26,764 research outputs found
Towards mechanized correctness proofs for cryptographic algorithms: Axiomatization of a probabilistic Hoare style logic
In [Corin, den Hartog in ICALP 2006] we build a formal verification technique for game based correctness proofs of cryptograhic algorithms based on a probabilistic Hoare style logic [den Hartog, de Vink in IJFCS 13(3), 2002]. An important step towards enabling mechanized verification within this technique is an axiomatization of implication between predicates which is purely semantically defined in [den Hartog, de Vink in IJFCS 13(3), 2002]. In this paper we provide an axiomatization and illustrate its place in the formal verification technique of [Corin, den Hartog in ICALP 2006]
Probabilistic modal {\mu}-calculus with independent product
The probabilistic modal {\mu}-calculus is a fixed-point logic designed for
expressing properties of probabilistic labeled transition systems (PLTS's). Two
equivalent semantics have been studied for this logic, both assigning to each
state a value in the interval [0,1] representing the probability that the
property expressed by the formula holds at the state. One semantics is
denotational and the other is a game semantics, specified in terms of
two-player stochastic parity games. A shortcoming of the probabilistic modal
{\mu}-calculus is the lack of expressiveness required to encode other important
temporal logics for PLTS's such as Probabilistic Computation Tree Logic (PCTL).
To address this limitation we extend the logic with a new pair of operators:
independent product and coproduct. The resulting logic, called probabilistic
modal {\mu}-calculus with independent product, can encode many properties of
interest and subsumes the qualitative fragment of PCTL. The main contribution
of this paper is the definition of an appropriate game semantics for this
extended probabilistic {\mu}-calculus. This relies on the definition of a new
class of games which generalize standard two-player stochastic (parity) games
by allowing a play to be split into concurrent subplays, each continuing their
evolution independently. Our main technical result is the equivalence of the
two semantics. The proof is carried out in ZFC set theory extended with
Martin's Axiom at an uncountable cardinal
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
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