This paper studies runtime verification of properties expressed either in lineartime temporal logic (LTL) or timed lineartime temporal logic (TLTL). It classifies runtime verification in identifying its distinguishing features to model checking and testing, respectively. It introduces a three-valued semantics (with truth values true, false, inconclusive) as an adequate interpretation as to whether a partial observation of a running system meets an LTL or TLTL property.For LTL, a conceptually simple monitor generation procedure is given, which is optimal in two respects: First, the size of the generated deterministic monitor is minimal, and, second, the monitor identifies a continuously monitored trace as either satisfying or falsifying a property as early as possible. The feasibility of the developed methodology is demontrated using a collection of real-world temporal logic specifications. Moreover, the presented approach is related to the properties monitorable in general and is compared to existing concepts in the literature. It is shown that the set of monitorable properties does not only encompass the safety and co-safety properties but is strictly larger.For TLTL, the same road map is followed by first defining a three-valued semantics. The corresponding construction of a timed monitor is more involved, yet, as shown, possible.

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When monitoring a system w.r.t. a property defined in a temporal logic such as LTL, a major concern is to settle with an adequate interpretation of observable system events; that is, models of temporal logic formulae are usually infinite words of events, whereas at runtime only finite but incrementally expanding prefixes are available.In this work, we review LTL-derived logics for finite traces from a runtime-verification perspective. In doing so, we establish four maxims to be satisfied by any LTL-derived logic aimed at runtime verification. As no pre-existing logic readily satisfies all of them, we introduce a new four-valued logic Runtime Verification Linear Temporal Logic RV-LTL in accordance to these maxims. The semantics of Runtime Verification Linear Temporal Logic (RV-LTL) indicates whether a finite word describes a system behaviour which either (i) satisfies the monitored property, (ii) violates the property, (iii) will presumably violate the property, or (iv) will presumably conform to the property in the future, once the system has stabilized. Notably, (i) and (ii) correspond to the classical semantics of LTL, whereas (iii) and (iv) are chosen whenever an observed system behaviour has not yet lead to a violation or acceptance of the monitored property.Moreover, we present a monitor construction for RV-LTL properties in terms of Moore machines signalizing the semantics of the so far obtained execution trace w.r.t. the monitored property.Runtime verification of a given correctness property ϕ formulated in linear temporal logic (LTL) [18] requires at its core the evaluation of the semantics of ϕ w.r.t. to a finite observed system behaviour. But the evaluation of LTL properties on finite traces proved to be an obstacle, as LTL is usually evaluated over infinite traces and since the standard semantics of LTL on finite traces [15] is unsatisfactory for the purpose at hand.While the syntax and semantics of LTL on infinite traces is well accepted in the literature, there is no consensus on defining LTL over finite traces. Besides the definition in [15], a number of two-valued semantics for LTL on finite traces have been proposed [9,13,14,12,20,6], see Eisner et al. [8] for a comprehensive survey on this topic. Alternatively, it has been proposed to restrict the syntax of LTL for runtime verification, such that formulae which may contain certain future obligations cannot be specified at all [10].In monitoring a property, there arise at least three different situations: in the first case, the property is satisfied after a finite number of steps, independently of the future continuation; second, the property is shown to evaluate to false for every possible continuation, and third, the finite, already observed prefix still allows different continuations leading to either satisfaction or falsification. A prefix leading Vol. 20 No. 3, We consider in this article the traditional two-valued semantics with truth values true, denoted with , and false, denoted with ⊥, next to truth values that give more information to ...

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Abstract. Software product line engineering combines the individual developments of systems to the development of a family of systems consisting of common and variable assets. In this paper we introduce the process algebra PL-CCS as a product line extension of CCS and show how to model the overall behavior of an entire family within PL-CCS. PL-CCS models incorporate behavioral variability and allow the derivation of individual systems in a systematic way due to a semantics given in terms of multi-valued modal Kripke structures. Furthermore, we introduce multi-valued modal µ-calculus as a property specification language for system families specified in PL-CCS and show how model checking techniques operate on such structures. In our setting the result of model checking is no longer a simple yes or no answer but the set of systems of the product line that do meet the specified properties.

Electric vehicles (EV) powered by batteries will play a significant role in the road traffic of the future. The unique characteristics of such EVs-limited cruising range, long recharge times, and the ability to regain energy during deceleration-require novel routing algorithms, since the task is now to determine the most economical route rather than just the shortest one. This paper proposes extensions to general shortestpath algorithms that address the problem of energy-optimal routing. Specifically, we (i) formalize energy-efficient routing in the presence of rechargeable batteries as a special case of the constrained shortest path problem (CSP) with hard and soft constraints, and (ii) present an adaption of a general shortest path algorithm (using an energy graph, i.e., a graph with a weight function representing the energy consumption) that respects the given constraints and has a worst case complexity of O(n 3). The presented algorithms have been implemented and evaluated within a prototypic navigation system for energy-efficient routing.

Controller synthesis addresses the question of how to limit the internal behavior of a given implementation to meet its specification, regardless of the behavior enforced by the environment. In this paper, we consider a model with probabilism and nondeterminism where the nondeterministic choices in some states are assumed to be controllable, while the others are under the control of an unpredictable environment. We first consider probabilistic computation tree logic as specification formalism, discuss the role of strategy-types for the controller and show the NP-hardness of the controller synthesis problem. The second part of the paper presents a controller synthesis algorithm for automata-specifications which relies on a reduction to the synthesis problem for PCTL with fairness.

This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a threevalued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique.