Trace Automata Research Articles

A Metric Temporal Logic Specification Interface for Real-Time Discrete-Event Control

In supervisory control of timed discrete-event systems (TDESs), a conceptually well founded finitary control synthesis framework is developed, and it requires specifications to be prescribed as finite (-trace) automata in the form of timed transition graphs (TTGs). However, prescribing real-time specifications as TTGs is a nontrivial task that must be resolved before the formal framework could expect to become widely used. In addressing this specification problem, metric temporal logic (MTL) is proposed in this paper as a control specification language for use with the TTG-based control synthesis framework. MTL is a designer-friendly formalism due to its human or natural language expressiveness and readability, and is well suited for specifying real-time control specifications. In automating TTG prescription, this paper proposes an MTL interface to the control synthesis framework. The interface is proved to be a correct and complete translation algorithm that converts finitary control specifications written in state-based MTL formulas for a given TDES model into deterministic finite TTGs. Integrated, the MTL interface and the control synthesis framework combine the human expressiveness and readability of MTL with the algorithmic computability of TTGs, and together provide a new and convenient MTL specification-based design tool for automated prescription of TTGs and real-time control synthesis. Illustrative examples demonstrate the utility of the MTL interface.

A Kleene-Schützenberger Theorem for Trace Series over Bounded Lattices

We study weighted trace automata with weights in strong bimonoids. Traces form a generalization of words that allow to model concurrency; strong bimonoids are algebraic structures that can be regarded as “semirings without distributivity”. A very important example for the latter are bounded lattices, especially non-distributive ones. We show that if both operations of the bimonoid are locally finite, then the classes of recognizable and mc-rational trace series coincide and, in general, are properly contained in the class of c-rational series. Moreover, if, in addition, in the bimonoid the addition is idempotent and the multiplication is commutative, then all three classes coincide.

REPRESENTATION OF SEMIAUTOMATA BY CANONICAL WORDS AND EQUIVALENCES, PART II: SPECIFICATION OF SOFTWARE MODULES

A theory of representation of semiautomata by canonical words and equivalences was developed in [7]. That work was motivated by trace-assertion specifications of software modules, but its focus was entirely on the underlying mathematical model. In the present paper we extend that theory to automata with Moore and Mealy outputs, and show how to apply the extended theory to the specification of modules. In particular, we present a unified view of the trace-assertion methodology, as guided by our theory. We illustrate this approach, and some specific issues, using several nontrivial examples. We include a discussion of finite versus infinite modules, methods of error handling, some awkward features of the trace-assertion method, and a comparison to specifications by automata. While specifications by trace assertions and automata are equivalent in power, there are cases where one approach appears to be more natural than the other. We conclude that, for certain types of system modules, formal specification by automata, as opposed to informal state machines, is not only possible, but practical.

Context-Free Event Domains Are Recognizable

The possibly non-distributive event domains which arise from Winskel's event structures with binary conflict are known to coincide with the domains of configurations of Stark's trace automata. We prove that whenever the transitive reduction of the order on finite elements in an event domain is a context-free graph in the sense of Müller and Schupp, the event domain may also be generated from a finite trace automaton, where both the set of states and the concurrent alphabet are finite. We show that the set of graph grammars which generate event domains is a recursive set. We obtain altogether an effective procedure which decides from an unlabeled graph grammar whether it generates an event domain and which constructs in that case a finite trace automaton recognizing that event domain.

CONCURRENT AUTOMATA AND DOMAINS

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.