Piloting an Empirical Study on Measures for Workflow Similarity

Service discovery of state dependent services has to take workflow aspects into account. To increase the usability of a service discovery, the result list of services should be ordered with regard to the relevance of the services. Means of ordering a list of workflows due to their similarity with regard to a query are missing. This paper presents a pilot of an empirical study on the influence of different measures on workflow similarity. It turns out that, although preliminary, relations between different measures are indicated and that a similarity definition depends on the application scenario in which the service discovery is applied

Construction of a Pushdown Automaton Accepting a Postfix Notation of a Tree Language Given by a Regular Tree Expression

Regular tree expressions are a formalism for describing regular tree languages, which can be accepted by a finite tree automaton as a standard model of computation. It was proved that the class of regular tree languages is a proper subclass of tree languages whose linear notations can be accepted by deterministic string pushdown automata. In this paper, we present a new algorithm for transforming regular tree expressions to equivalent real-time height-deterministic pushdown automata that accept the trees in their postfix notation

The Gremlin Graph Traversal Machine and Language

Gremlin is a graph traversal machine and language designed, developed, and distributed by the Apache TinkerPop project. Gremlin, as a graph traversal machine, is composed of three interacting components: a graph $G$, a traversal $\Psi$, and a set of traversers $T$. The traversers move about the graph according to the instructions specified in the traversal, where the result of the computation is the ultimate locations of all halted traversers. A Gremlin machine can be executed over any supporting graph computing system such as an OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph traversal language, is a functional language implemented in the user's native programming language and is used to define the $\Psi$ of a Gremlin machine. This article provides a mathematical description of Gremlin and details its automaton and functional properties. These properties enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, hybrid depth- and breadth-first evaluation, as well as the existence of a Universal Gremlin Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming Languages Conferenc

Target Code Selection by Tilling AST with the Use of Tree Pattern Pushdown Automaton

A new and simple method for target code selection by tilling an abstract syntax tree is presented. As it is usual, tree patterns corresponding to target machine instructions are matched in the abstract syntax tree. Matching tree patterns is performed with the use of tree pattern pushdown automaton, which accepts all tree patterns matching the abstract syntax tree in the linear postfix bar notation and represents a full index of the abstract syntax tree for tree patterns. The use of the index allows to match patterns quickly, in time depending on the size of patterns and not depending on the size of the tree. The selection of a particular target instruction corresponds to a modification of the abstract syntax tree and also a corresponding incremental modification of the index is performed. A reference to a fully functional prototype is provided

Beyond Zeno-behaviour

When modelling and analysing hybrid systems using techniques from computing science we may encounter problems with so-called Zeno-behaviour. This is the phenomenon that an innite number of events accumulates before a nite time (Zeno-time). When this happens the standard techniques from computing science fail to dis-tinguish between events that happen after that sequence of events. Many of those techniques have a semantics based on labelled transi-tion systems. In this article, we concentrate on those transition systems and try to nd a solution for the Zeno-problem. We rst introduce transi-tions over innite sequences, since an innite number of events needs to be described. Then we (re-)dene a notion of convergence over sequences in a metric space. Considering a transition system with a metric state space and transitions labelled by sequences we can dene a notion of prex- and accumulation-closedness. Finally within prex-and accumulation-closed transition systems, bisimilarity turns out to distinguish between various kinds of transnite behaviour. The bounc-ing ball, an example from hybrid system theory, is used to illustrate the relevance of these new denitions. 1

Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij

Hardness of deriving invertible sequences from finite state machines

© Springer International Publishing AG 2017.Many test generation algorithms use unique input/output sequences (UIOs) that identify states of the finite state machine specification M. However, it is known that UIO checking the existence of UIO sequences is PSPACE-complete. As a result, some UIO generation algorithms utilise what are called invertible sequences; these allow one to construct additional UIOs once a UIO has been found. We consider three optimisation problems associated with invertible sequences: deciding whether there is a (proper) invertible sequence of length at least K; deciding whether there is a set of invertible sequences for state set S′ that contains at most K input sequences; and deciding whether there is a single input sequence that defines invertible sequences that take state set S″ to state set S′. We prove that the first two problems are NP-complete and the third is PSPACE-complete. These results imply that we should investigate heuristics for these problems