On the structure of solution-sets to regular word equations

For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. For regular word equations – those for which each variable occurs at most once on each side of the equation – we investigate the properties of this graph, such as bounds on its diameter, size, and DAG-width, as well as providing some insights into symmetries in its structure. As a consequence, we obtain a combinatorial proof that the problem of deciding whether a regular word equation has a solution is in NP.

Models@Runtime: The Development and Re-Configuration Management of Python Applications Using Formal Methods

Models@runtime (models at runtime) are based on computation reflection. Runtime models can be regarded as a reflexive layer causally connected with the underlying system. Hence, every change in the runtime model involves a change in the reflected system, and vice versa. To the best of our knowledge, there are no runtime models for Python applications. Therefore, we propose a formal approach based on Petri Nets (PNs) to model, develop, and reconfigure Python applications at runtime. This framework is supported by a tool whose architecture consists of two modules connecting both the model and its execution. The proposed framework considers execution exceptions and allows users to monitor Python expressions at runtime. Additionally, the application behavior can be reconfigured by applying Graph Rewriting Rules (GRRs). A case study using Service-Level Agreement (SLA) violations is presented to illustrate our approach.

Graph rewriting rules for RDF database evolution: optimizing side-effect processing

Purpose Graph rewriting concerns the technique of transforming a graph; it is thus natural to conceive its application in the evolution of graph databases. This paper aims to propose a two-step framework where rewriting rules formalize instance or schema changes, ensuring graph’s consistency with respect to constraints, and updates are managed by ensuring rule applicability through the generation of side effects: new updates which guarantee that rule application conditions hold. Design/methodology/approach This paper proposes Schema Evolution Through UPdates, optimized version (SetUpOPT), a theoretical and applied framework for the management of resource description framework (RDF)/S database evolution on the basis of graph rewriting rules. The framework is an improvement of SetUp which avoids the computation of superfluous side effects and proposes, via SetUpoptND, a flexible and extensible package of solutions to deal with non-determinism. Findings This paper shows graph rewriting into a practical and useful application which ensures consistent evolution of RDF databases. It introduces an optimised approach for dealing with side effects and a flexible and customizable way of dealing with non-determinism. Experimental evaluation of SetUpoptND demonstrates the importance of the proposed optimisations as they significantly reduce side-effect generation and limit data degradation. Originality/value SetUp originality lies in the use of graph rewriting techniques under the closed world assumption to set an updating system which preserves database consistency. Efficiency is ensured by avoiding the generation of superfluous side effects. Flexibility is guaranteed by offering different solutions for non-determinism and allowing the integration of customized choice functions.

LNetReduce: tool for reducing linear dynamic networks with separated time scales

We introduce LNetReduce, a tool that simplifies linear dynamic networks. Dynamic networks are represented as digraphs labeled by integer timescale orders. Such models describe deterministic or stochastic monomolecular chemical reaction networks, but also random walks on weighted protein-protein interaction networks, spreading of infectious diseases and opinion in social networks, communication in computer networks. The reduced network is obtained by graph and label rewriting rules and reproduces the full network dynamics with good approximation at all time scales. The tool is implemented in Python with a graphical user interface. We discuss applications of LNetReduce to network design and to the study of the fundamental relation between time scales and topology in complex dynamic networks.

Compositionality of Rewriting Rules with Conditions

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of rule composition operations encodes the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting with application conditions based upon M-adhesive categories. We uncover an intricate interplay between the category-theoretical concepts of conditions on rules and morphisms, the compositionality and compatibility of certain shift and transport constructions for conditions, and thirdly the property of associativity of the composition of rules.

Parallel Multiset Rewriting Systems with Distorted Rules

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

Practical Examples of Automated Development of Efficient Parallel Programs

In this chapter, some examples of application of the developed software tools for design, generation, transformation, and optimization of programs for multicore processors and graphics processing units are considered. In particular, the algebra-algorithmic-integrated toolkit for design and synthesis of programs (IDS) and the rewriting rules system TermWare.NET are applied for design and parallelization of programs for multicore central processing units. The developed algebra-dynamic models and the rewriting rules toolkit are used for parallelization and optimization of programs for NVIDIA GPUs supporting the CUDA technology. The TuningGenie framework is applied for parallel program auto-tuning: optimization of sorting, Brownian motion simulation, and meteorological forecasting programs to a target platform. The parallelization of Fortran programs using the rewriting rules technique on sample problems in the field of quantum chemistry is examined.

A Bio-Inspired Model of Picture Array Generating P System with Restricted Insertion Rules

In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating P system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array P system.