Optimal Control of MDPs with Temporal Logic Constraints

In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem are sub-optimal. By leveraging ideas from automata-based model checking and game theory, we provide an optimal solution. We demonstrate the approach on an illustrative example.Comment: Technical report accompanying the CDC 2013 pape

Formal verification of a fault tolerant clock synchronization algorithm

A formal specification and mechanically assisted verification of the interactive convergence clock synchronization algorithm of Lamport and Melliar-Smith is described. Several technical flaws in the analysis given by Lamport and Melliar-Smith were discovered, even though their presentation is unusally precise and detailed. It seems that these flaws were not detected by informal peer scrutiny. The flaws are discussed and a revised presentation of the analysis is given that not only corrects the flaws but is also more precise and easier to follow. Some of the corrections to the flaws require slight modifications to the original assumptions underlying the algorithm and to the constraints on its parameters, and thus change the external specifications of the algorithm. The formal analysis of the interactive convergence clock synchronization algorithm was performed using the Enhanced Hierarchical Development Methodology (EHDM) formal specification and verification environment. This application of EHDM provides a demonstration of some of the capabilities of the system

Modular Compilation of a Synchronous Language

Synchronous languages rely on formal methods to ease the development of applications in an efficient and reusable way. Formal methods have been advocated as a means of increasing the reliability of systems, especially those which are safety or business critical. It is still difficult to develop automatic specification and verification tools due to limitations like state explosion, undecidability, etc... In this work, we design a new specification model based on a reactive synchronous approach. Then, we benefit from a formal framework well suited to perform compilation and formal validation of systems. In practice, we design and implement a special purpose language (LE) and its two semantics~: the ehavioral semantics helps us to define a program by the set of its behaviors and avoid ambiguousness in programs' interpretation; the execution equational semantics allows the modular compilation of programs into software and hardware targets (c code, vhdl code, fpga synthesis, observers). Our approach is pertinent considering the two main requirements of critical realistic applications~: the modular compilation allows us to deal with large systems, the model-based approach provides us with formal validation

Inferring Morphological Rules from Small Examples using 0/1 Linear Programming

We show how to express the problem of finding an optimal morpheme segmentation from a set of labelled words as a 0/1 linear programming problem, and how to build on this to analyse a language’s morphology. The result is an automatic method for segmentation and labelling that works well even when there is very little training data available

Verifying the interactive convergence clock synchronization algorithm using the Boyer-Moore theorem prover

The application of formal methods to the analysis of computing systems promises to provide higher and higher levels of assurance as the sophistication of our tools and techniques increases. Improvements in tools and techniques come about as we pit the current state of the art against new and challenging problems. A promising area for the application of formal methods is in real-time and distributed computing. Some of the algorithms in this area are both subtle and important. In response to this challenge and as part of an ongoing attempt to verify an implementation of the Interactive Convergence Clock Synchronization Algorithm (ICCSA), we decided to undertake a proof of the correctness of the algorithm using the Boyer-Moore theorem prover. This paper describes our approach to proving the ICCSA using the Boyer-Moore prover

Weaving of UML sequence diagrams using STAIRS

In this report we explore aspect-oriented modeling for UML 2.0 sequence diagrams. We ensure that the aspect weaving is semantics-based by using a formal trace model for sequence diagrams. A major challenge is to handle unbounded loops which produce infinite traces. We establish a systematic way to permutate and rewrite the original loop definition so that the weaving in many typical cases can be performed on a finite structure. We prove that it is always sufficient to consider a loop with upper bound relative to the pointcut definition to discover if the loop has infinitely repeating matches. A running example illustrates the approach and a prototype weaving tool is being implemented

Proofs and Refutations for Intuitionistic and Second-Order Logic

The ?^{PRK}-calculus is a typed ?-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend ?^{PRK} to encompass classical second-order logic, by incorporating parametric polymorphism and existential types. The system is shown to enjoy good computational properties, such as type preservation, confluence, and strong normalization, which is established by means of a reducibility argument. We identify a syntactic restriction on proofs that characterizes exactly the intuitionistic fragment of second-order ?^{PRK}, and we study canonicity results

A Mechanized Semantic Framework for Real-Time Systems

International audienceConcurrent systems consist of many components which may execute in parallel and are complex to design, to analyze, to verify, and to implement. The complexity increases if the systems have real-time constraints, which are very useful in avionic, spatial and other kind of embedded applications. In this paper we present a logical framework for defining and validating real-time formalisms as well as reasoning methods over them. For this purpose, we have implemented in the Coq proof assistant well known semantic domains for real-time systems based on labelled transitions systems and timed runs. We experiment our framework by considering the real-time CSP-based language fiacre, which has been defined as a pivot formalism for modeling languages (aadl, sdl, ...) used in the TOPCASED project. Thus, we define an extension to the formal semantic models mentioned above that facilitates the modeling of fine-grained time constraints of fiacre. Finally, we implement this extension in our framework and provide a proof method environment to deal with real-time system in order to achieve their formal certification

On-the-Fly Adaptation of Source Code Models using Meta-Learning

The ability to adapt to unseen, local contexts is an important challenge that successful models of source code must overcome. One of the most popular approaches for the adaptation of such models is dynamic evaluation. With dynamic evaluation, when running a model on an unseen file, the model is updated immediately after having observed each token in that file. In this work, we propose instead to frame the problem of context adaptation as a meta-learning problem. We aim to train a base source code model that is best able to learn from information in a file to deliver improved predictions of missing tokens. Unlike dynamic evaluation, this formulation allows us to select more targeted information (support tokens) for adaptation, that is both before and after a target hole in a file. We consider an evaluation setting that we call line-level maintenance, designed to reflect the downstream task of code auto-completion in an IDE. Leveraging recent developments in meta-learning such as first-order MAML and Reptile, we demonstrate improved performance in experiments on a large scale Java GitHub corpus, compared to other adaptation baselines including dynamic evaluation. Moreover, our analysis shows that, compared to a non-adaptive baseline, our approach improves performance on identifiers and literals by 44\% and 15\%, respectively.Comment: This paper has been withdrawn because we found a bug in the FOMAML implementation that invalidates some of the key claims in the pape