Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstraction, Up-to Techniques and Games for Systems of Fixpoint
  Equations   Systems of fixpoint equations over complete lattices, consisting of (mixed)
least and greatest fixpoint equations, allow one to express a number of
verification tasks such as model-checking of various kinds of specification
logics or the check of coinductive behavioural equivalences.
  In this paper we develop a theory of approximation for systems of fixpoint
equations in the style of abstract interpretation: a system over some concrete
domain is abstracted to a system in a suitable abstract domain, with conditions
ensuring that the abstract solution represents a sound/complete
overapproximation of the concrete solution.
  Interestingly, up-to techniques, a classical approach used in coinductive
settings to obtain easier or feasible proofs, can be interpreted as
abstractions in a way that they naturally fit in our framework and extend to
systems of equations.
  Additionally, relying on the approximation theory, we can provide a
characterisation of the solution of systems of fixpoint equations over complete
lattices in terms of a suitable parity game, generalising some recent work that
was restricted to continuous lattices.
  The game view opens the way to the development of on-the-fly algorithms for
characterising the solution of such equation systems.

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat