples from quantum field theory, where the symmetries of complicated tree structures of graphs play a crucial role, and can be handled elegantly using polynomial functors over groupoids. (These examples, although beyond species, are purely combinatorial and can be appreciated without background in quantum field theory.) Locally cartesian closed 2-categories provide semantics for 2-truncated intensional type theory. For a fullfledged type theory, locally cartesian closed \infty-categories seem to be needed. The theory of these is being developed by D.Gepner and the author as a setting for homotopical species, and several of the results exposed in this talk are just truncations of \infty-results obtained in joint work with Gepner. Details will appear elsewhere.Comment: This is the final version of my conference paper presented at the 28th Conference on the Mathematical Foundations of Programming Semantics (Bath, June 2012); to appear in the Electronic Notes in Theoretical Computer Science. 16p

DGD Gallery: Storage, sharing, and publication of digital research data

We describe a project, called the "Discretization in Geometry and Dynamics Gallery", or DGD Gallery for short, whose goal is to store geometric data and to make it publicly available. The DGD Gallery offers an online web service for the storage, sharing, and publication of digital research data.Comment: 19 pages, 8 figures, to appear in "Advances in Discrete Differential Geometry", ed. A. I. Bobenko, Springer, 201

Methods for Solving Extremal Problems in Practice

During the 20 th century there has been an incredible progress in solving theoretically hard problems in practice. One of the most prominent examples is the DPLL algorithm and its derivatives to solve the Boolean satisfiability problem, which can handle instances with millions of variables and clauses in reasonable time, notwithstanding the theoretical difficulty of solving the problem. Despite this progress, there are classes of problems that contain especially hard instances, which have remained open for decades despite their relative small size. One such class is the class of extremal problems, which typically involve finding a combinatorial object under some constraints (e.g, the search for Ramsey numbers). In recent years, a number of specialized methods have emerged to tackle extremal problems. Most of these methods are applied to a specific problem, despite the fact there is a great deal in common between different problems. Following a meticulous examination of these methods, we would like to extend them to handle general extremal problems. Further more, we would like to offer ways to exploit the general structure of extremal problems in order to develop constraints and symmetry breaking techniques which will, hopefully, improve existing tools. The latter point is of immense importance in the context of extremal problems, which often hamper existing tools when there is a great deal of symmetry in the search space, or when not enough is known of the problem structure. For example, if a graph is a solution to a problem instance, in many cases any isomorphic graph will also be a solution. In such cases, existing methods can usually be applied only if the model excludes symmetries