Duration Calculus Research Articles

Correct-by-Construction Reinforcement Learning of Cardiac Pacemakers from Duration Calculus Requirements

Correct-by-Construction Reinforcement Learning of Cardiac Pacemakers from Duration Calculus Requirements

Temporal Analysis and Classification of Sensor Signals

Understanding the behaviour of sensors, and in particular, the specifications of multisensor systems, are complex problems. The variables that need to be taken into consideration include, inter alia, the application domain, the way sensors are used, and their architectures. Various models, algorithms, and technologies have been designed to achieve this goal. In this paper, a new interval logic, referred to as Duration Calculus for Functions (DC4F), is applied to precisely specify signals originating from sensors, in particular sensors and devices used in heart rhythm monitoring procedures, such as electrocardiograms. Precision is the key issue in case of safety critical system specification. DC4F is a natural extension of the well-known Duration Calculus, an interval temporal logic used for specifying the duration of a process. It is suitable for describing complex, interval-dependent behaviours. Said approach allows one to specify temporal series, describe complex interval-dependent behaviours, and evaluate the corresponding data within a unifying logical framework. The use of DC4F allows one, on the one hand, to precisely specify the behaviour of functions modelling signals generated by different sensors and devices. Such specifications can be used for classifying signals, functions, and diagrams; and for identifying normal and abnormal behaviours. On the other hand, it allows one to formulate and frame a hypothesis. This is a significant advantage over machine learning algorithms, since the latter are capable of learning different patterns but fail to allow the user to specify the behaviour of interest.

An Interval Temporal Logic for Time Series Specification and Data Integration

The analysis of temporal series—in particular, analysis of multisensor data—is a complex problem. It depends on the application domain, the way the data have to be used, and sensors available, among other factors. Various models, algorithms, and technologies have been designed for this goal. Temporal logics are used to describe temporal properties of systems. The properties may specify the occurrence and the order of events in time, recurring patterns, complex behaviors, and processes. In this paper, a new interval logic, called duration calculus for functions (DC4F), is proposed for the specification of temporal series corresponding to multisensor data. DC4F is a natural extension of the well-known duration calculus, an interval temporal logic for the specification of process duration. The adequacy of the proposed logic is analyzed in the case of multisensor data concerning volcanic eruption monitoring. It turns out that the relevant behavior concerns time intervals, not only accumulated history as it is described in other kinds of temporal logics. The examples analyzed demonstrate that a description language is required to specify time series of various kind relative to time intervals. The duration calculus cannot be successfully applied for this task. The proposed calculus allows one to specify temporal series and complex interval-dependent behaviors, and to evaluate the corresponding data within a unifying logical framework. It allows to formulate hypotheses concerning volcano eruption phenomena. However, the expressivity of DC4F comes at the cost of its decidability.

Robust estimation of infant feeding indicators by data quality assessment of longitudinal electronic health records from birth up to 18 months of life

Background and objectiveThe Baby-Friendly Hospital Initiative (BFHI) is an international strategy aimed at improving breastfeeding practices in health care services. Regular monitoring of indicators is key for BFHI implementation and maintenance. Currently, routine data collected from electronic health records (EHR) is an excellent source for infant feeding monitoring, however data quality (DQ) assessment should be undertaken. The aim of this research is to enable robust estimations of infant feeding indicators through DQ assessment of routine EHR data. Materials and methodsWe use the longitudinal series of healthcare contacts belonging to 6427 children born from 2009 to 2018 in the Health Area V of Murcia (Spain). Longitudinal data came from EHR at hospital discharge and community infant health reviews up to 18 months. The data of each healthcare contact contained a 24-h recall of infant feeding. We perform a DQ process in three phases: (1) an assessment of each-single-contact and the definition of their infant feeding status; (2) a longitudinal DQ assessment of completeness and consistency of the series of contacts to obtain meta-information that guides the duration calculus, for each case, of the different types of breastfeeding: exclusive breastfeeding (EBF), full breastfeeding (FBF) and any breastfeeding (ABF); and finally (3) a robust estimation of indicators and description of DQ of each indicator. ResultsWe found deficiencies of DQ in 30.42% of single contacts for EBF, 19.02% for FBF and 22.50% for ABF that were used to establish the infant feeding status. However, after longitudinal DQ assessment, we obtained valid and reliable data rates for most indicators such as “median duration of breastfeeding” nearly 90%, both for FBF and ABF, not so for EBF. ConclusionsDespite the DQ deficiencies found in raw data, the DQ assurance approach by indicators proposed in this work, allowed us to obtain a robust estimation of indicators with a significant percentage of subjects with valid information for ABF and FBF monitoring. The estimations were consistent with results previously published. The methodology provided with this study allows a continuous and reliable population monitoring of infant feeding indicators of BFHI from routine EHR data.

Specification and Optimal Reactive Synthesis of Run-time Enforcement Shields

A system with sporadic errors (SSE) is a controller which produces high quality output but it may occasionally violate a critical requirement REQ(I,O). A run-time enforcement shield is a controller which takes (I,O) (coming from SSE) as its input, and it produces a corrected output O' which guarantees the invariance of requirement REQ(I,O'). Moreover, the output sequence O' must deviate from O "as little as possible" to maintain the quality. In this paper, we give a method for logical specification of shields using formulas of logic Quantified Discrete Duration Calculus (QDDC). The specification consists of a correctness requirement REQ as well as a hard deviation constraint HDC which must both be mandatorily and invariantly satisfied by the shield. Moreover, we also use quantitative optimization to give a shield which minimizes the expected value of cumulative deviation in an H-optimal fashion. We show how tool DCSynth implementing soft requirement guided synthesis can be used for automatic synthesis of shields from a given specification. Next, we give logical formulas specifying several notions of shields including the k-Stabilizing shield of Bloem "et al." as well as the Burst-error shield of Wu "et al.", and a new e,d-shield. Shields can be automatically synthesized for all these specifications using the tool DCSynth. We give experimental results showing the performance of our shield synthesis tool in relation to previous work. We also compare the performance of the shields synthesized under diverse hard deviation constraints in terms of their expected deviation and the worst case burst-deviation latency.

A practical approach to model checking Duration Calculus using Presburger Arithmetic

This paper investigates the feasibility of reducing a model-checking problem K ⊧ ϕ for discrete time Duration Calculus to the decision problem for Presburger Arithmetic. Theoretical results point at severe limitations of this approach: (1) the reduction in Franzle and Hansen (Int J Softw Inform 3(2–3):171–196, 2009) produces Presburger formulas whose sizes grow exponentially in the chop-depth of ϕ, where chop is an interval modality originating from Moszkowski (IEEE Comput 18(2):10–19, 1985), and (2) the decision problem for Presburger Arithmetic has a double exponential lower bound and a triple exponential upper bound. The generated Presburger formulas have a rich Boolean structure, many quantifiers and quantifier alternations. Such formulas are simplified using so-called guarded formulas, where a guard provides a context used to simplify the rest of the formula. A normal form for guarded formulas supports global effects of local simplifications. Combined with quantifier-elimination techniques, this normalization gives significant reductions in formula sizes and in the number of quantifiers. As an example, we solve a configuration problem using the SMT-solver Z3 as backend. Benefits and the current limits of the approach are illustrated by a family of examples.

Approximate Model Checking of Real-Time Systems for Linear Duration Invariants

Real-time systems are usually modelled with timed automata and real-time requirements relating to the state durations of the system are often specifiable using Linear Duration Invariants, which is a decidable subclass of Duration Calculus formulas. Various algorithms have been developed to check timed automata or real-time automata for linear duration invariants, but each needs complicated preprocessing and exponential calculation. To the best of our knowledge, these algorithms have not been implemented. In this paper, we present an approximate model checking technique based on a genetic algorithm to check real-time automata for linear durration invariants in reasonable times. Genetic algorithm is a good optimization method when a problem needs massive computation and it works particularly well in our case because the fitness function which is derived from the linear duration invariant is linear. ACM Computing Classification System (1998): D.2.4, C.3.

Reasoning about goal-directed real-time teleo-reactive programs

Abstract The teleo-reactive programming model is a high-level approach to developing real-time systems that supports hierarchical composition and durative actions. The model is different from frameworks such as action systems, timed automata and TLA + , and allows programs to be more compact and descriptive of their intended behaviour. Teleo-reactive programs are particularly useful for implementing controllers for autonomous agents that must react robustly to their dynamically changing environments. In this paper, we develop a real-time logic that is based on Duration Calculus and use this logic to formalise the semantics of teleo-reactive programs. We develop rely/guarantee rules that facilitate reasoning about a program and its environment in a compositional manner. We present several theorems for simplifying proofs of teleo-reactive programs and present a partially mechanised method for proving progress properties of goal-directed agents.

A normal specification of the abort-oriented concurency control for real-time database in duration calculus.

A normal specification of the abort-oriented concurency control for real-time database in duration calculus.

Mathematical analysis of stage-based programmable logic controller

The modern stage suspended boom system is automatically controlled by PLC (programmable logic controller), and represents a typical hybrid behavior. It is an important family of stage control machinery systems. This paper presents a formal approach to modeling the system behaviors of different scenes. The system is formally characterized and specified in a timed model. System properties are proved in the proof system of the extended duration calculus. The case study illustrates the feasibility of the proposed verification framework.

Metric propositional neighborhood logics on natural numbers

Interval logics formalize temporal reasoning on interval structures over linearly (or partially) ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined relative to time intervals, rather than time points. In this paper, we introduce and study Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is "met by" the current one and to an interval that "meets" the current one, plus an infinite set of length constraints, regarded as atomic propositions, to constrain the length of intervals. We argue that MPNL can be successfully used in different areas of computer science to combine qualitative and quantitative interval temporal reasoning, thus providing a viable alternative to well-established logical frameworks such as Duration Calculus. We show that MPNL is decidable in double exponential time and expressively complete with respect to a well-defined sub-fragment of the two-variable fragment $${{\rm FO}^2[\mathbb{N},=,<,s]}$$ of first-order logic for linear orders with successor function, interpreted over natural numbers. Moreover, we show that MPNL can be extended in a natural way to cover full $${{\rm FO}^2[\mathbb{N},=,<,s]}$$ , but, unexpectedly, the latter (and hence the former) turns out to be undecidable.

Reasoning about QoS Contracts in the Probabilistic Duration Calculus

The notion of contract was introduced to component-based software development in order to facilitate the semantically correct composition of components. We extend the form of this notion which is based on designs to capture probabilistic requirements on execution time. We show how reasoning about such requirements can be done in an infinite-interval-based system of probabilistic duration calculus.

A verification system for interval-based specification languages

Interval-based specification languages have been used to formally model and rigorously reason about real-time computing systems. This usually involves logical reasoning and mathematical computation with respect to continuous or discrete time. When these systems are complex, analyzing their models by hand becomes error-prone and difficult. In this article, we develop a verification system to facilitate the formal analysis of interval-based specification languages with machine-assisted proof support. The verification system is developed using a generic theorem prover, Prototype Verification System (PVS). Our system elaborately encodes a highly expressive set-based notation, Timed Interval Calculus (TIC), and can rigorously carry out the verification of TIC models at an interval level. We validated all TIC reasoning rules and discovered subtle flaws in the original rules. We also apply TIC to model Duration Calculus (DC), which is a popular interval-based specification language, and thus expand the capacity of the verification system. We can check the correctness of DC axioms, and execute DC proofs in a manner similar to the corresponding pencil-and-paper DC arguments.

A duration calculus with neighborhood modalities

To reason about continuous processes in some areas of artificial intelligence and embedded systems one has to express real-time properties. For such purpose a real-time logic has to be considered. Various such logics have been proposed. Some of these formalisms interpret formulas over intervals of time. These are called interval logics. Zhou Chaochen and Michael Hansen have introduced one such first-order interval logic called Neighborhood Logic (NL) which has two expanding modalities ◊r and ◊l. They have shown the adequacy of these modalities by deriving other unary and binary modalities from them; in particular, they show that chop can be expressed in terms of these modalities. The logic is subsequently expanded to get a Duration Calculus (called DC/NL) by expressing temporal variables as integrals of state variables. Liveness and fairness properties of a computing system can now be expressed in DC/NL by means of neighborhood (expanding) modalities. We take up an investigation of DC/NL in detail. We present a proof system for it. We further show that most of the results that hold in the original Duration Calculus continue to hold in our logic with some modifications. In this process we discuss soundness, completeness, and decidability results for DC/NL. Thus this paper establishes DC/NL as a useful formalism for specifying and verifying properties of real-time computing systems.

Parallel Model of DDS and Its Formalization

Although the model of DDS (deadline-driven scheduler) is a classical model of real-time system, the space-condition is not included in its original framework. Based on the extension of the original framework of DDS, multi-processes task scheduling with space-constraint is investigated. By studying the parallel model of DDS, the concept of maximal separated task-set, the primary scheduling algorithm and the general scheduling algorithm are presented. In order to formalize the parallel model of DDS, the paper extend duration calculus to DC* with the idea of separation logic, which can express the space-constraint successfully, and give the formalization too.

Exploration of the Dendritic Cell Algorithm with the Duration Calculus

As one of the newest members in Artificial Immune Systems (AIS), the Dendritic Cell Algorithm (DCA) has been applied to a range of problems. These applications mainly belong to the field of anomaly detection. However, real-time detection, a new challenge to anomaly detection, requires improvement on the real-time capability of the DCA. To assess such capability, formal methods in the research of real-time systems can be employed. The findings of the assessment can provide guideline for the future development of the algorithm. Therefore, in this paper we use an interval logic based method, named the Duration Calculus (DC), to specify a simplified single-cell model of the DCA. Based on the DC specifications with further induction, we find that each individual cell in the DCA can perform its function as a detector in real-time. Since the DCA can be seen as many such cells operating in parallel, it is potentially capable of performing real-time detection. However, the analysis process of the standard DCA constricts its real-time capability. As a result, we conclude that the analysis process of the standard DCA should be replaced by a real-time analysis component, which can perform periodic analysis for the purpose of real-time detection.

Model checking Duration Calculus: a practical approach

Model checking of real-time systems against Duration Calculus (DC) specifications requires the translation of DC formulae into automata-based semantics. The existing algorithms provide a limited DC...

Model checking Duration Calculus: a practical approach

Abstract Model checking of real-time systems against Duration Calculus (DC) specifications requires the translation of DC formulae into automata-based semantics. The existing algorithms provide a limited DC coverage and do not support compositional verification. We propose a translation algorithm that advances the applicability of model checking tools to realistic applications. Our algorithm significantly extends the subset of DC that can be checked automatically. The central part of the algorithm is the automatic decomposition of DC specifications into sub-properties that can be verified independently. The decomposition is based on a novel distributive law for DC. We implemented the algorithm in a tool chain for the automated verification of systems comprising data, communication, and real-time aspects. We applied the tool chain to verify safety properties in an industrial case study from the European Train Control System (ETCS).

Automatic Verification of Combined Specifications: An Overview

This paper gives an overview of results of the project “Beyond Timed Automata” carried out in the Collaborative Research Center AVACS (Automatic Verification and Analysis of Complex Systems) of the Universities of Oldenburg, Freiburg, and Saarbrücken. We discuss how properties of high-level specifications of real-time systems combining the dimensions of process behaviour, data, and time can be automatically verified, exploiting recent advances in semantics, constraint-based model checking, and decision procedures for complex data.As specification language we consider CS-OZ-DC, which integrates concepts from Communicating Sequential Processes (CSP), Object-Z (OZ), and Duration Calculus (DC). Our approach to automatic verification of CSP-OZ-DC rests on a compositional semantics of this languages in terms of Phase-Event-Automata. These can be translated into Transition Constraint Systems which serve as an input language of an abstract refinement model checker called ARMC which can handle constraints covering both real-time and infinite data. This is demonstrated by a case study concerning emergency messages in the European Train Control System (ETCS). For CSP-OZ-DC we also discuss a UML profile and tool support.

On Verification of Linear Occurrence Properties of Real-Time Systems

Duration Calculus of Weakly Monotonic Time (WDC) is an extension of DC to allow description of discrete processes where several steps of computation can occur at the same time point. In this paper, we introduce Linear Occurrence Invariants (LOI) using WDC and give an algorithm to check real-time automata for LOI by solving integer programming problems. LOI can be used effectively to specify system requirements in some cases including when the system is considered under the true synchrony assumption. We also extend WDC probabilistically to express dependability requirements of real-time systems and develop a technique to check deterministic probabilistic real-time automata for a class of probabilistic WDC formulas.