Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

On the Semantics of UML/MARTE Clock Constraints

Abstract: The UML goal of being a general-purpose modeling language discards the possibility to adopt too precise and strict a semantics. Users are to refine or define the semantics in their domain specific profiles. In the UML Profile for MARTE, we devised a broadly expressive Time Model to provide a generic timed interpretation for UML models. Our clock constraint specification language supports the specification of systems with multiple clock domains. Starting with a priori independent clocks, we progressively constrain them to get a family of possible executions. Our language supports both synchronous and asynchronous constraints, just like the synchronous language Signal, but also allows explicit non determinism. In this paper, we give a formal semantics to a core subset of MARTE clock constraint language and we give an equivalent interpretation of this kernel in two other very different formal languages, Signal and Time Petri nets.

MetaModelica: a unified equation-based semantical and mathematical modeling language

Abstract: For a long time, one of the major research goals in the computer science research community has been to raise the level of abstraction power of specification languages/programming languages. Many specification languages and formalisms have been invented, but unfortunately very few of those are practically useful, due to limited computer support of these languages and/or inefficient implementations. Thus, one important goal is executable specification languages of high abstraction power and with high performance, good enough for practical usage and comparable in execution speed to hand implementations of applications in low-level languages such as C or C++. In this paper we briefly describe our work in creating efficient executable specification languages for two application domains. The first area is formal specification of programming language semantics, whereas the second is formal specification of complex systems for which we have developed an object-oriented mathematical modeling language called Modelica, including architectural support for components and connectors. Based on these efforts, we are currently working on a unified equation-based mathematical modeling language that can handle modeling of items as diverse as programming languages, computer algebra, event-driven systems, and continuous-time physical systems. The key unifying feature is the notion of equation. In this paper we describe the design and implementation of the unified language. A compiler implementation is already up and running, and used for substantial applications.

Language driven hybrid systems

Abstract: In this paper the author shows how the type of hybrid models introduced previously by him (1993) can be used to evaluate the performance of motion control systems. He defines an appropriate class of formal languages, allowing one to frame such problems succinctly as word-to-position transducers. We show that models involving multiple triggers play an important role in modeling this type of motion control system. >

Full satisfiability of UML class diagrams

Abstract: UML class diagrams (UCDs) are the de-facto standard formalism for the analysis and design of information systems. By adopting formal language techniques to capture constraints expressed by UCDs one can exploit automated reasoning tools to detect relevant properties, such as schema and class satisfiability and subsumption between classes. Among the reasoning tasks of interest, the basic one is detecting full satisfiability of a diagram, i.e., whether there exists an instantiation of the diagram where all classes and associations of the diagram are non-empty and all the constraints of the diagram are respected. In this paper we establish tight complexity results for full satisfiability for various fragments of UML class diagrams. This investigation shows that the full satisfiability problem is ExpTime-complete in the full scenario, NP-complete if we drop isa between relationships, and NLogSpace-complete if we further drop covering over classes.

Insertion and iterated insertion as operations on formal languages

Abstract: The operations of insertion ((<---)) and iterated insertion ((<---)*) are simple variants of Kleene's operations (.) and (,*) ({Kle 56}) in a manner similar to the operations shuffle and iterated shuffle (see e.g. {Jan 81}). Using the operation of iterated insertion, we can generate both the semi-Dyck and the two-sided Dyck languages (see e.g. {Har 78}) from certain finite subsets of these languages. Thus the class of languages of the form S('(<---)*) for finite S forms a natural class of generalized Dyck languages. We present several combinatorial results that demonstrate that the problems of equivalence, of ambiguous representation, of confluence (see {Bk 82}) and of regularity are decidable for this class of languages. In obtaining the latter result, we give two important general results involving the application of the theory of well quasi orders (see e.g. {Kru 72}) to the study of regular languages. On the other hand, we show that the problem "S('(<---)*) (INTERSECT) T('(<---)*) = {(lamda)}?" is undecidable for finite, unambiguous S and T. Furthermore, by extending the regular expressions to include the operations (<---) and (<---)(,*) we obtain the class of insertion languages which generalizes both the regular languages and the Dyck languages, but is properly contained within the class of context-free languages. Our main result here is that the problem "L = (SIGMA)('*)?" is undecidable for the class of insertion languages. From this result, it follows that the equivalence problem and the problem "Is L regular?" are also undecidable for this class.