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This paper consider the problem of determining the reliability of a software system which can be decomposed in a number of modules. We have derived the expression of the reliability of a system using the Markovian model for the transfer of…
Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…
Hardware-software contracts are abstract specifications of a CPU's leakage behavior. They enable verifying the security of high-level programs against side-channel attacks without having to explicitly reason about the microarchitectural…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
Applying deductive verification to formally prove that a program respects its formal specification is a very complex and time-consuming task due in particular to the lack of feedback in case of proof failures. Along with a non-compliance…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
The technology of formal software verification has made spectacular advances, but how much does it actually benefit the development of practical software? Considerable disagreement remains about the practicality of building systems with…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…
We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…
Software artifacts are ubiquitous in our lives being an essential part of home appliances, cars, cel phones, and even in more critical activities like aeronautics and health sciences. In this context software failures may produce enormous…
Dedukti has been proposed as a universal proof checker. It is a logical framework based on the lambda Pi calculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of…
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such…
Answering complex questions often requires multi-step reasoning in order to obtain the final answer. Most research into decompositions of complex questions involves open-domain systems, which have shown success in using these decompositions…
Formal verification has been successfully developed in computer science for verifying combinatorial classes of models and specifications. In like manner, formal verification methods have been developed for dynamical systems. However, the…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine…
We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question "can we decide algorithmically when a criterion is less conservative than another". Our…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…