942 research outputs found
Possibilistic Information Flow Control for Workflow Management Systems
In workflows and business processes, there are often security requirements on
both the data, i.e. confidentiality and integrity, and the process, e.g.
separation of duty. Graphical notations exist for specifying both workflows and
associated security requirements. We present an approach for formally verifying
that a workflow satisfies such security requirements. For this purpose, we
define the semantics of a workflow as a state-event system and formalise
security properties in a trace-based way, i.e. on an abstract level without
depending on details of enforcement mechanisms such as Role-Based Access
Control (RBAC). This formal model then allows us to build upon well-known
verification techniques for information flow control. We describe how a
compositional verification methodology for possibilistic information flow can
be adapted to verify that a specification of a distributed workflow management
system satisfies security requirements on both data and processes.Comment: In Proceedings GraMSec 2014, arXiv:1404.163
A Bestiary of Sets and Relations
Building on established literature and recent developments in the
graph-theoretic characterisation of its CPM category, we provide a treatment of
pure state and mixed state quantum mechanics in the category fRel of finite
sets and relations. On the way, we highlight the wealth of exotic beasts that
hide amongst the extensive operational and structural similarities that the
theory shares with more traditional arenas of categorical quantum mechanics,
such as the category fdHilb. We conclude our journey by proving that fRel is
local, but not without some unexpected twists.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Pure Maps between Euclidean Jordan Algebras
We propose a definition of purity for positive linear maps between Euclidean
Jordan Algebras (EJA) that generalizes the notion of purity for quantum
systems. We show that this definition of purity is closed under composition and
taking adjoints and thus that the pure maps form a dagger category (which sets
it apart from other possible definitions.) In fact, from the results presented
in this paper, it follows that the category of EJAs with positive contractive
linear maps is a dagger-effectus, a type of structure originally defined to
study von Neumann algebras in an abstract categorical setting. In combination
with previous work this characterizes EJAs as the most general systems allowed
in a generalized probabilistic theory that is simultaneously a dagger-effectus.
Using the dagger structure we get a notion of dagger-positive maps of the form
f = g*g. We give a complete characterization of the pure dagger-positive maps
and show that these correspond precisely to the Jordan algebraic version of the
sequential product that maps (a,b) to sqrt(a) b sqrt(a). The notion of
dagger-positivity therefore characterizes the sequential product.Comment: In Proceedings QPL 2018, arXiv:1901.0947
Additive monotones for resource theories of parallel-combinable processes with discarding
A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a
symmetric monoidal category together with an all-object-including symmetric
monoidal subcategory. We think of the morphisms of this category as processes,
and the morphisms of the subcategory as those processes that are freely
executable. Via a construction we refer to as parallel-combinable processes
with discarding, we obtain from this data a partially ordered monoid on the set
of processes, with f > g if one can use the free processes to construct g from
f. The structure of this partial order can then be probed using additive
monotones: order-preserving monoid homomorphisms with values in the real
numbers under addition. We first characterise these additive monotones in terms
of the corresponding partitioned process theory.
Given enough monotones, we might hope to be able to reconstruct the order on
the monoid. If so, we say that we have a complete family of monotones. In
general, however, when we require our monotones to be additive monotones, such
families do not exist or are hard to compute. We show the existence of complete
families of additive monotones for various partitioned process theories based
on the category of finite sets, in order to shed light on the way such families
can be constructed.Comment: In Proceedings QPL 2015, arXiv:1511.0118
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