118 research outputs found
Refinement algebra for probabilistic programs
We identify a refinement algebra for reasoning about probabilistic program transformations in a total-correctness setting. The algebra is equipped with operators that determine whether a program is enabled or terminates respectively. As well as developing the basic theory of the algebra we demonstrate how it may be used to explain key differences and similarities between standard (i.e. non-probabilistic) and probabilistic programs and verify important transformation theorems for probabilistic action systems.29 page(s
Minimisation in Logical Form
Stone-type dualities provide a powerful mathematical framework for studying
properties of logical systems. They have recently been fruitfully explored in
understanding minimisation of various types of automata. In Bezhanishvili et
al. (2012), a dual equivalence between a category of coalgebras and a category
of algebras was used to explain minimisation. The algebraic semantics is dual
to a coalgebraic semantics in which logical equivalence coincides with trace
equivalence. It follows that maximal quotients of coalgebras correspond to
minimal subobjects of algebras. Examples include partially observable
deterministic finite automata, linear weighted automata viewed as coalgebras
over finite-dimensional vector spaces, and belief automata, which are
coalgebras on compact Hausdorff spaces. In Bonchi et al. (2014), Brzozowski's
double-reversal minimisation algorithm for deterministic finite automata was
described categorically and its correctness explained via the duality between
reachability and observability. This work includes generalisations of
Brzozowski's algorithm to Moore and weighted automata over commutative
semirings.
In this paper we propose a general categorical framework within which such
minimisation algorithms can be understood. The goal is to provide a unifying
perspective based on duality. Our framework consists of a stack of three
interconnected adjunctions: a base dual adjunction that can be lifted to a dual
adjunction between coalgebras and algebras and also to a dual adjunction
between automata. The approach provides an abstract understanding of
reachability and observability. We illustrate the general framework on range of
concrete examples, including deterministic Kripke frames, weighted automata,
topological automata (belief automata), and alternating automata
QoS-aware component composition
Component’s QoS constraints cannot be ignored when composing them to build reliable loosely-coupled, distributed systems. Therefore they should be explicitly taken into account in any formal model for component-based development. Such is the purpose of this paper: to extend a calculus of component composition to deal, in an effective way, with QoS constraints. Particular emphasis is put on how the laws that govern composition can be derived, in a calculational, pointfree style, in this new model
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