Interaction Expressions - A Powerful Formalism for Describing Inter-Workflow Dependencies

Current workflow management technology does not provide adequate means for describing and implementing workflow ensembles, i. e., dynamically evolving collections of more or less independent workflows which have to synchronize only now and then. Interaction expressions are proposed as a simple yet powerful formalism to remedy this shortcoming. Besides operators for sequential composition, iteration, and selection, which are well-known from regular expressions, they provide parallel composition and iteration, conjunction, and several advanced features like parametric expressions, multipliers, and quantifiers. The paper introduces interaction expressions semi-formally, gives examples of their typical use, and describes their implementation and integration with state-of-the-art workflow technology. Major design principles, such as orthogonality and implicit and predictive choice, are discussed and compared with several related approaches

Synchronizing Relations on Words

While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of parameterized systems, querying graph-structured data, and information extraction, for instance. Classes of well-behaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to non-equivalent notions of recognizable, regular, and rational relations. The goal of this paper is to propose a systematic way of defining classes of relations on words, of which these three classes are just natural examples, and to demonstrate its advantages compared to some of the standard techniques for studying word relations. The key idea is that of a synchronization of a pair of words, which is a word over an extended alphabet. Using it, we define classes of relations via classes of regular languages over a fixed alphabet, just {1,2} for binary relations. We characterize some of the standard classes of relations on words via finiteness of parameters of synchronization languages, called shift, lag, and shiftlag. We describe these conditions in terms of the structure of cycles of graphs underlying automata, thereby showing their decidability. We show that for these classes there exist canonical synchronization languages, and every class of relations can be effectively re-synchronized using those canonical representatives. We also give sufficient conditions on synchronization languages, defined in terms of injectivity and surjectivity of their Parikh images, that guarantee closure under intersection and complement of the classes of relations they define

Decomposition and Descriptional Complexity of Shuffle on Words and Finite Languages

We investigate various questions related to the shuffle operation on words and finite languages. First we investigate a special variant of the shuffle decomposition problem for regular languages, namely, when the given regular language is the shuffle of finite languages. The shuffle decomposition into finite languages is, in general not unique. Thatis,therearelanguagesL^,L2,L3,L4withLiluL2= £3luT4but{L\,L2}^ {I/3, L4}. However, if all four languages are singletons (with at least two combined letters), it follows by a result of Berstel and Boasson [6], that the solution is unique; that is {L\,L2} = {L3,L4}. We extend this result to show that if L\ and L2 are arbitrary finite sets and Lz and Z-4 are singletons (with at least two letters in each), the solution is unique. This is as strong as it can be, since we provide examples showing that the solution can be non-unique already when (1) both L\ and L2 are singleton sets over different unary alphabets; or (2) L\ contains two words and L2 is singleton. We furthermore investigate the size of shuffle automata for words. It was shown by Campeanu, K. Salomaa and Yu in [11] that the minimal shuffle automaton of two regular languages requires 2mn states in the worst case (where the minimal automata of the two component languages had m and n states, respectively). It was also recently shown that there exist words u and v such that the minimal shuffle iii DFA for u and v requires an exponential number of states. We study the size of shuffle DFAs for restricted cases of words, namely when the words u and v are both periods of a common underlying word. We show that, when the underlying word obeys certain conditions, then the size of the minimal shuffle DFA for u and v is at most quadratic. Moreover we provide an efficient algorithm, which decides for a given DFA A and two words u and v, whether u lu u C L(A)

Workflow- und Prozeßsynchronisation mit Interaktionsausdrücken und -graphen

Im Rahmen der Arbeit werden Interaktionsausdrücke und -graphen als deskriptiver Formalismus zur kompakten, übersichtlichen und modularen Spezifikation sowie zur effizienten Implementierung von Synchronisationsbedingungen unterschiedlichster Art konzipiert, theoretisch untersucht, praktisch implementiert und prototypisch zur Synchronisation von Workflows angewandt

Synchronization Expressions: Characterization Results and Implementation

Synchronization expressions are defined as restricted regular expressions that specify synchronization constraints between parallel processes and their semantics is defined using synchronization languages. In this paper we survey results on synchronization languages, in particular various approaches to obtain an exact characterization of this language class using closure properties under a set of rewriting rules or homomorphic characterizations. Also we discuss the implementation of synchronization expressions. 1 Introduction Synchronization expressions (SE's) were originally introduced in the parallel programming language ParC [7] as high-level constructs for specifying synchronization constraints between parallel processes. Synchronization requests are specified as expressions of tags for statements that are to be constrained by the synchronization requirements. The semantics of SE's is defined using synchronization languages. The corresponding synchronization language descri..