99 research outputs found
Finding polynomial loop invariants for probabilistic programs
Quantitative loop invariants are an essential element in the verification of
probabilistic programs. Recently, multivariate Lagrange interpolation has been
applied to synthesizing polynomial invariants. In this paper, we propose an
alternative approach. First, we fix a polynomial template as a candidate of a
loop invariant. Using Stengle's Positivstellensatz and a transformation to a
sum-of-squares problem, we find sufficient conditions on the coefficients.
Then, we solve a semidefinite programming feasibility problem to synthesize the
loop invariants. If the semidefinite program is unfeasible, we backtrack after
increasing the degree of the template. Our approach is semi-complete in the
sense that it will always lead us to a feasible solution if one exists and
numerical errors are small. Experimental results show the efficiency of our
approach.Comment: accompanies an ATVA 2017 submissio
Catoids and modal convolution algebras
We show how modal quantales arise as convolution algebras QX
of functions from catoids X, multisemigroups equipped with source and target maps, into modal quantales value or weight quantales Q. In the tradition of boolean algebras with operators we study modal correspondences between algebraic laws in X, Q and QX. The catoids introduced generalise Schweizer and Sklar’s function systems and single-set categories to structures isomorphic to algebras of ternary relations, as they are used for boolean algebras with operators and substructural logics. Our correspondence results support a generic construction of weighted modal quantales from catoids. This construction is illustrated by many examples. We also relate our results to reasoning with stochastic matrices or probabilistic predicate transformers
A Holistic Approach in Embedded System Development
We present pState, a tool for developing "complex" embedded systems by
integrating validation into the design process. The goal is to reduce
validation time. To this end, qualitative and quantitative properties are
specified in system models expressed as pCharts, an extended version of
hierarchical state machines. These properties are specified in an intuitive way
such that they can be written by engineers who are domain experts, without
needing to be familiar with temporal logic. From the system model, executable
code that preserves the verified properties is generated. The design is
documented on the model and the documentation is passed as comments into the
generated code. On the series of examples we illustrate how models and
properties are specified using pState.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338
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]
Stochastic Relations Interpreting Modal Logic
We propose an interpretation of modal logic through stochastic relations, providing a probabilistic complement to the usual nondeterministic interpretations using Kripke models. A simple temporal logic and a logic with a countable number of diamonds illustrate the approach. The main technical result of this paper is a probabilistic analogon to the well-known Hennessy-Milner Theorem characterizing models that have the same theories for their states and bisimilarity as equivalent properties. This requires the study of congruences for stochastic relations that underly the interpretation, for which a general bisimilarity result is also established. The results depend on the existence of semi-pullbacks for stochastic relations over analytic spaces
Computer-aided verification in mechanism design
In mechanism design, the gold standard solution concepts are dominant
strategy incentive compatibility and Bayesian incentive compatibility. These
solution concepts relieve the (possibly unsophisticated) bidders from the need
to engage in complicated strategizing. While incentive properties are simple to
state, their proofs are specific to the mechanism and can be quite complex.
This raises two concerns. From a practical perspective, checking a complex
proof can be a tedious process, often requiring experts knowledgeable in
mechanism design. Furthermore, from a modeling perspective, if unsophisticated
agents are unconvinced of incentive properties, they may strategize in
unpredictable ways.
To address both concerns, we explore techniques from computer-aided
verification to construct formal proofs of incentive properties. Because formal
proofs can be automatically checked, agents do not need to manually check the
properties, or even understand the proof. To demonstrate, we present the
verification of a sophisticated mechanism: the generic reduction from Bayesian
incentive compatible mechanism design to algorithm design given by Hartline,
Kleinberg, and Malekian. This mechanism presents new challenges for formal
verification, including essential use of randomness from both the execution of
the mechanism and from the prior type distributions. As an immediate
consequence, our work also formalizes Bayesian incentive compatibility for the
entire family of mechanisms derived via this reduction. Finally, as an
intermediate step in our formalization, we provide the first formal
verification of incentive compatibility for the celebrated
Vickrey-Clarke-Groves mechanism
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