A theory of regular MSC languages

Message sequence charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs. A commonly used technique to generate a collection of MSCs is to use a hierarchical message sequence chart (HMSC). We show that the class of languages arising from the so-called bounded HMSCs constitute a proper subclass of the class of regular MSC languages. In fact, we characterize the bounded HMSC languages as the subclass of regular MSC languages that are finitely generated

Towards a Theory of Regular MSC Languages

Message Sequence Charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the earlydesign stages in domains such as telecommunication software. It isfruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, weprovide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called boundedmessage-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending andreceiving messages over bounded FIFO channels. We also provide alogical characterization in terms of a natural monadic second-orderlogic interpreted over MSCs.A commonly used technique to generate a collection of MSCs isto use a Message Sequence Graph (MSG). We show that the class oflanguages arising from the so-called locally synchronized MSGs constitute a proper subclass of the languages which are regular in our sense.In fact, we characterize the locally synchronized MSG languages asthe subclass of regular MSC languages that are finitely generated

Symmetric Groups and Quotient Complexity of Boolean Operations

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively. Denote by o any binary boolean operation that is not a constant and not a function of one argument only. For m,n >= 2 with (m,n) not in {(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn if and only either (a) m is not equal to n or (b) m=n and the bases (ordered pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in {(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In proving these results we generalize the notion of uniform minimality to direct products of automata. We also establish a non-trivial connection between complexity of boolean operations and group theory

Escaping the Trap of too Precise Topic Queries

At the very center of digital mathematics libraries lie controlled vocabularies which qualify the {\it topic} of the documents. These topics are used when submitting a document to a digital mathematics library and to perform searches in a library. The latter are refined by the use of these topics as they allow a precise classification of the mathematics area this document addresses. However, there is a major risk that users employ too precise topics to specify their queries: they may be employing a topic that is only "close-by" but missing to match the right resource. We call this the {\it topic trap}. Indeed, since 2009, this issue has appeared frequently on the i2geo.net platform. Other mathematics portals experience the same phenomenon. An approach to solve this issue is to introduce tolerance in the way queries are understood by the user. In particular, the approach of including fuzzy matches but this introduces noise which may prevent the user of understanding the function of the search engine. In this paper, we propose a way to escape the topic trap by employing the navigation between related topics and the count of search results for each topic. This supports the user in that search for close-by topics is a click away from a previous search. This approach was realized with the i2geo search engine and is described in detail where the relation of being {\it related} is computed by employing textual analysis of the definitions of the concepts fetched from the Wikipedia encyclopedia.Comment: 12 pages, Conference on Intelligent Computer Mathematics 2013 Bath, U

On Global Types and Multi-Party Session

Global types are formal specifications that describe communication protocols in terms of their global interactions. We present a new, streamlined language of global types equipped with a trace-based semantics and whose features and restrictions are semantically justified. The multi-party sessions obtained projecting our global types enjoy a liveness property in addition to the traditional progress and are shown to be sound and complete with respect to the set of traces of the originating global type. Our notion of completeness is less demanding than the classical ones, allowing a multi-party session to leave out redundant traces from an underspecified global type. In addition to the technical content, we discuss some limitations of our language of global types and provide an extensive comparison with related specification languages adopted in different communities

Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore