Minimizing Deterministic Timed Finite State Machines
Timed automata and timed finite state machins (TFSMs) have been proposed to represent more accurately the behaviour of systems in continuous time. Recently, we introduced a model of TFSMs that extends the expressive power of FSMs by introducing a single clock, timed guards which restrict when the input/output transitions may happen, and timeouts on the transitions. We derived an abstraction procedure to convert a TFSM into an equivalent untimed FSM. Here, we extend the model with output timeouts and derive a minimal form for deterministic TFSMs that reduces the number of states, the number of transitions and the timeout values at each state.
The paper presents a formalism and a tool for modelling and analysis of distributed real-time systems of mobile agents. For that we use a time extension of our Resource Driven Automata Nets (TRDA-nets) formalism. A TRDA-net is a two-level system. The upper level represents distributed environment locations with a net of active resources. On the lower level agents are modeled by extended finite state machines, asynchronously consuming/producing shared resources through input/output system ports (arcs of the system net). We demonstrate modelling facilities of the formalism and show that specific layers of TRDA-nets can be translated into Timed Automata, as well as into Time Petri nets, thus TRDA-nets integrate merits of both formalisms.
Control and analysis of the timing of computations are crucial to many domains of system engineering, be it, e.g., for ensuring a timely response to stimuli originating in an uncooperative environment or for synchronizing components in VLSI. Reflecting this broad scope, timing aspects of systems from a variety of domains have been treated independently by different communities in computer science and control. Researchers interested in semantics, verification, and performance analysis study models such as timed automata and timed Petri nets, the digital design community focuses on propagation and switching delays, while designers of embedded controllers have to take account of the time taken by controllers to compute their responses after sampling the environment, as well as of the dynamics of the controlled process during this span. Timing-related questions in these separate disciplines have their particularities. However, there is growing awareness that there are basic problems that are common to all of them. In particular, all these subdisciplines treat systems whose behavior depends upon combinations of logical and temporal constraints; namely, constraints on the temporal distances between occurrences of events. Often, these constraints cannot be separated, as intrinsic dynamics of processes couples them, necessitating models, methods, and tools facilitating their combined analysis. Reflecting this fact, the aim of FORMATS is to promote the study of fundamental and practical aspects of timed systems, and to bring together researchers from different disciplines that share interests in modeling and analysis of timed systems and, as a generalization, hybrid systems. Typical topics include (but are not limited to): – Foundations and Semantics: Theoretical foundations of timed systems and languages; comparison between different models (such as timed automata, timed Petri nets, hybrid automata, timed process algebra, max-plus algebra, probabilistic models) – Methods and Tools: Techniques, algorithms, data structures, and software tools for analyzing or synthesizing timed or hybrid systems and for resolving temporal constraints (e.g., scheduling, worst-case execution time analysis, optimization, model checking, testing, constraint solving) – Applications: Adaptation and specialization of timing technology in application domains in which timing plays an important role (real-time software, embedded control, hardware circuits, and problems of scheduling in manufacturing and telecommunication, etc.)
In the paper, we address mission critical systems, such as automobile, avionic, mobile robotic, telecommunication, etc. Such systems must meet hard real-time constraints in order to avoid catastrophic consequences. To meet the real-time constraints, strict periodicity is used (i.e. for any periodic task, time between release points is constant). Sensors, actuators and feedback control functions are typical examples of strict periodic tasks. We study a monoprocessor preemptive scheduling problem for arbitrary number of strict periodic tasks. In this context, we focus on the following problem: how to find non-conflict set of task release points (i.e. sequences of instance release points for different tasks must not intersect). First, as a preliminaries, we introduce some fundamental definitions and prove several elementary schedulability conditions. Next, we investigate the correlation between the scheduling problem and a graph coloring problem for graphs of some special kinds. The graphs under consideration are built on the basis of the tasks' period values. We introduce a notion of divisibility graph for tasks' periods, and study compatibility of graphs' coloring with respect to the schedulability problem. At last, we prove a theorem that provides necessary and sufficient graph coloring conditions for schedulability of given strict periodic tasks. This theorem allows either to find non-conflict set of task release points directly, or to determine quickly that scheduling is impossible.
We consider regular realizability problems, which consist in verifying whether the intersection of a regular language which is the problem input and a fixed language (filter) which is a parameter of the problem is nonempty. We study the algorithmic complexity of regular realizability problems for context-free filters. This characteristic is consistent with the rational dominance relation of CF languages. However, as we prove, it is more rough. We also give examples of both P-complete and NL-complete regular realizability problems for CF filters. Furthermore, we give an example of a subclass of CF languages for filters of which the regular realizability problems can have an intermediate complexity. These are languages with polynomially bounded rational indices.
A new look at the problem of constructing a scheduler in the case of a group of strictly periodic tasks is proposed. The structure of the system of periods is represented in terms of graph theory. A criterion for the existence of a conflict-free schedule based on this representation is obtained, and generic schemes of algorithms for constructing such a schedule are described. The proposed approach is illustrated by building schedules for a number of strictly periodic tasks.