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Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the…
We consider a quantified version of the (propositional) modal logic $\mathsf{BK}$, proposed earlier by S. P. Odintsov and H. Wansing; this version will be denoted by $\mathsf{QBK}$. Using the canonical model method, we prove the strong…
We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…
We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional continuous functionals induced by Kleene's second model $K_2$. We prove that a formulation of the…
The present paper introduces Scala-of-Coq, a new compiler that allows a Coq-based synthesis of Scala programs which are "correct-by-construction". A typical workflow features a user implementing a Coq functional program, proving this…
We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show…
Improvements in data acquisition and processing techniques have lead to an almost continuous flow of information for financial data. High resolution tick data are available and can be quite conveniently described by a continuous time…
I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction…
Reinforcement learning algorithms solve sequential decision-making problems in probabilistic environments by optimizing for long-term reward. The desire to use reinforcement learning in safety-critical settings inspires a recent line of…
Path checking, the special case of the model checking problem where the model under consideration is a single path, plays an important role in monitoring, testing, and verification. We prove that for linear-time temporal logic (LTL), path…
Jasmin is a programming and verification framework for developing efficient, formally verified, cryptographic implementations. A main component of the framework is the Jasmin compiler, which empowers programmers to write efficient…
Reactive programs combine traditional sequential programming constructs with primitives to allow communication with other concurrent agents. They are ubiquitous in modern applications, ranging from components systems and web services, to…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
Gradual verification soundly combines static checking and dynamic checking to provide an incremental approach for software verification. With gradual verification, programs can be partially specified first, and then the full specification…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
Networks are hard to configure correctly, and misconfigurations occur frequently, leading to outages or security breaches. Formal verification techniques have been applied to guarantee the correctness of network configurations, thereby…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…