Minimization Strategies for Maximally Parallel Multiset Rewriting Systems

Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and many variants of P systems). In particular, this means that MPMRS are computationally complete; however, a direct translation leads to quite a big number of rules. Like for other classes of computationally complete devices, there is a challenge to find a universal system having the smallest number of rules. In this article we present different rule minimization strategies for MPMRS based on encodings and structural transformations. We apply these strategies to the translation of a small universal register machine (Korec, 1996) and we show that there exists a universal MPMRS with 23 rules. Since MPMRS are identical to a restricted variant of P systems with antiport rules, the results we obtained improve previously known results on the number of rules for those systems.Comment: This article is an improved version of [1

On the Properties of Language Classes Defined by Bounded Reaction Automata

Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in [4]. In this paper we continue the investigation of reaction automata with a focus on the formal language theoretic properties of subclasses of reaction automata, called linearbounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and lambda-LRAs. Further, we establish new relationships of language classes accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results include the following : (i) the class of languages accepted by lambda-LRAs forms an AFL with additional closure properties, (ii) any recursively enumerable language can be expressed as a homomorphic image of a language accepted by an LRA, (iii) the class of languages accepted by ERAs coincides with the class of context-sensitive languages.Comment: 23 pages with 3 figure

Reaction Automata

Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy.Comment: 19 pages, 6 figure

New Choice for Small Universal Devices: Symport/Antiport P Systems

Symport/antiport P systems provide a very simple machinery inspired by corresponding operations in the living cell. It turns out that systems of small descriptional complexity are needed to achieve the universality by these systems. This makes them a good candidate for small universal devices replacing register machines for different simulations, especially when a simulating parallel machinery is involved. This article contains survey of these systems and presents different trade-offs between parameters

Lifted Bayesian filtering in multi-entity systems

This thesis focuses on Bayesian filtering for systems that consist of multiple, interacting entites (e.g. agents or objects), which can naturally be described by Multiset Rewriting Systems (MRSs). The main insight is that the state space that is underling an MRS exhibits a certain symmetry, which can be exploited to increase inference efficiency. We provide an efficient, lifted filtering algorithm, which is able to achieve a factorial reduction in space and time complexity, compared to conventional, ground filtering.Diese Arbeit betrachtet Bayes'sche Filter in Systemen, die aus mehreren, interagierenden Entitäten (z.B. Agenten oder Objekten) bestehen. Die Systemdynamik solcher Systeme kann auf natürliche Art durch Multiset Rewriting Systems (MRS) spezifiziert werden. Die wesentliche Erkenntnis ist, dass der Zustandraum Symmetrien aufweist, die ausgenutzt werden können, um die Effizienz der Inferenz zu erhöhen. Wir führen einen effizienten, gelifteten Filter-Algorithmus ein, dessen Zeit- und Platzkomplexität gegenüber dem grundierten Algorithmus um einen faktoriellen Faktor reduziert ist

In Memoriam, Solomon Marcus

This book commemorates Solomon Marcus’s fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus’s research fields, some of whom have been influenced by his results and/or have collaborated with him

Algorithms and Software for Biological MP Modeling by Statistical and Optimization Techniques

I sistemi biologici sono gruppi di entit\ue0 biologiche (es. molecole ed organismi), che interagiscono producendo specifiche dinamiche. Questi sistemi sono solitamente caratterizzati da una elevata complessit\ue0 perch\ue8 coinvolgono un elevato numero di componenti con molte interconnessioni. La comprensione dei meccanismi che governano i sistemi biologici e la previsione dei loro comportamenti in condizioni normali e patologiche \ue8 una sfida cruciale della biologia dei sistemi (in inglese detta systems biology), un'area di ricerca al confine tra biologia, medicina, matematica ed informatica. In questa tesi i P sistemi metabolici, detti brevemente sistemi MP, sono stati utilizzati come modello discreto per l'analisi di dinamiche biologiche. Essi sono una classe deterministica dei P sistemi classici, che utilizzano regole di riscrittura per rappresentare le reazioni chimiche e "funzioni di regolazioni di flusso" per regolare la reattivit\ue0 di ciascuna reazione rispetto alla quantita' di sostanze presenti istantaneamente nel sistema. Dopo un excursus sulla letteratura relativa ad alcuni modelli convenzionali (come le equazioni differenziali ed i modelli stocastici proposti da Gillespie) e non-convenzionali (come i P sistemi ed i P sistemi metabolici), saranno presentati i risultati della mia ricerca. Essi riguardano tre argomenti principali: i) l'equivalenza tra sistemi MP e reti di Petri ibride funzionali, ii) le prospettive statistiche e di ottimizzazione nella generazione di sistemi MP a partire da dati sperimentali, iii) lo sviluppo di un laboratorio virtuale chiamato MetaPlab, un software Java basato sui sistemi MP. L'equivalenza tra i sistemi MP e le reti di Petri ibride funzionali \ue8 stata dimostrata per mezzo di due teoremi ed alcuni esperimenti al computer per il caso di studio del meccanismo regolativo del gene operone lac nella pathway glicolitica. Il secondo argomento di ricerca concerne nuovi approcci per la sintesi delle funzioni di regolazione di flusso. La regressione stepwise e le reti neurali sono state impiegate come approssimatori di funzioni, mentre algoritmi di ottimizzazione classici ed evolutivi (es. backpropagation, algoritmi genetici, particle swarm optimization ed algoritmi memetici) sono stati impiegati per l'addestramento dei modelli. Una completo workflow per l'analisi dei dati sperimentali \ue8 stato presentato. Esso gestisce ed indirizza l'intero processo di sintesi delle funzioni di regolazione, dalla preparazione dei dati alla selezione delle variabili, fino alla generazione dei modelli ed alla loro validazione. Le metodologie proposte sono state testate con successo tramite esperimenti al computer sui casi di studio dell'oscillatore mitotico negli embrioni anfibi e del non photochemical quenching (NPQ). L'ultimo tema di ricerca \ue8 infine piu' applicativo e riguarda la progettazione e lo sviluppo di una architettura Java basata su plugin e di una serie di plugin che consentono di automatizzare varie fasi del processo di modellazione con sistemi MP, come la simulazione di dinamiche, la determinazione dei flussi e la generazione delle funzioni di regolazione.Biological systems are groups of biological entities, (e.g., molecules and organisms), that interact together producing specific dynamics. These systems are usually characterized by a high complexity, since they involve a large number of components having many interconnections. Understanding biological system mechanisms, and predicting their behaviors in normal and pathological conditions is a crucial challenge in systems biology, which is a central research area on the border among biology, medicine, mathematics and computer science. In this thesis metabolic P systems, also called MP systems, have been employed as discrete modeling framework for the analysis of biological system dynamics. They are a deterministic class of P systems employing rewriting rules to represent chemical reactions and "flux regulation functions" to tune reactions reactivity according to the amount of substances present in the system. After an excursus on the literature about some conventional (i.e., differential equations, Gillespie's models) and unconventional (i.e., P systems and metabolic P systems) modeling frameworks, the results of my research are presented. They concern three research topics: i) equivalences between MP systems and hybrid functional Petri nets, ii) statistical and optimization perspectives in the generation of MP models from experimental data, iii) development of the virtual laboratory MetaPlab, a Java software based on MP systems. The equivalence between MP systems and hybrid functional Petri nets is proved by two theorems and some in silico experiments for the case study of the lac operon gene regulatory mechanism and glycolytic pathway. The second topic concerns new approaches to the synthesis of flux regulation functions. Stepwise linear regression and neural networks are employed as function approximators, and classical/evolutionary optimization algorithms (e.g., backpropagation, genetic algorithms, particle swarm optimization, memetic algorithms) as learning techniques. A complete pipeline for data analysis is also presented, which addresses the entire process of flux regulation function synthesis, from data preparation to feature selection, model generation and statistical validation. The proposed methodologies have been successfully tested by means of in silico experiments on the mitotic oscillator in early amphibian embryos and the non photochemical quenching (NPQ). The last research topic is more applicative, and pertains the design and development of a Java plugin architecture and several plugins which enable to automatize many tasks related to MP modeling, such as, dynamics computation, flux discovery, and regulation function synthesis

Evaluation of XPath Queries against XML Streams

XML is nowadays the de facto standard for electronic data interchange on the Web. Available XML data ranges from small Web pages to ever-growing repositories of, e.g., biological and astronomical data, and even to rapidly changing and possibly unbounded streams, as used in Web data integration and publish-subscribe systems. Animated by the ubiquity of XML data, the basic task of XML querying is becoming of great theoretical and practical importance. The last years witnessed efforts as well from practitioners, as also from theoreticians towards defining an appropriate XML query language. At the core of this common effort has been identified a navigational approach for information localization in XML data, comprised in a practical and simple query language called XPath. This work brings together the two aforementioned ``worlds'', i.e., the XPath query evaluation and the XML data streams, and shows as well theoretical as also practical relevance of this fusion. Its relevance can not be subsumed by traditional database management systems, because the latter are not designed for rapid and continuous loading of individual data items, and do not directly support the continuous queries that are typical for stream applications. The first central contribution of this work consists in the definition and the theoretical investigation of three term rewriting systems to rewrite queries with reverse predicates, like parent or ancestor, into equivalent forward queries, i.e., queries without reverse predicates. Our rewriting approach is vital to the evaluation of queries with reverse predicates against unbounded XML streams, because neither the storage of past fragments of the stream, nor several stream traversals, as required by the evaluation of reverse predicates, are affordable. Beyond their declared main purpose of providing equivalences between queries with reverse predicates and forward queries, the applications of our rewriting systems shed light on other query language properties, like the expressivity of some of its fragments, the query minimization, or even the complexity of query evaluation. For example, using these systems, one can rewrite any graph query into an equivalent forward forest query. The second main contribution consists in a streamed and progressive evaluation strategy of forward queries against XML streams. The evaluation is specified using compositions of so-called stream processing functions, and is implemented using networks of deterministic pushdown transducers. The complexity of this evaluation strategy is polynomial in both the query and the data sizes for forward forest queries and even for a large fragment of graph queries. The third central contribution consists in two real monitoring applications that use directly the results of this work: the monitoring of processes running on UNIX computers, and a system for providing graphically real-time traffic and travel information, as broadcasted within ubiquitous radio signals