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Mac Douglas Gondole Buni all-in-one back-to-back, 1 zipped compartment for coins and Finally, we show using combinatorial arguments that for these notions of test coverage we introduce, we can find a lower bound on the probability that a random test covers a given goal. Our general construction then explains why random testing tools achieve good coverage—and hence, find bugs—quickly.

This will be a presentation of a collaboration with Laure Daviaud and Florian Zuleger. We show how recent results concerning quantitative forms of automata help providing refined understanding of the properties of a system for instance, a program. In particular, combining the size-change abstraction together with results concerning the asymptotic behavior of tropical automata yields extremely fine complexity analysis of some pieces of code.

We propose a new formal criterion for secure compilation, giving strong end-to-end security guarantees for software components written in unsafe, low-level languages with C-style undefined behavior. Each component is protected from all the others—in particular, from components that have encountered undefined behavior and become compromised. Each component receives secure compilation guarantees up to the point when it becomes compromised, after which an attacker can take complete control over the component and use any of its privileges to attack the remaining uncompromised components.

More precisely, we ensure that dynamically compromised components cannot break the safety properties of the system at the target level any more than equally privileged components without undefined behavior already could in the source language. To illustrate this model, we build a secure compilation chain for an unsafe language with buffers, procedures, and components. We compile it to a simple RISC abstract machine with built-in compartmentalization and provide thorough proofs, many of them machine-checked in Coq, showing that the compiler satisfies our secure compilation criterion.

Finally, we show that the protection guarantees offered by the compartmentalized abstract machine can be achieved at the machine-code level using either software fault isolation or a tag-based reference monitor. In this talk, we propose an abstraction of these methods. Consider an algebra A in the sense of universal algebra, i.

A grammar over A is like a context-free grammar, except that it generates a subset of the algebra A, and the rules use operations from the algebra A. The classical context-free grammars are the special case when the algebra A is the free monoid with concatenation. In particular:.

Software-based countermeasures provide effective mitigation against side-channel attacks, often with minimal efficiency and deployment overheads. Their effectiveness is often amenable to rigorous analysis: However, in absence of further justification, the guarantees only hold for the language source, target, or intermediate representation on which the analysis is performed.

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We present a general method, based on the notion of 2-simulation, for proving that a compilation pass preserves the constant-time countermeasure. Using the Coq proof assistant, we verify the correctness of our method and of several representative instantiations. Maximisation vs. We consider opacity questions where an observation function provides to an external attacker a view of the states along executions and secret executions are those visiting some state from a fixed subset.

Disclosure occurs when the observer can deduce from a finite observation that the execution is secret. In a probabilistic and nondeterministic setting, where an internal agent can choose between actions, there are two points of view, depending on the status of this agent: In the former situation, corresponding to a worst case, the disclosure value is the supremum over the strategies of the probability to disclose the secret maximisation , whereas in the latter case, the disclosure is the infimum minimisation.

We address quantitative problems comparing the optimal value with a threshold and qualitative ones when the threshold is zero or one related to both forms of disclosure for a fixed or finite horizon. For all problems, we characterise their decidability status and their complexity.

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We discover a surprising asymmetry: On the other hand, for the questions addressed here, more minimisation problems than maximisation ones are decidable. Fault-tolerant distributed algorithms are notoriously hard to get right. I present an automated method that helps in that process: Our tool then automatically fills the missing parts. In particular, I will consider threshold-based distributed algorithms, where a process has to wait until the number of messages it receives reaches a certain threshold, in order to perform an action. Such algorithms are typically used for achieving fault tolerance in distributed algorithms for broadcast, atomic commitment, or consensus.

Using this method, one can synthesize distributed algorithms that are correct for every number n of processes and every number t of faults, provided some resilience condition holds, e. This approach combines recent progress in parameterized model checking of distributed algorithms—which I also address—with counterexample-guided synthesis.

Efficient implementations of concurrent objects such as atomic collections are essential to modern computing. Unfortunately their correctness criteria — linearizability with respect to given ADT specifications — are hard to verify. Verifying linearizability is undecidable in general, even on classes of implementations where the usual control-state reachability is decidable.

In this work we consider concurrent priority queues which are fundamental to many multi-threaded applications like task scheduling or discrete event simulation, and show that verifying linearizability of such implementations is reducible to control-state reachability. This reduction entails the first decidability results for verifying concurrent priority queues with an unbounded number of threads, and it enables the application of existing safety-verification tools for establishing their correctness.

In this talk, we present a proof of correctness for an algorithm computing strongly connected components in a directed graph by Tarjan []. It will be the starting point of a discussion about the readability of formal proofs. Looking at some monoids and semi rings natural numbers, integers and p-adic integers , and more generally, residually finite algebras in a strong sense , we prove the equivalence of two ways for a function on such an algebra to behave like the operations of the algebra.

The first way is to preserve congruences or stable preorders. We introduce constrained Horn clauses in higher-order logic, and decision problems concerning their satisfiability and the safety verification of higher-order programs.


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We show that, although satisfiable systems of higher-order clauses do not generally have least models, there is a notion of canonical model obtained via a reduction to a problem concerning a kind of monotone logic program. Following work in higher-order program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that an extension of the decision problem in which refinement types are used directly as guards on existential quantifiers can be reduced to the original problem.

This result can be used to show that properties of higher-order functions that are definable using refinement types are also expressible using higher-order constrained Horn clauses. In the context of deductive program verification, ghost code is part of the program that is added for the purpose of specification. Ghost code must not interfere with regular code, in the sense that it can be erased without any observable difference in the program outcome. In particular, ghost data cannot participate in regular computations and ghost code cannot mutate regular data or diverge.

The idea exists in the folklore since the early notion of auxiliary variables and is implemented in many state-of-the-art program verification tools. However, a rigorous definition and treatment of ghost code is surprisingly subtle and few formalizations exist. In this talk, we describe a simple ML-style programming language with mutable state and ghost code.

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Non-interference is ensured by a type system with effects, which allows, notably, the same data types and functions to be used in both regular and ghost code. We define the procedure of ghost code erasure and we prove its safety using bisimulation. A similar type system, with numerous extensions which we briefly discuss, is implemented in the program verification environment Why3.

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