David Harel

Statecharts: A visual formalism for complex systems

We present a broad extension of the conventional formalism of state machines and state diagrams, that is relevant to the specification and design of complex discrete-event systems, such as multi-computer real-time systems, communication protocols and digital control units. Our diagrams, which we call statecharts, extend conventional state-transition diagrams with essentially three elements, dealing, respectively, with the notions of hierarchy, concurrency and communica- tion. These transform the language of state diagrams into a highly structured and economical description language. Statecharts are thus compact and expressiv-small diagrams can express complex behavior-as well as compositional and modular. When coupled with the capabilities of computerized graphics, statecharts enable viewing the description at different levels of detail, and make even very large specifications manageable and comprehensible. In fact, we intend to demonstrate here that statecharts counter many of the objections raised against conventional state diagrams, and thus appear to render specification by diagrams an attractive and plausible approach. Statecharts can be used either as a stand-alone behavioral description or as part of a more general design methodology that deals also with the systems other aspects, such as functional decomposi- tion and data-flow specification. We also discuss some practical experience that was gained over the last three years in applying the statechart formalism to the specification of a particularly complex system.

On visual formalisms

The higraph, a general kind of diagramming object, forms a visual formalism of topological nature. Higraphs are suited for a wide array of applications to databases, knowledge representation, and, most notably, the behavioral specification of complex concurrent systems using the higraph-based language of statecharts.

The STATEMATE semantics of statecharts

We describe the semantics of statecharts as implemented in the STATEMATE system. This was the first executable semantics defined for the language and has been in use for almost a decade. In terms of the controversy around whether changes made in a given step should take effect in the current step or in the next one, this semantics adopts the latter approach.

On the development of reactive systems

Some observations are made concerning the process of developing complex systems. A broad class of systems, termed reactive, is singled out as being particularly problematic when it comes to finding satisfactory methods for behavioral description. In this paper we recommend the recently proposed statechart method for this purpose. Moreover, it is observed that most reactive systems cannot be developed in a linear stepwise fashion, but, rather, give rise to a two-dimensional development process, featuring behavioral aspects in the one dimension and implementational ones in the other. Concurrency may occur in both dimensions, as orthogonality of states in the one and as parallelism of subsystems in the other. A preliminary approach to working one’s way through this “magic square” of system development is then presented. The ideas described herein seem to be relevant to a wide variety of application areas.

Structure and complexity of relational queries

This paper is an attempt at laying the foundations for the classification of queries on relational data bases according to their structure and their computational complexity. Using the operations of composition and fixpoints, a Σ-Π hierarchy of height, ω2, called the fixpoint query hierarchy, is defined, and its properties investigated. The hierarchy includes most of the queries considered in the literature including those of Codd and Aho and Ullman. The hierarchy to level ω characterizes the first-order queries, and the levels up to ω are shown to be strict. Sets of queries larger than the fixpoint query hierarchy are obtained by considering the queries computable in polynomial time, queries computable in polynomial space, etc. It is shown that classes of queries defined from such complexity classes behave (with respect to containment) in a manner very similar to the corresponding complexity classes. Also, the set of second-order queries turns out to be the same as the set of queries defined from the polynomialtime hierarchy. Finally, these classes of queries are used to characterize a set of queries defined from language considerations: those expressible in a programming language with only typed (or ranked) relation variables. At the end of the paper is a list of symbols used therein.

Drawing graphs nicely using simulated annealing

The paradigm of simulated annealing is applied to the problem of drawing graphs “nicely.” Our algorithm deals with general undirected graphs with straight-line edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the “spring method” and its variants.

Meaningful modeling: what's the semantics of "semantics"?

The Unified Modeling Language (UML) is a complex collection of mostly diagrammatic notations for software modeling, and its standardization has prompted an animated discussion about UMLs semantics and how to represent it. We have thus set out to clarify some of the notions involved in defining modeling languages, with an eye toward the particular difficulties arising in defining UML. We are primarily interested in distinguishing a languages notation, or syntax, from its meaning, or semantics, as well as recognizing the differences between variants of syntax and semantics in their nature, purpose, style, and use.

LSCs: Breathing Life into Message Sequence Charts

While message sequence charts (MSCs) are widely used in industry to document the interworking of processes or objects, they are expressively quite weak, being based on the modest semantic notion of a partial ordering of events as defined, e.g., in the ITU standard. A highly expressive and rigorously defined MSC language is a must for serious, semantically meaningful tool support for use-cases and scenarios. It is also a prerequisite to addressing what we regard as one of the central problems in behavioral specification of systems: relating scenario-based inter-object specification to state-machine intra-object specification. This paper proposes an extension of MSCs, which we call live sequence charts (or LSCs),since our main extension deals with specifying “liveness”, i.e., things that must occur. In fact, LSCs allow the distinction between possible and necessary behavior both globally, on the level of an entire chart and locally, when specifying events, conditions and progress over time within a chart. This also makes it possible to specify forbidden scenarios, and strengthens structuring constructs like as subcharts, branching and iteration.

Computable queries for relational data bases

Abstract The concept of “reasonable” queries on relational data bases is investigated. We provide an abstract characterization of the class of queries which are computable, and define the completeness of a query language as the property of being precisely powerful enough to express the queries in this class. This definition is then compared with other proposals for measuring the power of query languages. Our main result is the completeness of a simple programming language which can be thought of as consisting of the relational algebra augmented with the power of iteration.

HORN CLAUSE QUERIES AND GENERALIZATIONS

Abstract A logic program consists of a set of Horn clauses, and can be used to express a query on relational data bases. It is shown that logic programs express precisely the queries in YE + (the set of queries representable by a fixpoint applied to a positive existential query). Queries expressible by logic programs are thus not first-order queries in general, nor are all the first-order queries expressible as logic programs. Several ways of adding negation to logic programs are examined. The most general case is where arbitrary first-order formulas (with “nonterminal” relation symbols) are allowed. The resulting class has the expressive power of universally quantified second-order logic.