Solving scheduling problems by untimed model checking

In this paper, we show how scheduling problems can be modelled in untimed process algebra, by using special tick actions. A minimal-time trace leading to a particular action, is one that minimizes the number of tick steps. As a result, we can use any (timed or untimed) model checking tool to find shortest schedules. Instantiating this scheme t

Schedulability analysis of timed CSP models using the PAT model checker

Timed CSP can be used to model and analyse real-time and concurrent behaviour of embedded control systems. Practical CSP implementations combine the CSP model of a real-time control system with prioritized scheduling to achieve efficient and orderly use of limited resources. Schedulability analysis of a timed CSP model of a system with respect to a scheduling scheme and a particular execution platform is important to ensure that the system design satisfies its timing requirements. In this paper, we propose a framework to analyse schedulability of CSP-based designs for non-preemptive fixed-priority multiprocessor scheduling. The framework is based on the PAT model checker and the analysis is done with dense-time model checking on timed CSP models. We also provide a schedulability analysis workflow to construct and analyse, using the proposed framework, a timed CSP model with scheduling from an initial untimed CSP model without scheduling. We demonstrate our schedulability analysis workflow on a case study of control software design for a mobile robot. The proposed approach provides non-pessimistic schedulability results

06172 Abstracts Collection -- Directed Model Checking

From 26.04.06 to 29.04.06, the Dagstuhl Seminar 06172 ``Directed Model Checking\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Optimal Reachability in Divergent Weighted Timed Games

Weighted timed games are played by two players on a timed automaton equipped with weights: one player wants to minimise the accumulated weight while reaching a target, while the other has an opposite objective. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the quality of controllers. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. Decidability results exist for subclasses of one-clock games, and for a subclass with non-negative weights defined by a semantical restriction on the weights of cycles. In this work, we introduce the class of divergent weighted timed games as a generalisation of this semantical restriction to arbitrary weights. We show how to compute their optimal value, yielding the first decidable class of weighted timed games with negative weights and an arbitrary number of clocks. In addition, we prove that divergence can be decided in polynomial space. Last, we prove that for untimed games, this restriction yields a class of games for which the value can be computed in polynomial time

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

Interrupt Timed Automata: verification and expressiveness

We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is undecidable for hybrid automata we show that it is decidable for ITA. More precisely we prove that the untimed language of an ITA is regular, by building a finite automaton as a generalized class graph. We then establish that the reachability problem for ITA is in NEXPTIME and in PTIME when the number of clocks is fixed. To prove the first result, we define a subclass ITA- of ITA, and show that (1) any ITA can be reduced to a language-equivalent automaton in ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without any class graph). In the next step, we investigate the verification of real time properties over ITA. We prove that model checking SCL, a fragment of a timed linear time logic, is undecidable. On the other hand, we give model checking procedures for two fragments of timed branching time logic. We also compare the expressive power of classical timed automata and ITA and prove that the corresponding families of accepted languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), that extend timed automata. We finally combine ITA with CRTA, in a model which encompasses both classes and show that the reachability problem is still decidable. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection