278,611 research outputs found
Automatic Probabilistic Program Verification through Random Variable Abstraction
The weakest pre-expectation calculus has been proved to be a mature theory to
analyze quantitative properties of probabilistic and nondeterministic programs.
We present an automatic method for proving quantitative linear properties on
any denumerable state space using iterative backwards fixed point calculation
in the general framework of abstract interpretation. In order to accomplish
this task we present the technique of random variable abstraction (RVA) and we
also postulate a sufficient condition to achieve exact fixed point computation
in the abstract domain. The feasibility of our approach is shown with two
examples, one obtaining the expected running time of a probabilistic program,
and the other the expected gain of a gambling strategy.
Our method works on general guarded probabilistic and nondeterministic
transition systems instead of plain pGCL programs, allowing us to easily model
a wide range of systems including distributed ones and unstructured programs.
We present the operational and weakest precondition semantics for this programs
and prove its equivalence
Asymptotic tail behavior of phase-type scale mixture distributions
We consider phase-type scale mixture distributions which correspond to
distributions of a product of two independent random variables: a phase-type
random variable and a nonnegative but otherwise arbitrary random variable
called the scaling random variable. We investigate conditions for such a
class of distributions to be either light- or heavy-tailed, we explore
subexponentiality and determine their maximum domains of attraction. Particular
focus is given to phase-type scale mixture distributions where the scaling
random variable has discrete support --- such a class of distributions has
been recently used in risk applications to approximate heavy-tailed
distributions. Our results are complemented with several examples.Comment: 18 pages, 0 figur
Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information
A usual code for quantum wiretap channel requires an auxiliary random
variable subject to the perfect uniform distribution. However, it is difficult
to prepare such an auxiliary random variable. We propose a code that requires
only an auxiliary random variable subject to a non-uniform distribution instead
of the perfect uniform distribution. Further, we evaluate the exponential
decreasing rate of leaked information and derive its equivocation rate. For
practical constructions, we also discuss the security when our code consists of
a linear error correcting code
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