Interval tree clocks: a logical clock for dynamic systems

Lecture Notes in Computer Science 5401, 2008Causality tracking mechanisms, such as vector clocks and version vectors, rely on mappings from globally unique identifiers to integer counters. In a system with a well known set of entities these ids can be preconfigured and given distinct positions in a vector or distinct names in a mapping. Id management is more problematic in dynamic systems, with large and highly variable number of entities, being worsened when network partitions occur. Present solutions for causality tracking are not appropriate to these increasingly common scenarios. In this paper we introduce Interval Tree Clocks, a novel causality tracking mechanism that can be used in scenarios with a dynamic number of entities, allowing a completely decentralized creation of processes/replicas without need for global identifiers or global coordination. The mechanism has a variable size representation that adapts automatically to the number of existing entities, growing or shrinking appropriately. The representation is so compact that the mechanism can even be considered for scenarios with a fixed number of entities, which makes it a general substitute for vector clocks and version vectors

Real-Time Synthesis is Hard!

We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BRRS subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In this paper, we precise the decidability border of MITL synthesis. We show RS is undecidable on finite words too, and present a landscape of restrictions (both on the logic and on the possible controllers) that are still undecidable. On the positive side, we revisit BRRS and introduce an efficient on-the-fly algorithm to solve it

Analyzing Timed Systems Using Tree Automata

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions)

Polynomial Interrupt Timed Automata

Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA). We prove the decidability of the reachability and model checking of a timed version of CTL by an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. Moreover, we show that PolITA are incomparable with stopwatch automata. Finally additional features are introduced while preserving decidability

Thunderstriking constraints with JUPITER

We present JUPITER, a tool for analysing multi-constrained systems. JUPITER was built to explore three basic ideas. First, how to use controller synthesis so as to find the exact conditions under which a particular constraint will be satisfied. Second, how to successively refine the models used for the controller synthesis so as to obtain a series of more easily understandable and more robust controllers. Last but not least, how to structure & explain the synthesised controllers and provide hints to designers for further optimisations through the use of machine learning techniques. Thus, JUPITER can help in the design and analysis of multi-constraint systems through the automatic synthesis of control logic for certain of the constraints and the aid it provides to designers for discovering further optimisations. The controllers it synthesises can be easily implemented on top of a standard real-time OS

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE