Model Checking Timeline-based Systems over Dense Temporal Domains?

In this paper, we introduce an automaton-theoretic approach to model checking linear time properties of timeline-based systems over dense temporal domains. The system under consideration is specified by means of (a decidable fragment of) timeline structures, timelines for short, which are a formal setting proposed in the literature to model planning problems in a declarative way. Timelines provide an interval-based description of the behavior of the system, instead of a more conventional point-based one. The relevant system properties are expressed by formulas of the logic MITL (a well-known timed extension of LTL) to be checked against timelines. In the paper, we prove that the model checking problem for MITL formulas (resp., its fragment MITL(0,∞)) over timelines is EXPSPACE-complete (resp., PSPACE-complete)

Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground

In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). While the temporal domain is usually assumed to be discrete, here we consider the dense case. Dense timeline-based planning has been recently shown to be undecidable in the general case; decidability (NP-completeness) can be recovered by restricting to purely existential synchronization rules (trigger-less rules). In this paper, we investigate the unexplored area of intermediate cases in between these two extremes. We first show that decidability and non-primitive recursive-hardness can be proved by admitting synchronization rules with a trigger, but forcing them to suitably check constraints only in the future with respect to the trigger (future simple rules). More "tractable" results can be obtained by additionally constraining the form of intervals in future simple rules: EXPSPACE-completeness is guaranteed by avoiding singular intervals, PSPACE-completeness by admitting only intervals of the forms [0,a] and [b,$\infty$[.Comment: In Proceedings GandALF 2018, arXiv:1809.0241

Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground

In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). While the temporal domain is usually assumed to be discrete, here we consider the dense case. Dense timeline-based planning has been recently shown to be undecidable in the general case; decidability (NP-completeness) can be recovered by restricting to purely existential synchronization rules (trigger-less rules). In this paper, we investigate the unexplored area of intermediate cases in between these two extremes. We first show that decidability and non-primitive recursive-hardness can be proved by admitting synchronization rules with a trigger, but forcing them to suitably check constraints only in the future with respect to the trigger (future simple rules). More "tractable" results can be obtained by additionally constraining the form of intervals in future simple rules: EXPSPACE-completeness is guaranteed by avoiding singular intervals, PSPACE-completeness by admitting only intervals of the forms [0,a] and [b,$\infty$[.Comment: In Proceedings GandALF 2018, arXiv:1809.0241

Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains

In this paper we look into the problem of planning over hybrid domains, where change can be both discrete and instantaneous, or continuous over time. In addition, it is required that each state on the trajectory induced by the execution of plans complies with a given set of global constraints. We approach the computation of plans for such domains as the problem of searching over a deterministic state model. In this model, some of the successor states are obtained by solving numerically the so-called initial value problem over a set of ordinary differential equations (ODE) given by the current plan prefix. These equations hold over time intervals whose duration is determined dynamically, according to whether zero crossing events take place for a set of invariant conditions. The resulting planner, FS+, incorporates these features together with effective heuristic guidance. FS+ does not impose any of the syntactic restrictions on process effects often found on the existing literature on Hybrid Planning. A key concept of our approach is that a clear separation is struck between planning and simulation time steps. The former is the time allowed to observe the evolution of a given dynamical system before committing to a future course of action, whilst the later is part of the model of the environment. FS+ is shown to be a robust planner over a diverse set of hybrid domains, taken from the existing literature on hybrid planning and systems.Comment: 17 page

Probabilistic Hybrid Action Models for Predicting Concurrent Percept-driven Robot Behavior

This article develops Probabilistic Hybrid Action Models (PHAMs), a realistic causal model for predicting the behavior generated by modern percept-driven robot plans. PHAMs represent aspects of robot behavior that cannot be represented by most action models used in AI planning: the temporal structure of continuous control processes, their non-deterministic effects, several modes of their interferences, and the achievement of triggering conditions in closed-loop robot plans. The main contributions of this article are: (1) PHAMs, a model of concurrent percept-driven behavior, its formalization, and proofs that the model generates probably, qualitatively accurate predictions; and (2) a resource-efficient inference method for PHAMs based on sampling projections from probabilistic action models and state descriptions. We show how PHAMs can be applied to planning the course of action of an autonomous robot office courier based on analytical and experimental results

Extracting Interval Temporal Logic Rules: A First Approach

Discovering association rules is a classical data mining task with a wide range of applications that include the medical, the financial, and the planning domains, among others. Modern rule extraction algorithms focus on static rules, typically expressed in the language of Horn propositional logic, as opposed to temporal ones, which have received less attention in the literature. Since in many application domains temporal information is stored in form of intervals, extracting interval-based temporal rules seems the natural choice. In this paper we extend the well-known algorithm APRIORI for rule extraction to discover interval temporal rules written in the Horn fragment of Halpern and Shoham\u27s interval temporal logic

A methodology for the requirements analysis of critical real-time systems

PhD ThesisThis thesis describes a methodology for the requirements analysis of critical real-time systems. The methodology is based on formal methods, and provides a systematic way in which requirements can be analysed and specifications produced. The proposed methodology consists of a framework with distinct phases of analysis, a set oftechniques appropriate for the issues to be analysed at each phase of the framework, a hierarchical structure of the specifications obtained from the process of analysis, and techniques to perform quality assessment of the specifications. The phases of the framework, which are abstraction levels for the analysis of the requirements, follow directly from a general structure adopted for critical real-time systems. The intention is to define abstraction levels, or domains, in which the analysis of requirements can be performed in terms of specific properties of the system, thus reducing the inherent complexity of the analysis. Depending on the issues to be analysed in each domain, the choice of the appropriate formalism is determined by the set of features, related to that domain, that a formalism should possess. In this work, instead of proposing new formalisms we concentrate on identifying and enumerating those features that a formalism should have. The specifications produced at each phase of the framework are organised by means of a specification hierarchy, which facilitates our assessment of the quality of the requirements specifications, and their traceability. Such an assessment should be performed by qualitative and quantitative means in order to obtain high confidence (assurance) that the level of safety is acceptable. In order to exemplify the proposed methodology for the requirements analysis of critical real-time systems we discuss a case study based on a crossing of two rail tracks (in a model railway), which raises safety issues that are similar to those found at a traditional level crossing (i.e. rail-road)CAPES/Ministry of Education (Brazil