Runtime monitoring is one of the central tasks in the area of operational decision support for business process management. In particular, it helps process executors to check on-the-fly whether a running process instance satisfies business constraints of interest, providing an immediate feedback when deviations occur. We study runtime monitoring of properties expressed in LTL on finite traces (LTLf), and in its extension LDLf. LDLf is a powerful logic that captures all monadic second order logic on finite traces, and that is obtained by combining regular expressions with LTLf, adopting the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its greater expressivity, \LDLf has exactly the same computational complexity of LTLf.
We show that LDLf is able to declaratively express, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors. On the one hand, this enables us to directly employ the standard characterization of LDLf based on finite-state automata to monitor constraints in a fine-grained way. On the other hand, it provides the basis for declaratively expressing sophisticated metaconstraints that predicate on the monitoring state of other constraints, and to check them by relying on standard logical services instead of ad-hoc algorithms.
In addition, we devise a direct translation of LDLf formulae into nondeterministic finite-state automata, avoiding to detour to Buchi automata or alternating automata. We then report on how this approach has been effectively implemented using Java to manipulate LDLf formulae and their corresponding monitors, and the well-known ProM process mining suite as underlying operational decision support infrastructure.
Signal Temporal Logic monitoring over numerical simulation traces has emerged as an effective approach to approximate verification of continuous and hybrid systems. In this report we explore an exact verification procedure for STL properties based on monitoring verified traces in the form of Taylor model flowpipes as produced by the Flow* verified integrator. We explore how tight integration with Flow*'s symbolic flowpipe representation can lead to more precise and more efficient monitoring. We then show how the performance of monitoring can be increased substantially by introducing masks, a p…
A bitmap is a data structure designed to compactly represent sets of integers; it provides very fast operations for querying and manipulating such sets, exploiting bit-level parallelism. In this paper, we describe a technique for the offline verification of arbitrary expressions of Linear Temporal Logic using bitmap manipulation. An event trace is first preprocessed and transformed into a set of bitmaps. The LTL expression is then evaluated through a recursive procedure manipulating these bitmaps. Experimental results show that, for complex LTL formulas containing almost 20 operators, event tr…
This paper presents a new technique for optimizing formal analysis of propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely the formula simplification table. A formula simplification table is a mathematical table that shows all possible simplifications of the formula under different truth assignments of its variables. The advantages of constructing a simplification table of a formula are two-fold. First, it can be used to compute the logical influence weight of each variable in the formula, which is a metric that shows the importance of the variable in affecting the out…
Cyber-Physical Systems~(CPS) consist of collaborative, networked and tightly intertwined computational (logical) and physical components, each operating at different spatial and temporal scales. Hence, the spatial and temporal requirements play an essential role for their correct and safe execution. Furthermore, the local interactions among the system components result in global spatio-temporal emergent behaviors often impossible to predict at the design time. In this work, we pursue a complementary approach by introducing STREL a novel spatio-temporal logic that enables the specification of s…
This paper presents an extension of the safety fragment of Hennessy-Milner Logic with recursion over sets of traces, in the spirit of Hyper-LTL. It then introduces a novel monitoring setup that employs circuit-like structures to combine verdicts from regular monitors. The main contribution of this study is the monitors and their semantics themselves, as well as a monitor-synthesis procedure from formulae in the logic that yields `circuit-like monitors' of this type that are sound and violation complete over a finite set of infinite traces.
From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically interconnected and arranged in a particular spatial configuration. Spatio-Temporal Reach and Escape Logic (STREL) is a recent logic-based formal language designed to specify and to reason about spatio-temporal properties. STREL considers each system's entity as a node of a dynamic weighted graph representing their spatial arrangement. Each node generates a set of mixe…
We present MoonLight, a tool for monitoring temporal and spatio-temporal properties of mobile and spatially distributed cyber-physical systems (CPS). In the proposed framework, space is represented as a weighted graph, describing the topological configurations in which the single CPS entities (nodes of the graph) are arranged. Both nodes and edges have attributes modelling physical and logical quantities that can change in time. MoonLight is implemented in Java and supports the monitoring of Spatio-Temporal Reach and Escape Logic (STREL). MoonLight can be used as a standalone command line tool…
Quantitative Monitoring of Signal First-Order Logic
Zeroth Research（零次研究）；Institute of Science and Technology Austria（奥地利科学技术研究所）；CISPA Helmholtz Center for Information Security（CISPA赫尔姆霍兹信息安全中心）；Leiden University（莱顿大学）
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved by an efficient and rigorous monitoring algorithm. This algorithm performs a forward simulation of a continuous-time dynamical system, detects a set of time intervals in which the atomic propositions hol…
We introduce a new logic called Signal Convolution Logic (SCL) that combines temporal logic with convolutional filters from digital signal processing. SCL enables to reason about the percentage of time a formula is satisfied in a bounded interval. We demonstrate that this new logic is a suitable formalism to effectively express non-functional requirements in Cyber-Physical Systems displaying noisy and irregular behaviours. We define both a qualitative and quantitative semantics for it, providing an efficient monitoring procedure. Finally, we prove SCL at work to monitor the artificial pancreas…
Signal temporal logic (STL) was introduced for monitoring temporal properties of continuous-time signals for continuous and hybrid systems. Differential dynamic logic (dL) was introduced to reason about the end states of a hybrid program. Over the past decade, STL and its variants have significantly gained in popularity in the industry for monitoring purposes, while dL has gained in popularity for verification of hybrid systems. In this paper, we bridge the gap between the two different logics by introducing signal temporal dynamic logic (STdL) -- a dynamic logic that reasons about a subset of…
Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other and are thus not monitorable by tools that consider computations in isolation. We present the monitoring approach implemented in the latest version of RVHyper, a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic HyperLTL, which extends linear-time temporal logic (LTL) with trace quantifiers and trace variables. RVHyper processes execution traces sequentially until a violation of the specification is detecte…
We present HySIA: a reliable runtime verification tool for nonlinear hybrid automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA with interval analysis techniques so that a trajectory is enclosed sharply within a set of intervals. Then, HySIA computes whether the simulated trajectory satisfies a given STL property; the computation is performed again with interval analysis to achieve reliability. Simulation and verification using HySIA are demonstrated through several example HA and STL formulas.
Techniques for runtime verification often utilise specification languages that are (i) reasonably expressive, and (ii) relatively abstract (i.e. they operate on a level of abstraction that separates them from the system being monitored). Inspired by the problem of monitoring systems involved in processing data generated by the high energy physics experiments at CERN, this report proposes a specification language, Control Flow Temporal Logic (CFTL), whose distinguishing characteristic is its tight coupling with the control flow of the programs for which it is used to write specifications. This …
Verifying hyperproperties at runtime is a challenging problem as hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other. It is necessary to store previously seen traces, because every new incoming trace needs to be compatible with every run of the system observed so far. Furthermore, the new incoming trace poses requirements on future traces. In our monitoring approach, we focus on those requirements by rewriting a hyperproperty in the temporal logic HyperLTL to a Boolean constraint system. A hyperproperty is then violated by…
Hyperproperties, such as non-interference and observational determinism, relate multiple system executions to each other. They are not expressible in standard temporal logics, like LTL, CTL, and CTL*, and thus cannot be monitored with standard runtime verification techniques. HyperLTL extends linear-time temporal logic (LTL) with explicit quantification over traces in order to express Hyperproperties. We investigate the runtime verification problem of HyperLTL formulas for three different input models: (1) The parallel model, where a fixed number of system executions is processed in parallel. …
Faculty of Engineering, Free University of Bozen-Bolzano（博洛尼亚-博尔扎诺自由大学工程学院）；Department of Computer, Control and Management Engineering, Sapienza, Università di Roma（罗马大学计算机、控制与管理工程系）
We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible finite-length, future continuations. This makes monitoring at least as hard as satisfiability and validity. Traces consist of finite sequences of assignments of a fixed set of variables to numerical values. Properties are specified in a logic we call ALTLf, combining LTLf (LTL on finite traces) with linear arithmetic constraints that may carry lookahead, i.e., variables…
This paper presents a novel framework for decentralized monitoring of Linear Temporal Logic (LTL), under the situation where processes are synchronous, uniform (i.e. all processes are peers), and the formula is represented as a tableau. The tableau technique allows one to construct a semantic tree for the input formula, which can be used to optimize the decentralized monitoring of LTL in various ways. Given a system P and an LTL formula L, we construct a tableau for L. The tableauis used for two purposes: (a) to synthesize an efficient round-robin communication policy for processes, and (b) to…
We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential blowup in the syntactic size of the monitors, and a triple-exponential blowup when the goal is a deterministic monitor. We show that these bounds are tight and that they also hold for translations between corresponding fragments of Hennessy-Milner logic with recursion over infinite traces.
Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic
University of Antwerp（安特卫普大学）；Flanders Make（法兰德斯制造）；LaBRI, University of Bordeaux（波尔多大学LaBRI实验室）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；Technical University of Dortmund（多特蒙德工业大学）；Center for Data Science and Security, University Alliance Ruhr（鲁尔大学联盟数据科学与安全中心）
We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages accepted by MK-fuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introd…
University of Tartu（塔尔图大学）；Free University of Bozen-Bolzano（博尔扎诺自由大学）；University of Milano-Bicocca（米兰比可卡大学）
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of uncertainty which cannot be handled with classical logics. We thus propose a new probabilistic temporal logic over finite traces using superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We then stu…
We present RTAMT, an online monitoring library for Signal Temporal Logic (STL) and its interface-aware variant (IA-STL), providing both discrete- and dense-time interpretation of the logic. We also introduce RTAMT4ROS, a tool that integrates RTAMT with Robotic Operating System (ROS), a common environment for developing robotic applications. We evaluate RTAMT and RTAMT4ROS on two robotic case studies.
Where full static analysis of systems fails to scale up due to system size, dynamic monitoring has been increasingly used to ensure system correctness. The downside is, however, runtime overheads which are induced by the additional monitoring code instrumented. To address this issue, various approaches have been proposed in the literature to use static analysis in order to reduce monitoring overhead. In this paper we generalise existing work which uses control-flow static analysis to optimise properties specified as automata, and prove how similar analysis can be applied to more expressive sym…
We consider the problem of monitoring a Linear Time Logic (LTL) specification that is defined on infinite paths, over finite traces. For example, we may need to draw a verdict on whether the system satisfies or violates the property "p holds infinitely often." The problem is that there is always a continuation of a finite trace that satisfies the property and a different continuation that violates it. We propose a two-step approach to address this problem. First, we introduce a counting semantics that computes the number of steps to witness the satisfaction or violation of a formula for each p…
In this paper we introduce a new data-driven run-time monitoring system for analysing the behaviour of time evolving complex systems. The monitor controls the evolution of the whole system but it is mined from the data produced by its single interacting components. Relevant behavioural changes happening at the component level and that are responsible for global system evolution are captured by the monitor. Topological Data Analysis is used for shaping and analysing the data for mining an automaton mimicking the global system dynamics, the so-called Persistent Entropy Automaton (PEA). A slight …
