On Probability Distributions for Trees: Representations, Inference and Learning

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied class of tree series is the class of rational (or recognizable) tree series which can be defined either in an algebraic way or by means of multiplicity tree automata. We argue that the algebraic representation is very convenient to model probability distributions over a free algebra of trees. First, as in the string case, the algebraic representation allows to design learning algorithms for the whole class of probability distributions defined by rational tree series. Note that learning algorithms for rational tree series correspond to learning algorithms for weighted tree automata where both the structure and the weights are learned. Second, the algebraic representation can be easily extended to deal with unranked trees (like XML trees where a symbol may have an unbounded number of children). Both properties are particularly relevant for applications: nondeterministic automata are required for the inference problem to be relevant (recall that Hidden Markov Models are equivalent to nondeterministic string automata); nowadays applications for Web Information Extraction, Web Services and document processing consider unranked trees

Web Services: A Process Algebra Approach

It is now well-admitted that formal methods are helpful for many issues raised in the Web service area. In this paper we present a framework for the design and verification of WSs using process algebras and their tools. We define a two-way mapping between abstract specifications written using these calculi and executable Web services written in BPEL4WS. Several choices are available: design and correct errors in BPEL4WS, using process algebra verification tools, or design and correct in process algebra and automatically obtaining the corresponding BPEL4WS code. The approaches can be combined. Process algebra are not useful only for temporal logic verification: we remark the use of simulation/bisimulation both for verification and for the hierarchical refinement design method. It is worth noting that our approach allows the use of any process algebra depending on the needs of the user at different levels (expressiveness, existence of reasoning tools, user expertise)

A novel approach to symbolic algebra

A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far had to be done manually in a semi-automatic fashion.Comment: 15 page

An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

Issues about the Adoption of Formal Methods for Dependable Composition of Web Services

Web Services provide interoperable mechanisms for describing, locating and invoking services over the Internet; composition further enables to build complex services out of simpler ones for complex B2B applications. While current studies on these topics are mostly focused - from the technical viewpoint - on standards and protocols, this paper investigates the adoption of formal methods, especially for composition. We logically classify and analyze three different (but interconnected) kinds of important issues towards this goal, namely foundations, verification and extensions. The aim of this work is to individuate the proper questions on the adoption of formal methods for dependable composition of Web Services, not necessarily to find the optimal answers. Nevertheless, we still try to propose some tentative answers based on our proposal for a composition calculus, which we hope can animate a proper discussion

Integrating multiple sources to answer questions in Algebraic Topology

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and deduction. The architecture allows the system not only to interface several systems, but also to make them cooperate in shared calculations.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201